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Uncertainty in the conjunctive approach to fuzzy inference

Kudłacik Przemysław

International Journal of Applied Mathematics and Computer Science

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2021

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Vol. 31, no. 3

431--444

EN

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.

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An analysis of using triangular truth function in fuzzy reasoning based on a fuzzy truth value

Kudłacik P.

Journal of Medical Informatics & Technologies

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2013

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Vol. 22

103--110

EN

Fuzzy systems are widely used in research and applications considering complex information like gene recognition and classification. Because of the character of genetic data, the extensive knowledge bases of such systems contain complex rules described by even thousands of atomic premises. This paper presents an analysis of fuzzy reasoning based on a fuzzy truth value, presented by Baldwin. The solution is an interesting, alternative approach to fuzzy inference. Considering the Zadeh’s compositional rule of inference, the idea of Baldwin has an advantage of resolving the whole inference process within the truth space. The approach is especially convenient for systems with large number of premises in rules, like mentioned gene classification systems. Although the solution of Baldwin is characterized by significantly lower computational complexity than the full implementation of the compositional rule of inference, it is not applied in contemporary systems. Over the years different researchers proposed simplified approaches, which are easier to implement and faster. The analysis presented in this paper considers possible simplifications that could be applied to the approach of Baldwin, where facts and fuzzy truth values are described by triangular membership functions. Such assumptions open the possibility of implementation of fast Baldwin’s inference and applications even for complex genetic data. Nevertheless, the solution would preserve one of the biggest advantage, which is the fuzzy relation, in form of the truth function, between a fact and a premise, throughout the whole inference process. Other fast approaches reduce this relation to only one value.

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Advantages of an approximate reasoning based on a fuzzy truth value

Kudłacik P.

Journal of Medical Informatics & Technologies

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2010

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Vol. 16

125--131

EN

The approximate reasoning based on a fuzzy truth value is based on a different view of linguistic statements and comparing with the compositional rule of inference has some advantages. Benefits of the method are especially important for fuzzy expert systems with large sets of premises. The problem is very common for many applications in medicine, biology and biometry. By a short analysis of the approach and comparing to the compositional rule of inference the paper emphasizes the most important advantages of a possible implementation, which is particularly significant for the mentioned fields.