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Study of a linear-physical-programming-based approach for web service selection under uncertain service quality

Data publikacji: 29 Apr 2022
Tom & Zeszyt: AHEAD OF PRINT
Zakres stron: -
Otrzymano: 09 Sep 2021
Przyjęty: 23 Jan 2022
Informacje o czasopiśmie
License
Format
Czasopismo
eISSN
2444-8656
Pierwsze wydanie
01 Jan 2016
Częstotliwość wydawania
2 razy w roku
Języki
Angielski
Abstract

To promote the practical use of web service technologies, it is critical to select a proper web service that will meet users’ preferences from a pool of web services with similar functions. It is usually a core issue during web service selection to describe and evaluate the quality of these web services. Average value can be employed to describe certain service quality and to evaluate the quality with multiple criteria through the Simple Additive Weight Method. Based on an analysis of various deficiencies in existing approaches proposed in some studies, four indicators were used: Price, Response Time, Reliability and Credibility. On top of that, recent sampling data sets were introduced to describe the uncertain quality of service (QoS) criteria; linear physical programming was used to evaluate QoS with comprehensive criteria to meet the need to objectively describe uncertain QoS criteria, and preference regions were set to adapt to interval characteristics of criteria. Finally, a computational example is provided to demonstrate the feasibility and effectiveness of the method.

Keywords

Background

With the rapid development and popularisation of web service technologies, there are many Web services (WSs) with the same functions in universal description, discovery and integration (UDDI) registry. As a result, it is critical to choose a proper service provider from those that can best serve a user's preference. Most WSs are different from non-functional properties although they could also have diverse functions. To meet the functional requirements of users, quality of service (QoS), referring to a group of non-functional properties such as price, response time and reliability in the process of web service selection (WSS), is usually used as a standard to evaluate candidate services. And it has become an important factor to determine whether the service provider is successful. What's more, WS providers generally set different prices for different levels of QoS for WSs [1].

In recent years, WS selection issues (WSSIs) have caught the attention of many scholars [2], and the core issues are the description and evaluation of quality criteria. At present, definite value is often used to describe every criterion of QoS, but in reality, non-functional properties of WSs are variables with greater uncertainty due to network, periods and other causal factors. So, definite value cannot reflect a network's true status. At the same time, Simple Additive Weight Method (SAWM) is often employed in a comprehensive assessment of multiple criteria [3]. These weights will show the comparative importance but not the extent of users’ satisfaction. And during the implementation of WSs, more iterations are required to find better weights, which is strenuous to use computational resources.

To meet the need to objectively describe uncertain QoS criteria and be well adaptive to interval characteristics of criteria through setting preference regions, recent sampling data set is used to describe uncertain QoS criteria and to evaluate comprehensive criteria based on Linear Physical Programming (LPP), for LPP can banish traditional weight setting and integrate the design process into a more flexible framework.

Literature review

A WSSI is a multi-objective optimisation process [4], in which, WS quality variables play a positive role on customers’ satisfaction, the extent of which is different according to web types with different QoS [5]. UDDI, as criteria, helps users to find suitable WSs. Curbera et al. [6] introduced SOAP, WSDL and UDDI to unravel the WS web. Typical QoS properties include execution cost and time, availability, successful execution rate, reputation and usage frequency [7]. Response Time, trust degree and monetary cost are also considered as criteria for WSS by Zhao et al. [8]. Wang et al. [9] used three factors, such as service providers, the context of customers and historical statistics, to measure QoS. But QoS results could not be coherent when they are measured with different tools [10]. Therefore, it is critical to choose an appropriate method to evaluate QoS values.

A quality constraint tree [11] and a probability theory [12, 13] could be used to build different methods or models to address or measure QoS. Collaborative filtering algorithms are also used to select WSs [14, 15]. Other methods based on genetic algorithm (GA) were introduced in WSS [4, 16, 17]. There are still some other-theory-based approaches used for service selection and reuse, for example, QoS ontology [18] and group decision [19]. Some studies integrated multiple methods to improve selection effectiveness. For a ubiquitous web environment, Wang et al. [20] proposed a service selection approach involving three methods that are fuzzy logic control, mean particle swarm optimisation algorithm and local selection. Purohit and Kumar [21] used classification technique for WSS. Purohit and Kumar [22] discussed a trip planning case study to highlight the role of WSs in a smart city and described six learning models. Although these mentioned approaches could be effective to select suitable services that meet customers’ requirements, they could be too complex and it is necessary to build a simpler approach that can be easily conducted for customers to select WSs. Linear programming could be used to select services as a good approach, and a linear programming approach was used to optimise the multiple attribute QoS [23]. Through WS composition [24], a WS flow can be obtained that includes many candidate WSs with the same functional attribute and different non-functional attributes (QoS).

WSS means to choose a WS candidate from a WS set that could best meet users’ requests. Composite services have more than one QoS criterion, which means WSS is a multiple-attribute-decision-making (MADM) issue. As a method most commonly used to assess composite service QoS, SAWM has two main limitations, namey (1) it cannot show the extent of the users’ satisfaction and provide clear guidance to setting the right weights, and (2) it often has to conduct more iterations taxing to computational resources to have better weights. So, it is most necessary to clarify QoS factors affecting customers’ satisfaction.

Messac [25] and Messac et al. [26] discussed the limitations of SAWM and designed a new effective approach named physical programming (PP) that aims to cut down the computational intensity of massive problems and to put the design process into a more flexible framework. With PP, the value of the objective is divided into some continuous regions to uncover preference for each criterion. Moreover, preference functions are obtained from piecewise spline segment interpolation. After that, all preference functions are integrated into an aggregate preference function which is the objective function. The option with the minimum value will be optimum. Among the linear programming methods, the LPP method is one of the typical preference-based algorithms that is often used with dynamic weight for multi-objective collaborative optimisation [27]. The LPP method has been applied in more environments [28,29,30] or integrated into other methods [31,32,33,34]. Therefore, in this paper, we use LPP to analyse QoS to solve WSSIs by simplifying the process of WSS.

Modelling based on LPP
Description of uncertain QoS criteria

QoS can be modelled based on different criteria that have been defined in a wide range [35]. From the perspective of stability, the criteria can be categorised into static and dynamic. Static criteria are those that remain the same in a certain stage, such as service price, while dynamic criteria are those of a more dynamic nature due to network conditions, host performance, location, periods and so on. For example, the Response Time of an online ticketing service is longer during holidays than on business days. However, a definite value is not suitable to show the true state of a WS from a dynamic perspective.

In this article, to simulate a true state, sampling data sets are used to describe a dynamic criterion. A sample size will be set according to potential candidates and is decided by a true environment. For instance, Response Time could be different and a corresponding set can be built with different Response Times. Now there are five sampling selected data, and they form a sampling data set that is 3.4s, 3.5s, 3.3s, 3.4s and 3.6s.

Price, Response Time, Reliability and Credibility constitute a set of criteria that are widely used to describe their QoS. Among the four criteria, Price is static, while Response Time, Reliability and Credibility are dynamic. The sampling pool of five with all sampling data of these four criteria (QoS of WS1) is listed in Table 1.

QoS of WS (WS1)

Price ($) 1.5
Response Time (s) [3.5, 3.4, 3.3, 3.7, 3.6]
Reliability [0.88, 0.85, 0.90, 0.84, 0.83]
Credibility [7.6, 7.8, 7.5, 8.0, 7.9]
Description and solution of WS selection issue under uncertain quality
Method description

Messac [25] proposed Physical Programming to reduce the computational intensity and simplify the complex process to put it into a more flexible and simplified framework when dealing with massive complicated issues. QoS values were represented to address a WSSI [36]. Objective values in a PP model can be divided into some continuous regions to express users’ preference for the criteria, and the preference functions can be got from the piecewise spline segment interpolation. Then, all the preference functions will be integrated into an aggregate preference function that is an objective function. LPP is a further simplified type of Physical Programming, with which many computational burdens can be further reduced. In an LPP model, preference functions are piecewise-linear, which are used to show users’ preference for generic criteria. In general, preference could fall into four types, each of which has two cases (soft and hard), as the following shows.

(i) Class-1: Smaller-Is-Better (SIB);

(ii) Class-2: Larger-Is-Better (LIB);

(iii) Class-3: Centre-Is-Better (CIB);

(iv) Class-4: Range-Is-Better (RIB).

In this article, the objective gi is assumed to be the abscissa, and the relevant preference function Zi is set to the ordinate. The value of a preference function is considered to indicate the significance, the lower and the better. The qualitative meaning of 1-S and 2-S preference functions is described in Figures 1 and 2 [37].

Fig. 1

Qualitative meaning of a 1-S preference function

Fig. 2

Qualitative meaning of a 2-S preference function

There are six preference regions used to express both qualitative and quantitative depictions. The six preference regions of the 1-S preference function are shown in Figure 1.

Highly Desirable: giti1+ {g_i} \le t_{i1}^ + ;

Desirable: ti1+<giti2+ t_{i1}^ + < {g_i} \le t_{i2}^ + ;

Tolerable: ti2+<giti3+ t_{i2}^ + < {g_i} \le t_{i3}^ + ;

Undesirable: ti3+<giti4+ t_{i3}^ + < {g_i} \le t_{i4}^ + ;

Highly Undesirable: ti4+<giti5+ t_{i4}^ + < {g_i} \le t_{i5}^ + ;

Unacceptable: ti5+<gi t_{i5}^ + < {g_i} .

The One vs. Other criteria rule (OVO rule) will be applied to operating PP [37]. There are two options for calculating the values of preference functions.

Option 1: ‘Full reduction for one criterion across a given region (region k, k = 3, 4, 5)’.

Option 2: ‘Full reduction for all the other criteria across the next better region (region (k-1))’.

For the OVO rule, Option 1 is preferred than the Option 2, which means that the worst candidate will always be helped first.

Mathematical representation of the preference function

A preference function has the following properties:

A lower value of the preference function is preferred than a higher value.

The function is strictly positive.

The function is continuous, piecewise linear and convex.

The values of the function at given regions are the same for different types.

The magnitude of the function's vertical excursion across any region must satisfy the OVO rule.

The five properties above can be turned into a set of mathematical formulas as follows: Zs=Zi(tis+)=Zi(tis)i;(2s5);Z1=0, {Z^s} = {Z_i}(t_{is}^ + ) = {Z_i}(t_{is}^ - )\quad \forall {\rm{i}};\quad (2 \le {\rm{s}} \le 5);\quad {{\rm{Z}}^1} = 0, Where, i is a sequence number of the criterion, and s is a sequence number of the preference regions. Z¯s=ZsZs1;(2s5). {\overline Z ^s} = {Z^s} - {Z^{s - 1}};\quad (2 \le s \le 5). Z¯s=βnsc1Z¯s1;(3s5);nsc>1;β>1 {\overline Z ^s} = \beta {n_{sc}} - 1{\overline Z ^{s - 1}};\quad (3 \le s \le 5);\quad {n_{sc}} > 1;\quad \beta > 1 Eq. (1c) can meet the requirements of the OVO rule. To analyse the requirement of convexity, it is defined as follows: t˜is+=tis+ti(s1)+;t˜is=tisti(s1);(2s5). \widetilde t_{is}^ + = t_{is}^ + - t_{i(s - 1)}^ + ;\quad \widetilde t_{is}^ - = t_{is}^ - - t_{i(s - 1)}^ - ;\quad (2 \le {\rm{s}} \le 5). The slope of the preference function of the generic i-th criterion is shown in the following form: wis+=Z¯s/t˜is+;wis=Z¯s/t˜is;(2s5). w_{is}^ + = {\overline Z ^s}/\widetilde t_{is}^ + ;\quad w_{is}^ - = {\overline Z ^s}/\widetilde t_{is}^ - ;\quad (2 \le {\rm{s}} \le {\rm{5)}}. The requirement of convexity can be verified through the following form: w¯min=mini,s{w¯is+,w¯is}>0;{(2s5)i:softcriteria {\overline w _{\min }} = \mathop {\min }\limits_{i,s} \{ \overline w _{is}^ + ,\overline w _{is}^ - \} > 0;\left\{ {\matrix{ {(2 \le s \le 5)} \hfill \cr {i:soft{\kern 1pt} criteria} \hfill \cr } } \right. where w¯is+=wis+wi(s1)+;w¯is=wiswi(s1);wi1+=wi1=0. \overline w _{is}^ + = w_{is}^ + - w_{i(s - 1)}^ + ;\quad \overline w _{is}^ - = w_{is}^ - - w_{i(s - 1)}^ - ;\quad w_{i1}^ + = w_{i1}^ - = 0. The requirement of convexity can always be satisfied by simply increasing the magnitude of β, the convexity parameter.

Finally, the preference function takes the form as shown in the following: s=25(w¯is+dis++w¯isdis) \sum\limits_{s = 2}^5 \left( {\overline w _{is}^ + d_{is}^ + + \overline w _{is}^ - d_{is}^ - } \right) where dis+ d_{is}^ + and dis d_{is}^ - are deviational variables.

Then, the form of the aggregate preference function is shown in the following form: i=1ns=25((w¯is+dis++w¯isdis)) \sum\limits_{i = 1}^n \sum\limits_{s = 2}^5 \left( {\left( {\overline w _{is}^ + d_{is}^ + + \overline w _{is}^ - d_{is}^ - } \right)} \right) With an initial value of nsc equal to the amount of soft criteria, Z˜2=0.1 {\widetilde Z^2} = 0.1 , β = 1.1, wi1+=wi1=0 w_{i1}^ + = w_{i1}^ - = 0 , and it can be evaluated in sequences: Z¯s {\overline Z ^s} , t˜is+ \widetilde t_{is}^ + , t˜is \widetilde t_{is}^ - , wis+ w_{is}^ + , wis w_{is}^ - , w¯is+ {\overline w _{is}}^ + , w¯is {\overline w _{is}}^ - , w¯min {\overline w _{\min }} .

Improved LPP
Determine initial value of convexity parameter β

There are two effects of the convexity parameter β. The first is that the parameter is in accordance with the OVO rule through Eq. (1) and the second is that the parameter meets the requirements through Eq. (2). Messac et al. [26] gave β an initial value that is ‘1.1’, which is in accordance with the OVO rule but is not guaranteed to meet the convexity requirement. If so, it is necessary to change the value of β with iterations. In order to make the computational process simpler and to reduce the computational workload, the convexity requirement can be analysed through an algorithm without too much iteration by assigning β a proper initial value.

For the s-th region, the form of the convexity requirement is: w¯is+=[β(nsc1)s2Z¯2]l(s)[β(nsc1)s3Z¯2]l(s1)>0, \overline w _{is}^ + = {{[\beta {{({n_{sc}} - 1)}^{s - 2}}{{\overline Z }^2}]} \over {l(s)}} - {{[\beta {{({n_{sc}} - 1)}^{s - 3}}{{\overline Z }^2}]} \over {l(s - 1)}} > 0, where l(s) is the length of the s-th region.

By simplifying the above inequality equation, a new inequality system can be got as the following shows: {β>l(3)l(2)(nsc1)β>l(4)l(3)(nsc1)β>l(5)l(4)(nsc1)β>1 \left\{ {\matrix{ {\beta > {{l(3)} \over {l(2)({n_{sc}} - 1)}}} \hfill \cr {\beta > {{l(4)} \over {l(3)({n_{sc}} - 1)}}} \hfill \cr {\beta > {{l(5)} \over {l(4)({n_{sc}} - 1)}}} \hfill \cr {\beta > 1} \hfill \cr } } \right. So, a proper initial value of β can be found by calculating Eq. (4) when satisfying both the OVO rule and the convexity requirement.

A simple form of preference function

Messac et al. [26] built a preference function, like Eq. (3) rather than a simpler form because linear programming models are used to solve optimisation problems, and no ‘if’-statements exist in LP models. So, it is not easy to evaluate the former. After calculating the value of β, a simple form of a 1-S preference function can be formulated, and the piecewise linear function is shown as follows: Z¯2{0;giti1+Z¯2(giti1+)l(2);ti1+<gi<ti2+Z2+β(nsc1)Z¯2(giti1+)l(3);ti1+<gi<ti2+Z3+β(nsc1)2Z¯2(giti1+)l(4);ti3+<gi<ti4+Z4+β(nsc1)3Z¯2(giti1+)l(5);ti4+<gi<ti5+ {\overline Z ^2}\left\{ {\matrix{ {0;} \hfill & {{g_i} \le t_{i1}^ + } \hfill \cr {{{{{\overline Z }^2}\left( {{g_i} - t_{i1}^ + } \right)} \over {l(2)}};} \hfill & {t_{i1}^ + < {g_i} < t_{i2}^ + } \hfill \cr {{Z^2} + {{\beta ({n_{sc}} - 1){{\overline Z }^2}({g_i} - t_{i1}^ + )} \over {l(3)}};} \hfill & {t_{i1}^ + < {g_i} < t_{i2}^ + } \hfill \cr {{Z^3} + {{\beta {{({n_{sc}} - 1)}^2}{{\overline Z }^2}({g_i} - t_{i1}^ + )} \over {l(4)}};} \hfill & {t_{i3}^ + < {g_i} < t_{i4}^ + } \hfill \cr {{Z^4} + {{\beta {{({n_{sc}} - 1)}^3}{{\overline Z }^2}({g_i} - t_{i1}^ + )} \over {l(5)}};} \hfill & {t_{i4}^ + < {g_i} < t_{i5}^ + } \hfill \cr } } \right. It can be found that it is simpler to evaluate the above equation than Eq. (3) in implementation.

Problem description and solution of WS selection
Problem description

There are many WSs with same functional properties but different QoS, and a WSSI means a process during which users select a proper WS. WS is a set of WSs, and W S = {W S1, W S2, …, W Sm}.

QoS of these WSs is described by a set of QoS: Q, and Q = {Q1, Q2, …, Qm}. Here, Qm is a QoS vector, which includes n components, and Qi = {Qi1, Qi2, …, Qin} (i = 1, 2, …, m), which are shown as Eq. (5). QoS(WS)=QoS(WS1WS2WSm)=(Q1Q2Qm)=(Q11Q12Q1nQ21Q22Q2nQm1Qm2Qmn) QoS(WS) = QoS\left( {\matrix{ {W{S_1}} \cr {W{S_2}} \cr \ldots \cr {W{S_m}} \cr } } \right) = \left( {\matrix{ {{Q_1}} \cr {{Q_2}} \cr \ldots \cr {{Q_m}} \cr } } \right) = \left( {\matrix{ {{Q_{11}}} & {{Q_{12}}} & \ldots & {{Q_{1n}}} \cr {{Q_{21}}} & {{Q_{22}}} & \ldots & {{Q_{2n}}} \cr \ldots & \ldots & \ldots & \ldots \cr {{Q_{m1}}} & {{Q_{m2}}} & \ldots & {{Q_{mn}}} \cr } } \right) Where, all components, Qi1, Qi2, …, Qin (i=1, 2, …, m), are uncertain criteria, and they can be described by the recent sampling data set: P, and P = {Pijk}, i = 1, 2, …, m, j = 1, 2, …, n, and k = r, s, …, t. So, the QoS matrix of WS can be shown as Eq. (6). QoS(WS)=([P111,P112,,P11r][P121,P122,,P12s][P1n1,P1n2,,P1nt][P211,P212,,P21r][P221,P222,,P22s][P2n1,P2n2,,P2nt][Pm11,Pm12,,Pm1r][Pm21,Pm22,,Pmrs][Pmn1,Pmn2,,Pmnt]) QoS(WS) = \left( {\matrix{ {[{P_{111}},{P_{112}}, \ldots ,{P_{11r}}]} & {[{P_{121}},{P_{122}}, \ldots ,{P_{12s}}]} & \ldots & {[{P_{1n1}},{P_{1n2}}, \ldots ,{P_{1nt}}]} \cr {[{P_{211}},{P_{212}}, \ldots ,{P_{21r}}]} & {[{P_{221}},{P_{222}}, \ldots ,{P_{22s}}]} & \ldots & {[{P_{2n1}},{P_{2n2}}, \ldots ,{P_{2nt}}]} \cr \ldots & \ldots & \ldots & \ldots \cr {[{P_{m11}},{P_{m12}}, \ldots ,{P_{m1r}}]} & {[{P_{m21}},{P_{m22}}, \ldots ,{P_{mrs}}]} & \ldots & {[{P_{mn1}},{P_{mn2}}, \ldots ,{P_{mnt}}]} \cr } } \right) A WSSI is to choose one service with optimal QoS from a WS set using a certain algorithm. Because QoS of each WS contains more than one criterion, a WSSI is a multi-objective optimisation issue. And there is no absolute optimal solution. Optimal QoS means to achieve the best according to each criterion of different users’ preferences.

Solution

At present, a conventional solution to WSSIs under uncertain QoS is using a definite value (average value) to characterise each criterion first, and then take the weighted average value of each criterion to comprehensively evaluate QoS. On one hand, this method cannot describe the uncertainty of each indicator accurately; on the other hand, it is difficult to set the weight of each indicator objectively. In an improved LPP, it is not necessary to set weights but to express users’ preferences through preference regions, which will precisely adapt to interval characteristics of uncertain QoS criteria. Thus, improved LPP is proposed in this paper as the solution to WSSIs under uncertain quality.

In the QoS matrix of a WS set shown in Eq. (6), the n-th column involves m criterion sets that correspond to the n-th QoS criterion. To these m sets, a minimum value (Ki) and a maximum value (Kj) can come from any element and from all the elements, which means that the n-th quality criterion of all WSs in the set, WS, will fall into the region, [Ki,Kj]. Based on LPP, the region, [Ki,Kj], can be taken as a preference region boundary, [ti1+,ti5+] [t_{i1}^ + ,t_{i5}^ + ] , of the n-th QoS criterion, and its preferred function is defined. In the same way, each preference function of all criteria can be singled out.

For each QoS criterion, its value is also a kind of set. We can calculate the value by using its preferred function for each element and then take the sum of these values as the evaluation value of this criterion. The sum of evaluation values of all criteria is the comprehensive assessment value of QoS of the WS. When we get all comprehensive assessment values of all WSs, the minimum value should be selected from these comprehensive assessment values, for the WS that the minimum value corresponds to is the one that best serves the users’ preferences.

An experimental case
Case description

There are 50 WS candidates with same functional properties but different quality, and among them, anyone could be right to fit users’ preferences. Three criteria that are Response Time, Reliability and Credibility constitute a QoS vector, and the sample size is five. A QoS matrix of a WS set with 50 candidates is shown in Table 2.

QoS matrix of WS set

WSs Response Time Reliability Credibility

WS1 [3.0,3.7,3.5,3.6,4.0] [0.78,0.85,0.79,0.89,0.81] [7.1,7.4,7.7,7.9,8.0]
WS2 [4.0,3.6,3.1,4.1,4.5] [0.69,0.71,0.77,0.79,0.80] [6.8,6.9,7.7,7.1,7.5]
WS3 [2.8,2.9,3.4,5.4,3.0] [0.80,0.79.0.90,0.88,0.85] [7.5,7.9,8.0,8.5.8.3]
WS50 [2.8,4.5,4.1,3.7,3.9] [0.77,0.75,0.80,0.71,0.68] [7.9,6.9,7.2,7.4,7.5]
Solving process

Five steps are designed to provide a solution to the above case.

First step: Values range must be obtained for all criteria.

Response Time: [2.5, 5.5]

Reliability: [0.69, 0.90]

Credibility: [6.4, 8.3]

Second step: Preference should be set. Value range is used as a preference boundary of the criteria, and within these boundaries, a preference can be obtained.

Response Time is of 1-S types based on users’ preference. The preference regions are shown in Table 3.

Preference regions for Response Time

Criterion ti1+ t_{i1}^ + ti2+ t_{i2}^ + ti3+ t_{i3}^ + ti4+ t_{i4}^ + ti5+ t_{i5}^ +
Response Time 2.5 3.0 3.5 4.2 5.5

Both Reliability and Credibility are of 2-S types whose preference regions are shown in Table 4.

Preference regions for Reliability and Credibility

Criterion ti1 t_{i1}^ - ti2 t_{i2}^ - ti3 t_{i3}^ - ti4 t_{i4}^ - ti5 t_{i5}^ -

Reliability 0.90 0.85 0.80 0.75 0.69
Credibility 8.3 8.0 7.5 7.0 6.4

Third step: An initial value of the convexity parameter, beta, should be calculated. With the known initial value: nsc = 3 and Z¯2=0.1 {\overline Z ^2} = 0.1 , and based on preference regions of the above-mentioned three criteria, the following unbalanced systems can be worked out: {β>l(3)l(2)(nsc1)β>l(4)l(3)(nsc1)β>l(5)l(4)(nsc1)β>1 \left\{ {\matrix{ {\beta > {{l(3)} \over {l(2)({n_{sc}} - 1)}}} \hfill \cr {\beta > {{l(4)} \over {l(3)({n_{sc}} - 1)}}} \hfill \cr {\beta > {{l(5)} \over {l(4)({n_{sc}} - 1)}}} \hfill \cr {\beta > 1} \hfill \cr } } \right. Then, the initial value of β will be 1.22, which satisfies w¯is+>0;3s5 {\overline w _{is}}^ + > 0;3 \le s \le 5 .

Fourth step: The preference functions of the three criteria can be worked out.

With the solving process of LPP, based on both preference regions and the convexity parameter, β, the preference functions of each criterion can be calculated.

Set the initial value: nsc=3,Z¯2=0.1;β=1.22 {{\rm{n}}_{{\rm{sc}}}} = 3,{\kern 1pt} {\overline Z ^2} = 0.1;{\kern 1pt} \beta = 1.22

Calculate Z¯2 {\overline Z ^2} : Z¯3=0.244;Z¯4=0.595;Z¯5=1.452 {\overline Z ^3} = 0.244;{\kern 1pt} {\overline Z ^4} = 0.595;{\kern 1pt} {\overline Z ^5} = 1.452

Figure out Zs: Z2=0.1;Z3=0.344;Z4=0.939 {Z^2} = 0.1;{\kern 1pt} {Z^3} = 0.344;{\kern 1pt} {Z^4} = 0.939

Work out the preference functions of the three criteria:

Preference functions of all dynamic criteria can be solved after parameters are calculated. All the functions are as follows:

The preference function for Response Time is: Z1={0.2(gi2.5);2.5<gi3.00.1+0.488(gi3.0);3.0<gi3.50.344+0.85(gi3.5);3.5<gi4.20.939+1.12(gi4.2);4.2<gi5.5 {Z_1} = \left\{ {\matrix{ {0.2({g_i} - 2.5);} \hfill & {2.5 < {g_i} \le 3.0} \hfill \cr {0.1 + 0.488({g_i} - 3.0);} \hfill & {3.0 < {g_i} \le 3.5} \hfill \cr {0.344 + 0.85({g_i} - 3.5);} \hfill & {3.5 < {g_i} \le 4.2} \hfill \cr {0.939 + 1.12({g_i} - 4.2);} \hfill & {4.2 < {g_i} \le 5.5} \hfill \cr } } \right.

The preference function for Reliability is: Z2={2(0.9gi);0.85gi<0.90.1+4.88(0.85gi);0.80gi<0.850.344+11.9(0.80gi);0.75gi<0.800.939+24.2(0.75gi);0.69gi<0.75 {Z_2} = \left\{ {\matrix{ {2(0.9 - {g_i});} \hfill & {0.85 \le {g_i} < 0.9} \hfill \cr {0.1 + 4.88(0.85 - {g_i});} \hfill & {0.80 \le {g_i} < 0.85} \hfill \cr {0.344 + 11.9(0.80 - {g_i});} \hfill & {0.75 \le {g_i} < 0.80} \hfill \cr {0.939 + 24.2(0.75 - {g_i});} \hfill & {0.69 \le {g_i} < 0.75} \hfill \cr } } \right.

The preference function for Credibility is: Z3={0.333(8.3gi);8.0gi<8.30.1+0.488(8.0gi);7.5gi<8.00.344+1.19(7.5gi);7.0gi<7.50.939+2.42(7.0gi);6.4gi<7.0 {Z_3} = \left\{ {\matrix{ {0.333(8.3 - {g_i});} \hfill & {8.0 \le {g_i} < 8.3} \hfill \cr {0.1 + 0.488(8.0 - {g_i});} \hfill & {7.5 \le {g_i} < 8.0} \hfill \cr {0.344 + 1.19(7.5 - {g_i});} \hfill & {7.0 \le {g_i} < 7.5} \hfill \cr {0.939 + 2.42(7.0 - {g_i});} \hfill & {6.4 \le {g_i} < 7.0} \hfill \cr } } \right.

Fifth step: All comprehensive assessment values will be obtained and the minimum should be chosen.

Based on the preference functions of the three criteria, evaluation values of all criteria can be obtained for the comprehensive values of QoS of each candidate. Among these comprehensive values, QoS (WS23)=14.528 is the minimum. Thus, the minimum value corresponds to WS23, which is the final WS. As a result, WS23 best suits users’ preferences.

Conclusion

Setting boundaries for preference region, tis: in the above-mentioned model, preference regions of each criterion are evenly distributed, that is, when any of the three criteria has a great advantage, the WS will, in the end, turn out to be a good option. However, in reality, users could have their unique preferences with one criterion. For example, when users are scholars or academic students who have a high preference for the credibility of contents in a WS, the WS whose credibility level only lands in the middle to the upper level will not turn out to be the best choice. In such cases, the chance that the preference region of credibility is categorised as the boundary of the Tolerable preference region will be increased. Therefore, to meet the needs of different user groups, it is necessary to set a different preference region boundary, tis, for the three criteria.

Setting of dynamic weight, wis: the LPP method involves different weights for different preference regions since the better the preference region is, the smaller its weight is. So, a WS with the minimum value will be the final choice. Similarly, different groups have different preferences for the dynamic weights, wis, of different preference regions. When β is small, the score gradient of the neighbouring preference region boundary is small, that is, if the values of three criteria are all in the upper middle level, the final value will also be small. Oppositely, when β is big, the score gradient of the neighbouring preference region boundary is big, that is, if one criterion of a WS has a large advantage, the final value will be small despite its other criteria maybe just in a relatively low level. Therefore, the gradient setting among the dynamic weights, wis, depends on whether users focus more on the integrated services or more on the characteristics of WSs.

As a result, it is necessary to consider users’ specific needs and the psychology of different user groups when the evaluation standards of WSs are set. For different user groups, it is necessary to set a unique preference region boundary, tis, and a dynamic weight, wis, to make the evaluation results based on the LLP model closer to users’ needs to provide users with more accurate references, which in return also makes the evaluation method more flexible and more practical.

Discussion

LPP is an optimisation algorithm, which entirely releases the decision-makers from the process of choosing weights [26]. Specifically, LPP avoids subjectivity when determining physically meaningless weights and ratings, to calculate the total scores of the decision. Thus, in contrast with other methods, LPP costs less time to make the criteria design as well as lessens the risk of costly design changes [38]. Additionally, in a multiple criteria environment, LPP can allow decision-makers to employ a rational manner to express their preference for each objective of interest [39], and it brings an efficient and practical decision-making process into practice.

Recent sampling data sets are used to describe uncertain QoS criteria, which indicates that it could be better to follow the true state of uncertain criteria. Because of the limitations of the SAWM in solving MADM problems, LPP with the OVO rule can be used to solve this type of WSSIs, which can adapt to interval characteristics of criteria through setting preference regions, for LPP can banish traditional weight setting, and significantly reduce computational burden in the process of solution. Compared with this method, other evaluation methods for WSS are lack of maneuverability manoeuvrability. For example, the black box method based on genetic algorithm and neural network needs large sample data and occupies larger computational memory. Therefore, it is not easy to reflect users’ actual preferences and psychology for its calculation process is not transparent, and the actual evaluation processes of the method are lack of readability. Even though Skyline component computation also can be applied for multiple-objective decisions and can prune the redundant components for cyber-physical-social systems [40], it will take this algorithm a longer response time when facing big data. However, LPP can deal with this problem.

To improve the computational efficiency, an improved LPP is conducted, with which a proper initial value of convexity parameters is determined without iteration, and the form of a preference function can be simplified. A WS with a minimum comprehensive assessment value is the optimal selection. The computational example proves that the LPP-based method with a general description is feasible and effective to evaluate aggregate QoS values of composite services.

In fact, the LLP algorithm can also be extended to other evaluation models that are composed of multiple dynamic criteria. When it needs to determine the range of each criterion and the preference range of each criterion can be defined through satisfaction, and the criterion finally evaluated can be determined by setting dynamic weight values. An LLP-based evaluation model with the OVO principle attaches more importance to the apparent advantages of a single criterion rather than the tiny merits of all other criteria and is very close to the customers’ satisfaction evaluation. Moreover, it can simplify the calculation process of the scores of multiple dynamic criteria when it is faced with multiple samples. Therefore, the above-mentioned LLP-based evaluation system has a certain validity to evaluate situations involving multiple dynamic criteria and is easier to understand and use in practice.

Fig. 1

Qualitative meaning of a 1-S preference function
Qualitative meaning of a 1-S preference function

Fig. 2

Qualitative meaning of a 2-S preference function
Qualitative meaning of a 2-S preference function

QoS of WS (WS1)

Price ($) 1.5
Response Time (s) [3.5, 3.4, 3.3, 3.7, 3.6]
Reliability [0.88, 0.85, 0.90, 0.84, 0.83]
Credibility [7.6, 7.8, 7.5, 8.0, 7.9]

Preference regions for Response Time

Criterion ti1+ t_{i1}^ + ti2+ t_{i2}^ + ti3+ t_{i3}^ + ti4+ t_{i4}^ + ti5+ t_{i5}^ +
Response Time 2.5 3.0 3.5 4.2 5.5

QoS matrix of WS set

WSs Response Time Reliability Credibility

WS1 [3.0,3.7,3.5,3.6,4.0] [0.78,0.85,0.79,0.89,0.81] [7.1,7.4,7.7,7.9,8.0]
WS2 [4.0,3.6,3.1,4.1,4.5] [0.69,0.71,0.77,0.79,0.80] [6.8,6.9,7.7,7.1,7.5]
WS3 [2.8,2.9,3.4,5.4,3.0] [0.80,0.79.0.90,0.88,0.85] [7.5,7.9,8.0,8.5.8.3]
WS50 [2.8,4.5,4.1,3.7,3.9] [0.77,0.75,0.80,0.71,0.68] [7.9,6.9,7.2,7.4,7.5]

Preference regions for Reliability and Credibility

Criterion ti1 t_{i1}^ - ti2 t_{i2}^ - ti3 t_{i3}^ - ti4 t_{i4}^ - ti5 t_{i5}^ -

Reliability 0.90 0.85 0.80 0.75 0.69
Credibility 8.3 8.0 7.5 7.0 6.4

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