Calculation of resolvent based on similarity ratio in fuzzy resolution method

Abstract

This article presents a fuzzy resolution method based on disjunctive syllogism and applicable for reasoning with uncertainty in arguments and conclusions. In this case, the degree of truth of each variable is assessed by a number in the interval [0,1], and one of the main problems is defining the conditions that would allow for a meaningful logical conclusion. To construct a resolution conclusion, the degree of similarity for a pair of contrary literals is used, which could potentially be selected for constructing a fuzzy resolvent. The article presents systems of axioms that postulate the properties of fuzzy similarity/dissimilarity relationships between pairs of fuzzy sets. Each system reflects a specific combination of sets. Based on these, considering the formal representation of fuzzy logical connectors, a set of scalar comparison indices can be constructed. Therefore, this result has independent significance and can be used in applications where the problem of comparing fuzzy sets or their particular case-fuzzy numbers-arises. The article provides a rationale for the fuzzy resolution method using the concept of a fuzzy conditional subset. A scheme of the method is proposed, in which the fuzzy resolvent is constructed based on the similarity of selected literals. An illustrative example demonstrates the capabilities of the method and confirms its applicability for generating plausible reasoning under conditions of uncertainty.