The rapid progress of artificial intelligence has accelerated the development of society. Nowadays, people punch in and out of work using fingerprint identification, which avoids the need to wait in a queue for a long time; such an arrangement not only saves each worker's time but also ensures that the company does not need to maintain or rely on any manual record of attendance, and that absentees, latecomers and early leavers can be known at a glance. Scanning code payment and scanning code collection are achieved everywhere by a mobile phone [1], which saves people a lot of unnecessary trouble and makes their lives tend to be simplified and convenient. At the same time, ‘talking’ robots can sing, tell jokes and chat with people, which relieves people's mental stress [2]. Therefore, the development of intelligence has promoted the growth of human happiness index and the continuous progress of society.

In the field of artificial intelligence research, to make the research results more beneficial to people's lives, it is necessary that the computer be able to not only handle the calculation of general numerical information but also manage the data processing of intelligent information (that is, non-numerical information) close to the human daily thinking mode [3]. In the natural environment, most things that people come into contact with are uncertain, and in the process of reasoning and decision, more emphasis is placed on the use of natural languages with strong fuzziness, such as ‘a little low’, ‘absolutely true’ and ‘very high’ [4]. Therefore, the development of intelligent information processing is particularly important. It can penetrate into any part of people's daily life, and moreover, computers can be used to imitate the thinking mode of the human brain, which accelerates the development of artificial intelligence [5].

Concept lattice, as an effective mathematical tool, can effectively handle knowledge processing and data mining [6, 7], which are widely used in the research of reasoning decision, machine learning, recommendation system, intelligent evaluation, human factor engineering and other fields [8]. Concept lattice is a formal concept model composed of intension and extension that was first proposed by R Wille in 1982 [9]. Nowadays, it is being widely used in the fields of knowledge representation, data mining and machine learning [10, 11].

Extracting implicit and potential rules from information systems is the key step to achieve knowledge acquisition. In the traditional expert system or fuzzy reasoning system, rules are often given by experts according to their experience, which may lead to some problems [12] owing to the fact that the rules acquired based on classical rough set theory are often clear rules with steep truncation, and compared with fuzzy rules, their generalisation ability and practicability are weak [13]. Intuitionistic fuzzy sets (IFS) constitute an important extension of fuzzy sets; their mathematical description is more in line with the nature of fuzzy objects in the objective world, and IFS have thus become a new research hotspot in recent years [14]. Based on retaining the membership function of fuzzy set, IFS adds a new attribute parameter – non-membership function [15], which can further describe the ‘fuzzy concept of either this or the other’; that is, membership, non-membership and hesitation of IFS can represent the three states of support, opposition and neutrality, respectively [16].

Concept lattice is a very effective tool in the field of decision analysis. In real life, people are more accustomed to expressing information with linguistic values rather than numerical values [17], and sometimes consider problems with both pros and cons aspects. In order to better deal with linguistic values expressed in terms of both positive and negative aspects, concept lattice theory is used to deal with IFS and fuzzy linguistic values. Moreover, concept lattice of intuitionistic fuzzy language is established [18], and a method of attribute reduction is proposed in the context of intuitionistic fuzzy language.

Define (^{′}) as an formal context of intuitionistic fuzzy language, in which _{1}, _{2}, ⋯ , _{n}_{1}, ⋯ , _{m}^{′} is binary relation between ^{′} ⊆

Further, _{μ}_{ν}

Define (^{′}) as an intuitionistic fuzzy language formal context, where ∀

Define (^{′}) as an intuitionistic fuzzy language formal context; if a tuple (^{≺} = ^{≺}, (

Define (^{′}) as an intuitionistic fuzzy language form context, make ^{′}) represent (^{′}) on the whole intuitionistic fuzzy language concept [21] and ^{′}) is called intuitionistic fuzzy language concept lattice, for ∀(_{1}, _{1}), (_{2}, _{2}) ∈ ^{′}), defining its partial order relation as
_{1}, _{2}) is called the child concept of (_{2}, _{2}) and (_{2}, _{2}) is called the parent concept of (_{1}, _{2}).

Define the lower and upper bounds of ^{′}) as [22]
^{′}) is a complete lattice.

^{′}) _{1}, _{2}, _{3}), _{0} = verylow, _{1} = low, _{2} = medium, _{3} = high, _{4} = veryhigh}. ^{′} (_{1}, _{0}, _{4} _{1}

Formal context of Intuitionistic fuzzy linguistic (^{′})

_{1} | 〈_{0}, _{4}〉 | 〈_{2}, _{2}〉 | 〈_{1}, _{2}〉 |

_{2} | 〈_{3}, _{0}〉 | 〈_{0}, _{2}〉 | 〈_{3}, _{1}〉 |

_{3} | 〈_{1}, _{1}〉 | 〈_{3}, _{1}〉 | 〈_{2}, _{1}〉 |

Table 1 shows the formal context of intuitionistic fuzzy language (^{′}) The generated concept is:

#1 (_{0}, _{4}_{0}, _{2}_{1}, _{2}})

#2 ({_{1}_{3}}, {_{0}, _{4}_{2}, _{2}_{1}, _{2}})

#3 ({_{2}_{3}}, {_{1}, _{1}_{0}, _{2}_{2}, _{1}})

#4 ({_{2}}, {_{3}, _{0}_{0}, _{2}_{3}, _{1}})

#5 ({_{3}}, {_{1}, _{1}_{3}, _{1}_{2}, _{1}})

#6 (∅, {_{3}, _{0}_{3}, _{1}_{3}, _{1}})

The intuitionistic fuzzy language concept lattice is built as shown in Figure 1:

According to the above definition, the following properties can be obtained:

Property 1, applicable in the context of intuitionistic fuzzy language form (^{′}): Next, for any

^{≺≺}, ^{≺≺}

^{≺} = ^{≺≺≺}, ^{≺} = ^{≺≺≺}

^{≺} ⇔ ^{≺}

(^{≺≺}, ^{≺}) and (^{≺}, ^{≺≺}) are all concepts.

Property 2, applicable in the context of intuitionistic fuzzy language form (^{′}): For any _{1}, _{2} ⊆

_{1}, _{1}_{2}, _{2}^{′}), _{1} ∩ _{2},(_{1} ∪ _{2})^{≺≺}) _{1} ∪ _{2})^{≺≺}, _{1}_{2})

It is evidently proved by the above nature and definition.

In the era of big data, the amount of information is huge. Under this context, the construction of concept lattice is very complicated, and it is thus necessary to reduce the attributes of concept lattice [23]. In this section, the related definitions and properties of attribute reduction in the context of intuitionistic fuzzy language form are obtained [24].

Define
^{′}, which is called

If

Under the formal context of intuitionistic fuzzy language (^{′}), ∀^{≺}(^{≺D} (^{≺}(

^{′}) ^{≺} ⊆ ^{≺D}.

It can be easily proved by property 1 and definition 5.

^{′})

^{≺D} = ^{≺D} = ^{≺≺}, ^{≺}) ∈ ^{′}), ^{≺<}. According to theorem 2, ^{≺D} ⊆ ^{≺} ^{≺≺} ⊆ ^{≺} ⊆ ^{≺D} = ^{′}) ≤

(^{′}) is the formal context of intuitionistic fuzzy language; if ∃^{′}), and then ^{′}). About Jane. All the intersection of (^{′})reduction is called the core of (^{′}).

The following theorems can be obtained through definition 6:

^{′})

Assumes that all reductions of the formal context of intuitionistic fuzzy language (^{′}) are {_{i}D_{i}

Absolutely necessary attribute (core attribute)

Relative essential attribute

Absolutely unnecessary attribute

Unnecessary attribute

^{′}),

If for any ^{′}), then

If it exists _{1} ∈ ^{′}), then _{1}} is about Jane; if
_{1}} needs to be discussed. Since A is a finite set, at least one reduction will be found.

Generally, the reduction intuition blurs the formal context of (^{′}) is not unique.

^{′}), _{1}, _{2}, _{3}, _{4}},

Intuitionistic fuzzy linguistic for mal context (^{′})

_{1} | 〈_{4}, _{0}〉 | 〈_{3}, _{1}〉 | 〈_{1}, _{2}〉 | 〈_{3}, _{0}〉 | 〈_{3}, _{0}〉 |

_{2} | 〈_{3}, _{0}〉 | 〈_{3}, _{1}〉 | 〈_{3}, _{0}〉 | 〈_{1}, _{2}〉 | 〈_{1}, _{3}〉 |

_{3} | 〈_{0}, _{3}〉 | 〈_{1}, _{2}〉 | 〈_{0}, _{4}〉 | 〈_{3}, _{1}〉 | 〈_{1}, _{2}〉 |

_{4} | 〈_{3}, _{1}〉 | 〈_{3}, _{0}〉 | 〈_{2}, _{0}〉 | 〈_{1}, _{2}〉 | 〈_{1}, _{3}〉 |

The formal context of intuitionistic fuzzy language shown in Table 2 has nine concepts:

#1 ({_{0}, _{3}_{1}, _{2}_{0}, _{4}_{1}, _{2}_{1}, _{3}})

#2 ({_{1}_{2}_{4}}, {_{3}, _{1}_{3}, _{1}_{1}, _{2}_{1}, _{2}_{1}, _{3}})

#3 ({_{1}_{2}}, {_{3}, _{0}_{3}, _{1}_{1}, _{2}_{1}, _{2}_{1}, _{3}})

#4 ({_{1}_{3}}, {_{0}, _{3}_{1}, _{2}_{0}, _{4}_{3}, _{1}_{1}, _{2}})

#5 ({_{2}_{4}}, {_{3}, _{1}_{3}, _{1}_{2}, _{0}_{1}, _{2}_{1}, _{3}})

#6 ({_{1}}, {_{4}, _{0}_{3}, _{1}_{1}, _{2}_{4}, _{0}_{3}, _{0}})

#7 ({_{2}}, {_{3}, _{0}_{3}, _{1}_{3}, _{0}_{1}, _{2}_{1}, _{3}})

#8 ({_{4}}, {_{3}, _{1}_{3}, _{0}_{2}, _{0}_{1}, _{2}_{1}, _{3}})

#9 (∅, {_{3}, _{1}_{3}, _{1}_{1}, _{2}_{1}, _{2}_{1}, _{3}})

Its intuitionistic fuzzy language concept lattice ^{′}) is shown in Figure 2.

Define _{1} = {

#1 (_{0}, _{3}_{1}, _{2}_{0}, _{4}_{1}, _{2}})

#2 ({_{1}_{2}_{4}}, {_{3}, _{1}_{3}, _{1}_{1}, _{2}_{1}, _{2}})

#3 ({_{1}_{2}}, {_{3}, _{0}_{3}, _{1}_{1}, _{2}_{1}, _{2}})

#4 ({_{1}_{3}}, {_{0}, _{3}_{1}, _{2}_{0}, _{4}_{3}, _{1}})

#5 ({_{2}_{4}}, {_{3}, _{1}_{3}, _{1}_{2}, _{0}_{1}, _{2}})

#6 ({_{1}}, {_{4}, _{0}_{3}, _{1}_{1}, _{2}_{4}, _{0}})

#7 ({_{2}}, {_{3}, _{0}_{3}, _{1}_{3}, _{0}_{1}, _{2}})

#8 ({_{4}}, {_{3}, _{1}_{3}, _{0}_{2}, _{0}_{1}, _{2}})

#9 (∅, {_{3}, _{1}_{3}, _{1}_{1}, _{2}_{1}, _{2}})

Its intuitionistic fuzzy language concept lattice

As can be seen from Figures 2 and 3,
_{1} ∈ _{1} to make
_{1} = {^{′}). Similarly, _{2} = {^{′}).

To sum up, intuitionistic fuzzy language formal context of (^{′}) has two reductions: _{1} = {_{2} = {

^{′})

^{′})

^{′})

The reduction

∀

Therefore, for attribute reduction, it is necessary to determine whether the attribute subset is a coordination set, and the judgment theorem of the coordination set is given as follows:

^{′}) ^{≺≺D≺D} = ^{≺},

Necessity: Assuming that ^{≺}, ^{≺≺}) ∈ ^{′}). According to definition 5,
^{′} = ^{≺≺D} and □^{≺} = □^{′≺□}; therefore ^{≺≺D≺D} = ^{≺}.

Sufficiency:
^{≺≺D≺D} = ^{≺}. Asuming that (^{′}), that is, there is ^{≺} = ^{≺} = ^{′} = ^{≺≺D}, ^{′≺D} = ^{≺≺D≺D} = ^{≺} = ^{′}),

^{′}) ^{′≺D} = ^{≺}.

^{′}) ^{′≺D} = ^{≺E}.

Necessity: ^{′}); then, for
_{2} = _{1}, in which
^{′≺D} = ^{≺E}.

Sufficiency: For
^{′<D} = ^{≺E}. Suppose (_{2}) ∈ ^{′}), then ^{≺} = _{2} and
_{2} = _{1}, in which
_{2}^{≺} = (_{1})^{≺} = ^{≺} ∩ _{1}^{≺} = ^{≺D} ∩ _{1}^{≺E}. Therefore
^{≺D} ∩ _{1}^{≺E} = _{1}^{≺D} ∩ ^{′≺D} = (^{′})^{≺D} =

To sum up, ^{′}).

Discernibility matrix is a common tool for attribute reduction. The identification matrix and identification function are used to reduce the concept lattice of intuitionistic fuzzy language [30].

Assume that (^{′}) is the formal context of intuitionistic fuzzy language, (_{i},B_{i}_{j},B_{j}_{i},B_{i}_{j},B_{j}^{′}). Then,

^{′}) _{i},B_{i}_{j},B_{j}^{′}), (_{i},B_{i}_{j},B_{j}

If

(1)_{i} ⊄ X_{j}_{Xi}_{Xj}

Assume that (^{′}) is the intuitionistic fuzzy linguistic form context; D^{*R} is the identification matrix on (^{′}); define

Then,
^{′}).

^{′})

Make _{k}_{r}r_{k}_{k}k^{′}).

It can be seen from the above that to find the attribute reduction of the conceptual lattice of intuitionistic fuzzy language, the following conditions need to be obtained:

The smallest coordination set

^{′}) ^{≺0D} ⊆ ^{α<}.

Table 3 gives the intuitionistic fuzzy language form context of (^{′}) identifiable matrix.

Discernible matrix of Intuitionistic fuzzy linguistic formal context (^{′})

□_{□}/□_{□} | □_{1} | □_{2} | □_{4} | □_{1}□_{2} | □_{1}□_{3} | □_{2}□_{4} | □_{1}□_{2}□_{4} |
---|---|---|---|---|---|---|---|

□_{1} | |||||||

□_{2} | |||||||

□_{4} | |||||||

□_{1}□_{2} | |||||||

□_{1}□_{3} | |||||||

□_{2}□_{4} | |||||||

□_{1}□_{2}□_{4} |

The formal context of intuitionistic fuzzy language shown in Table 3 has two reductions, namely: and. Among them,

Rule extraction is an important branch in the field of concept lattice. In the era of big data, knowledge acquired from complex data is largely given in the form of rules [31]. Based on the formal context of intuitionistic fuzzy language, this paper puts forward the formal context of intuitionistic fuzzy language decision, studies the acquisition method of rules, discusses the similarity between intuitionistic fuzzy language sets and constructs a rule extraction method based on concept lattice of intuitionistic fuzzy language.

Assume that (^{′}, ^{′}) is a decision formal context of intuitionistic fuzzy language, in which (^{′}) and (^{′}) are the context of intuitionistic fuzzy language, ^{′} is Intuitionistic fuzzy language binary relation between ^{′} is intuitionistic fuzzy language binary relation between

Under the decision formal context of intuitionistic fuzzy language (^{′}, ^{′}),

Assuming that (^{′}, ^{′}) is an intuitionistic fuzzy language decision formal context, if ^{′}) ≤ ^{′}), the context is regarded to be coordinated.

^{′}) is a conditional concept lattice of intuitionistic fuzzy language, whereas ^{′}) is a decision concept lattice for intuitionistic fuzzy language.

Assuming that (^{′}, ^{′}) is a decision formal context of intuitionistic fuzzy language, ^{′}) ≤ ^{′}); if (^{′}), (^{′}), satisfy

Assuming that (^{′}) is a formal context of intuitionistic fuzzy language, for ∀^{′}) then the distance between two intuitionistic fuzzy language sets _{α1}, _{β1} _{α2}, _{β2} ⋯ _{αm}, _{βm}} and _{γ1}, _{λ1} _{γ2}, _{λ2} ⋯ _{γm}, _{λm}} is:

Among them,

_{α1}, _{β1} _{α2}, _{β2} ⋯ _{αm}, _{βm}}, _{γ1}, _{λ1} _{γ2}, _{λ2} ⋯ _{γm}, _{λm}}

0 ≤

Assume _{κ1}, _{ρ1}〉, 〈_{κ2}, _{ρ2}〉 ⋯ 〈_{κm}_{ρm}

_{l},β_{l},κ_{l},ρ_{l}

|_{l}_{l}_{l}_{l}_{l}_{l}_{l}_{l}

then

⇔ |_{l}_{l}_{l}_{l}

⇔_{l}_{l}_{l}_{l}

⇔

If _{l}_{l}_{1}, _{l}_{l}_{l}_{l}_{l}_{l}_{l}_{l}_{l}_{l}_{l}

Similarly, d(GQ)≤ d(B,Q) can be proved.

To sum up, theorem 10 is realised.

Assuming that (^{′}) is a formal context of intuitionistic fuzzy language, for ∀^{′}), then the similarity between two intuitionistic fuzzy languages is _{α1}, _{β1}〉 〈 _{α2}, _{β2}〉 ⋯ 〈 _{αm}, _{βm}〉} and _{γ1}, _{λ1}〉 〈_{γ2}, _{λ2}〉 ⋯ 〈 _{γm}, _{λm}〉}:

_{α1}, _{β1}〉 〈_{α2}, _{β2}〉 ⋯ 〈_{αm}, _{βm}〉}, _{γ1}, _{λ1}〉 〈_{γ2}, _{λ2}〉 ⋯ 〈_{γm}, _{λm}〉}: _{II}(

0 ≤ sim_{II}(

sim_{II}(

sim_{II}(_{II}(

Assume _{κ1}, _{ρ1}〉, 〈_{κ2}, _{ρ2}〉 ⋯ 〈_{κm}_{ρm}_{II}(_{II}(_{II}(_{II}(

Assuming that (^{′}) is a formal context of intuitionistic fuzzy language, for ∀^{′}), _{II} = (_{1}, _{2}, _{m}^{T} is the weight vector then the weighted distance between two intuitionistic fuzzy language sets _{α1}, _{β1}〉 〈_{α2}, _{β2}〉 ⋯ 〈_{αm}, _{βm}〉} and _{γ1}, _{λ1}〉 〈_{γ2}, _{λ2}〉 ⋯ 〈_{γm}, _{λm}〉} is:
_{l}

_{α1}, _{β1}〉 〈_{α2}, _{β2}〉 ⋯ 〈_{αm}, _{βm}〉}, _{γ1}, _{λ1}〉 〈_{γ2}, _{λ2}〉 ⋯ 〈_{γm}, _{λm}〉} _{II} = (_{1}, _{2}, _{m}_{l}_{w}

0 ≤ _{w}

dw(B,G)=0 if and only if B=G;

_{w}_{w}

Assume _{κ1}, _{ρ1}〉, 〈_{κ2}, _{ρ2}〉 ⋯ 〈_{κm}_{ρm}_{w}_{w}_{w}_{w}

Assuming that (^{′}) is a formal context of intuitionistic fuzzy language, for ∀^{′}), _{II} = (_{1}, _{2}, _{m}^{T} is the weight vectorthen, the weighted similarity between two intuitionistic fuzzy language sets _{α1}, _{β1}〉 〈_{α2}, _{β2}〉 ⋯ 〈_{αm}, _{βm}〉} and _{γ1}, _{λ1}〉 〈_{γ2}, _{λ2}〉 ⋯ 〈_{γm}, _{λm}〉} is:
_{l}

_{α1}, _{β1}〉 〈_{α2}, _{β2}〉 ⋯ 〈_{αm}, _{βm}〉}, _{γ1}, _{λ1}〉 〈_{γ2}, _{λ2}〉 ⋯ 〈_{γm}, _{λm}〉}: _{II} = (_{1}, _{2}, _{m}_{l}_{w}_{II}(

0 ≤ sim_{wI}(

sim_{wII}(

sim_{wI}(_{wI}(

Assume _{κ1}, _{ρ1}〉 〈_{κ2}, _{ρ2}〉 ⋯ 〈_{κm}_{ρm}

Under the context of intuitionistic fuzzy language decision formal, language rules are extracted. First, the conditional concept lattice and decision concept lattice are constructed; then, according to the detailed relationship between concept lattices, the rule set under the context of intuitionistic fuzzy language decision formal is obtained. Finally, the given intuitionistic fuzzy language set is compared with each rule antecedent in the rule set, and according to the formula of weighted similarity, the rules of a given intuitionistic fuzzy language set are judged. The specific steps are as follows:

Step 1: Generate all concepts (^{′}) of intuitionistic fuzzy language to construct conditional concept lattice. ^{′});

Step 2: Generate all concepts (^{′}) of intuitionistic fuzzy language to construct decision concept lattice. ^{′});

Step 3: Judge the relationship between the two concept lattices ^{′}) and ^{′}). According to

Step 4: Construct a given intuitionistic fuzzy language set:

Combine intuitionistic fuzzy language set G with rule set Φ(

Step 5: According to the weighted similarity formula:

Calculate the weighted similarity between intuitionistic fuzzy language set G and antecedent B in each rule, so as to obtain the maximum weighted similarity;

Step 6: Compare the maximum weighted similarity with the similarity threshold; if it is greater than or equal to the similarity threshold, then the rule B^{′}→ C^{′} corresponding to the maximum weighted similarity is the rule to be searched, then G→ C^{′}, the algorithm ends, and G→ C^{′} is output. If the maximum weighted similarity is less than the similarity threshold, return to step 1 and add the context until the matching rule is found.

By the symptoms and diseases of some patients, the possibility of a patient with certain symptoms suffering from these diseases can be judged. Assuming that (^{′}, ^{′}) is a formal context of intuitionistic fuzzy language decision, _{1}, _{2}, _{3}, _{4}} represents patient set, _{1}, _{2}, _{3}, _{4}} represents disease set. The specific definitions of each of the symptoms under set A are as follows: a is fever, b is headache, c is stomach-ache, d is cough and e is chest pain. The specific definition of disease T is as follows: t_{1} is viral fever, t_{2} is typhoid fever, t_{3} is gastropathy and t_{4} is thoracic lung disease. The language set S = {s_{0} = extremely few, s_{1} = few, s_{2} = medium, s_{3} = many, S_{4} = extremely many} indicates the frequency of certain symptoms in patients, and the linguistic set R = { r_{0} = small, r_{1} = small, r_{2} = medium, r_{3} = large, r_{4} = extremely large} indicates that patients suffer from certain diseases. The formal context of intuitionistic fuzzy language decision is shown in Table 4.

Intuitionistic fuzzy linguistic formal decision context (^{′}, ^{′})

_{1} | _{3} | _{3} | _{4} | ||||||
---|---|---|---|---|---|---|---|---|---|

_{1} | 〈_{3}, _{1}〉 | 〈_{2}, _{2}〉 | 〈_{0}, _{4}〉 | 〈_{2}, _{2}〉 | 〈_{2}, _{1}〉 | 〈_{3}, _{0}〉 | 〈_{2}, _{2}〉 | 〈_{0}, _{4}〉 | 〈_{2}, _{1}〉 |

_{2} | 〈_{4}, _{0}〉 | 〈_{2}, _{1}〉 | 〈_{4}, _{0}〉 | 〈_{3}, _{0}〉 | 〈_{3}, _{1}〉 | 〈_{4}, _{0}〉 | 〈_{3}, _{1}〉 | 〈_{4}, _{0}〉 | 〈_{3}, _{1}〉 |

_{3} | 〈_{1}, _{2}〉 | 〈_{3}, _{1}〉 | 〈_{2}, _{1}〉 | 〈_{0}, _{3}〉 | 〈_{1}, _{2}〉 | 〈_{1}, _{2}〉 | 〈_{2}, _{2}〉 | 〈_{2}, _{1}〉 | 〈_{1}, _{2}〉 |

_{4} | 〈_{2}, _{2}〉 | 〈_{4}, _{0}〉 | 〈_{3}, _{1}〉 | 〈_{4}, _{0}〉 | 〈_{0}, _{3}〉 | 〈_{3}, _{1}〉 | 〈_{4}, _{0}〉 | 〈_{3}, _{0}〉 | 〈_{0}, _{3}〉 |

Step 1: Construct a conditional concept lattice of intuitionistic fuzzy language;

According to Table 4, the concepts under the context of (^{′}) form are as follows:

#1 (∅,{〈_{4}, _{0}〉, 〈_{4}, _{0}〉 〈_{4}, _{0}〉 〈_{4}, _{0}〉 〈_{3}, _{1}〉}),

#2 ({_{2}}, {〈_{4}, _{0}〉 〈_{2}, _{1}〉 〈_{4}, _{0}〉 〈_{3}, _{0}〉 〈_{3}, _{1}〉}),

#3 ({_{3}}, {〈_{1}, _{2}〉 〈_{3}, _{1}〉 〈_{2}, _{1}〉 〈_{0}, _{3}〉 〈_{1}, _{2}〉}),

#4 ({_{4}}, {〈_{2}, _{2}〉 〈_{4}, _{0}〉 〈_{3}, _{1}〉 〈_{4}, _{0}〉 〈_{0}, _{3}〉}),

#5 ({_{1}_{2}}, {〈_{3}, _{1}〉 〈_{2}, _{2}〉 〈_{0}, _{4}〉 〈_{2}, _{2}〉 〈_{2}, _{1}〉}),

#6 ({_{2}_{3}}, {〈_{1}, _{2}〉 〈_{2}, _{1}〉 〈_{2}, _{1}〉 〈_{0}, _{3}〉 〈_{1}, _{2}〉}),

#7 ({_{2}_{4}}, {〈_{2}, _{2}〉 〈_{2}, _{1}〉 〈_{3}, _{1}〉 〈_{3}, _{0}〉 〈_{0}, _{3}〉}),

#8 ({_{3}_{4}}, {〈_{1}, _{2}〉 〈_{3}, _{1}〉 〈_{2}, _{1}〉 〈_{0}, _{3}〉 〈_{0}, _{3}〉}),

#9 ({_{1}_{2}_{3}}, {〈_{1}, _{2}〉 〈_{2}, _{2}〉 〈_{0}, _{4}〉 〈_{0}, _{3}〉 〈_{1}, _{2}〉}),

#10 ({_{1}_{2}_{4}}, {〈_{2}, _{2}〉 〈_{2}, _{2}〉 〈_{0}, _{4}〉 〈_{2}, _{2}〉 〈_{0}, _{3}〉}),

#11 ({_{2}_{3}_{4}}, {〈_{1}, _{2}〉 〈_{2}, _{1}〉 〈_{2}, _{1}〉 〈_{0}, _{3}〉 〈_{0}, _{3}〉}),

#12 (_{1}, _{2}〉 〈_{2}, _{2}〉 〈_{0}, _{4}〉 〈_{0}, _{3}〉 〈_{0}, _{3}〉}).

Construct conditional concept lattice of intuitionistic fuzzy language according to concepts ^{′}), as indicated in Figure 4.

Step 2: Construct the concept lattice of intuitionistic fuzzy language decision;

The concepts under the formal context (^{′}) are as follows:

#1 (∅, {〈_{4}, _{0}〉 〈_{4}, _{0}〉 〈_{4}, _{0}〉 〈_{3}, _{1}〉}), #2 ({_{2}}, {〈_{4}, _{0}〉 〈_{3}, _{1}〉 〈_{4}, _{0}〉 〈_{3}, _{1}〉})

#3 ({_{4}}, {〈_{3}, _{1}〉 〈_{4}, _{0}〉 〈_{3}, _{0}〉 〈_{0}, _{3}〉}), #4 ({_{1}_{2}}, {〈_{3}, _{0}〉 〈_{2}, _{2}〉 〈_{0}, _{4}〉 〈_{2}, _{1}〉}),

#5 ({_{2}_{3}}, {〈_{1}, _{2}〉 〈_{2}, _{2}〉 〈_{2}, _{1}〉 〈_{1}, _{2}〉}), #6 ({_{2}_{4}}, {〈_{3}, _{1}〉 〈_{3}, _{1}〉 〈_{3}, _{0}〉 〈_{0}, _{3}〉})

#7 ({_{1}_{2}_{3}}, {〈_{1}, _{2}〉 〈_{2}, _{2}〉 〈_{0}, _{4}〉 〈_{1}, _{2}〉}), #8 ({_{1}_{2}_{4}}, {〈_{3}, _{1}〉 〈_{2}, _{2}〉 〈_{0}, _{4}〉 〈_{0}, _{3}〉})

#9 ({_{2}_{3}_{4}}, {〈_{1}, _{2}〉 〈_{2}, _{2}〉 〈_{2}, _{1}〉 〈_{0}, _{3}〉}), #10 (_{1}, _{2}〉 〈_{2}, _{2}〉 〈_{0}, _{4}〉 〈_{0}, _{3}〉})

Construct intuitionistic fuzzy language decision concept lattice according to concepts ^{′}) as indicated in Figure 5.

Step 3: Obtain the rule set. Φ(

As can be seen from Figures 4 and 5, ^{′}) ≤ ^{′}), and the rule set can be made available as follows:

Step 4: Judge whether there is a rule precursor in the rule set (a) that is the same as the known patient symptoms; by comparing the rule sets Φ(

Step 5: Calculate the weighted similarity between the intuitive fuzzy language set G of the patient's symptoms and each rule antecedent in the rule set, so as to obtain the maximum weighted similarity;

Taking the possibility of the patient suffering from viral fever as an example, the weight corresponding to viral fever is given as

Therefore,

It can be seen from the above that the weighted similarity between _{s}

Step 6: Output the result.

When the similarity threshold is selected as 0.75, the maximum weighted similarity under viral fever is obtained. When sim_{wI1} (_{S},G

That is, the possibility of the patient suffering from viral fever is 〈_{1}, _{2}〉. Similarly, the given corresponding weight of typhoid fever
_{II}^{3} = {0.1,0.2,0.5,0.1,0.1}, chest and lung diseases corresponding to the right
_{wII3} (_{6}, _{wII4} (_{7},

That is, the possibility of the patient suffering from viral fever is 〈_{1}, _{2}〉, the possibility of typhoid fever is 〈_{2}, _{2}〉, the possibility of gastropathy is 〈_{0}, _{4}〉 and the possibility of suffering from thoracic lung disease is 〈_{0}, _{3}〉.

Taking the threshold as 〈_{2}, _{2}〉, that is, when the probability of suffering from a certain disease is greater than or equal to 〈_{2}, _{2}〉, it should be noticed. Therefore, the patient should pay attention to typhoid fever.

The above examples show that the results are consistent with the analysis in real life, which indicates that the algorithm is effective and practical. In this paper, intelligent diagnosis with linguistic values in the field of disease diagnosis can better express the description of the disease, reduce data loss and thus get smarter diagnosis results.

Based on the concept lattice of intuitionistic fuzzy language, the rule extraction in the context of intuitionistic fuzzy language decision formal is defined in this paper. In order to handle the rules on the concept lattice, the similarity is defined. In addition, by considering the various influences of each attribute on the object, the weight is added to the similarity, and the weighted similarity is proposed. Finally, using an example connected with disease diagnosis, it is demonstrated that the algorithm proposed in this paper is effective and that the proposed decision method has strong operability and is suitable for practical application.

#### Formal context of Intuitionistic fuzzy linguistic (U,A,S′)

_{1} |
〈_{0}, _{4}〉 |
〈_{2}, _{2}〉 |
〈_{1}, _{2}〉 |

_{2} |
〈_{3}, _{0}〉 |
〈_{0}, _{2}〉 |
〈_{3}, _{1}〉 |

_{3} |
〈_{1}, _{1}〉 |
〈_{3}, _{1}〉 |
〈_{2}, _{1}〉 |

#### Intuitionistic fuzzy linguistic for mal context (U,A,S′)

_{1} |
〈_{4}, _{0}〉 |
〈_{3}, _{1}〉 |
〈_{1}, _{2}〉 |
〈_{3}, _{0}〉 |
〈_{3}, _{0}〉 |

_{2} |
〈_{3}, _{0}〉 |
〈_{3}, _{1}〉 |
〈_{3}, _{0}〉 |
〈_{1}, _{2}〉 |
〈_{1}, _{3}〉 |

_{3} |
〈_{0}, _{3}〉 |
〈_{1}, _{2}〉 |
〈_{0}, _{4}〉 |
〈_{3}, _{1}〉 |
〈_{1}, _{2}〉 |

_{4} |
〈_{3}, _{1}〉 |
〈_{3}, _{0}〉 |
〈_{2}, _{0}〉 |
〈_{1}, _{2}〉 |
〈_{1}, _{3}〉 |

#### Discernible matrix of Intuitionistic fuzzy linguistic formal context (U,A,S′)

□_{□}/□_{□} |
□_{1} |
□_{2} |
□_{4} |
□_{1}□_{2} |
□_{1}□_{3} |
□_{2}□_{4} |
□_{1}□_{2}□_{4} |
---|---|---|---|---|---|---|---|

□_{1} |
|||||||

□_{2} |
|||||||

□_{4} |
|||||||

□_{1}□_{2} |
|||||||

□_{1}□_{3} |
|||||||

□_{2}□_{4} |
|||||||

□_{1}□_{2}□_{4} |

#### Intuitionistic fuzzy linguistic formal decision context (U,A,S′, T,R′)

_{1} |
_{3} |
_{3} |
_{4} |
||||||
---|---|---|---|---|---|---|---|---|---|

_{1} |
〈_{3}, _{1}〉 |
〈_{2}, _{2}〉 |
〈_{0}, _{4}〉 |
〈_{2}, _{2}〉 |
〈_{2}, _{1}〉 |
〈_{3}, _{0}〉 |
〈_{2}, _{2}〉 |
〈_{0}, _{4}〉 |
〈_{2}, _{1}〉 |

_{2} |
〈_{4}, _{0}〉 |
〈_{2}, _{1}〉 |
〈_{4}, _{0}〉 |
〈_{3}, _{0}〉 |
〈_{3}, _{1}〉 |
〈_{4}, _{0}〉 |
〈_{3}, _{1}〉 |
〈_{4}, _{0}〉 |
〈_{3}, _{1}〉 |

_{3} |
〈_{1}, _{2}〉 |
〈_{3}, _{1}〉 |
〈_{2}, _{1}〉 |
〈_{0}, _{3}〉 |
〈_{1}, _{2}〉 |
〈_{1}, _{2}〉 |
〈_{2}, _{2}〉 |
〈_{2}, _{1}〉 |
〈_{1}, _{2}〉 |

_{4} |
〈_{2}, _{2}〉 |
〈_{4}, _{0}〉 |
〈_{3}, _{1}〉 |
〈_{4}, _{0}〉 |
〈_{0}, _{3}〉 |
〈_{3}, _{1}〉 |
〈_{4}, _{0}〉 |
〈_{3}, _{0}〉 |
〈_{0}, _{3}〉 |

Law of interest rate changes in financial markets based on the differential equation model of liquidity Research and implementation of smart city public information mining analysis system based on mobile edge model of game theory Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Design of college education evaluation based on accompanying data acquisition and mathematical analysis Enterprise financial strategy and performance management analysis based on principal component analysis Study on the Dynamic Change of Regional Water Level and Climate Based on Forecast Equation Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Municipal Civil Engineering Construction Based on Finite Element Differential Equations Financial Risk Prevention Model of Financial Institutions Based on Linear Partial Differential Equation Influence of heterogeneity of local officials on the economy of resource-based cities developed with high quality Analysis of influencing factors of SPOC course teaching effect using structural equation modelling Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation Research on the construction of rural interface style based on aesthetic rules Optimization Algorithm of New Media Hot Event Push Based on Nonlinear Differential Equation Mathematical Differential Equation in Calculating the Strength of Building Beam Structure Impact Resistance Stability of Building Structural Engineering Based on Fractional Differential Equations The Technical Research on the Assessment of Network Security Situation Based on D-S Evidence Theory Computer big data modeling system based on finite element mathematical equation simulation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation The Composition System of Pop Music Movement Based on Finite Element Differential Equations The Structure and Influencing Factors of Innovation and Entrepreneurship Ability of Higher Vocational Students Based on Structural Equation Model Model System Study of Accordion Score Based on Fractional Differential Equations Data mining of Chain convenience stores location Parameter Id of Metal Hi-pressure State Equation P-Matrix Reasoning and Information Intelligent Mining Symmetry Analysis and Exact Solutions of Extended Kadomtsev-Petviashvili Equation in Fluids Research on Detection Model of Abnormal Data in Engineering Cost List Research on deformation monitoring of tunnel engineering based on 3D laser scanning Solidification treatment effect of wellsite waste mud based on physical adsorption of a composite curing agent A study of immersive technology for product usability improvement design based on comprehensive value evaluation Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Prediction of surface quality in end milling based on modified convolutional recurrent neural network Analysis of IPO pricing efficiency under the registration system Case application data research of traditional ink art elements in packaging design Research on an early warning model of effectiveness evaluation in ideological and political teaching based on big data Application of intelligent teaching resource organisation model and construction of performance evaluation model Secure transmission of simultaneous wireless information and power transfer system for Internet of things Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Numerical simulation of vortex vibration in main girder of cable-stayed bridge based on bidirectional fluid–structure coupling Research on location algorithm of new energy vehicle charging station based on multi-objective decision Optimisation of construction mode of residential houses based on the genetic algorithm under BIM technology A study on the reform of college English education inspired by the cultural differences between China and the United States Research on innovative strategies of college students’ English teaching under the blessing of big data Research on multi-dimensional optimisation design of user interface under Rhino/GH platform Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer A long command subsequence algorithm for manufacturing industry recommendation systems with similarity connection technology Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Evaluation of spoken English self-study system considering speech knowledge recognition algorithm Application research on piano teaching in colleges and universities based on remote wireless network communication Construction of Financial Risk Evaluation Index System for Biomass Graphene Fibre Industrialisation Project System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system An online statistical analysis of the hotel management and operation performance model Research on the post-purchase behaviour tendency of the product quality to customers in fast-selling marketing Motion about equilibrium points in the Jupiter-Europa system with oblateness Ultra-short-term power forecast of photovoltaic power station based on VMD–LSTM model optimised by SSA Optimal preview repetitive control for impulse-free continuous-time descriptor systems Design of information management system based on wireless communication under the background of Internet of Things The impact of global warming on the small Scottish Fishing Company Development of main functional modules for MVB and its application in rail transit Analysis of agricultural economic development and optimisation measures under the strategy of rural revitalisation Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Research on the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry Research on the protection and inheritance of intangible cultural heritage under the background of rural revitalisation Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model Computer vision recognition and tracking algorithm based on convolutional neural network A review of the treatment techniques of VOC Study on structural parameter design and life analysis of large four-point contact ball bearing channel Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}Digital marketing solutions based on consumer data and homomorphic encryption The consistency method of linguistic information and other four preference information in group decision-making Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Research on the driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials Application research of bel canto performance based on artificial intelligence technology Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Application of regression function model based on panel data in financial risk management of bank resource allocation Application of knowledge graph in smart grid fault diagnosis University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Research on the optimisation of logistics parcel intelligent sorting and conveying chain combined with variable clustering mathematical method Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus Research on urban landscape big data information processing system based on ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Application of Discriminative Training Algorithm Based on Intelligent Computing in English Translation Evaluation Research on the application of GLE teaching mode in English-medium colleges The application of directional derivative in the design of animation characters and background elements Research on product process design and optimisation model based on IoT intelligent computing Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education LTE wireless network coverage optimisation based on corrected propagation model The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform Study on tourism development income index calculation of finite element ordinary differential mathematical equation The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas Criminal law imputation path for biometric information Research on composite dynamic disaster prevention and control system of mine earthquake and shock in thick and hard rock mines Research on innovative strategies of college students’ English teaching under the background of artificial intelligence Electromagnetic interference prediction technology of new energy motor drive system Research on the application of PLC technology in electrical automation engineering Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Application of matrix multiplication in signal sensor image perception Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Analysing the variation of metadiscourse verb patterns in English academic papers from within and between disciplines Impact of COVID-19 policy on stock prices of listed property companies Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Research on the experimental principle of deep integration of LETS software and criminal procedure under the background of artificial intelligence Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations VR-based computer maintenance practical training platform development design and application research Research on innovative human capital for China’s economic development based on STI model In-depth analysis of the artistic expression of paper-cut elements in the design of boat space Knowledge graph construction and Internet of Things optimisation for power grid data knowledge extraction Modeling the pathway of breast cancer in the Middle East Construction and intelligent analysis of power grid physical data knowledge graph based on Internet of Things for power system Research on industrial Internet of Things and power grid technology application based on knowledge graph and data asset relationship model Research on the effects of financial literacy on rural household credit constraint Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on educational resource recommendation system based on MRLG Rec The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A study on the phenomenon of anaphoric correction in college students’ English conversation Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model AtanK-A New SVM Kernel for Classification Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Design and evaluation of intelligent teaching system on basic movements in PE Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsResearch on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network