<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Fuzzy inference using the conjunctive approach is very popular in many practical applications. It is intuitive for engineers, simple to understand, and characterized by the lowest computational complexity. However, it leads to incorrect results in the cases when the relationship between a fact and a premise is undefined. This article analyses the problem thoroughly and provides several possible solutions. The drawbacks of uncertainty in the conjunctive approach are presented using fuzzy inference based on a fuzzy truth value, first introduced by Baldwin (1979c). The theory of inference is completed with a new truth function named 0-undefined for two-valued logic, which is further generalized into fuzzy logic as <italic>α</italic>-undefined. Eventually, the proposed modifications allow altering existing implementations of conjunctive fuzzy systems to interpret the undefined state, giving adequate results.</p>
</abstract>

Fuzzy inference using the conjunctive approach is very popular in many practical applications. It is intuitive for engineers, simple to understand, and characterized by the lowest computational complexity. However, it leads to incorrect results in the cases when the relationship between a fact and a premise is undefined. This article analyses the problem thoroughly and provides several possible solutions. The drawbacks of uncertainty in the conjunctive approach are presented using fuzzy inference based on a fuzzy truth value, first introduced by Baldwin (1979c). The theory of inference is completed with a new truth function named 0-undefined for two-valued logic, which is further generalized into fuzzy logic as α-undefined. Eventually, the proposed modifications allow altering existing implementations of conjunctive fuzzy systems to interpret the undefined state, giving adequate results.

Uncertainty in the Conjunctive Approach to Fuzzy Inference

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Uncertainty in the Conjunctive Approach to Fuzzy Inference"}

Fuzzy inference using the conjunctive approach is very popular in many practical applications. It is intuitive for engineers, simple to understand, and...

Uncertainty in the Conjunctive Approach to Fuzzy Inference

Published Online: Sep 27, 2021

Page range: 431 - 444

Received: Dec 11, 2020

Accepted: Jul 05, 2021

DOI: https://doi.org/10.34768/amcs-2021-0029

Keywords
fuzzy inference, conjunctive approach, fuzzy truth value

© 2021 Przemysław Kudłacik, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Uncertainty in the Conjunctive Approach to Fuzzy Inference

Published Online: Sep 27, 2021

Page range: 431 - 444

Received: Dec 11, 2020

Accepted: Jul 05, 2021

DOI: https://doi.org/10.34768/amcs-2021-0029

Keywordsfuzzy inference, conjunctive approach, fuzzy truth value

© 2021 Przemysław Kudłacik, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
fuzzy inference, conjunctive approach, fuzzy truth value