Evaluation of Fuzzy Relational Coefficients as Relational Indicators

Abstract

In previous work, we proposed a method for defining type-1 and type-2 fuzzy partition tables by applying t-norms used in fuzzy set operations. This approach enables the fuzzification of fuzzy relational coefficients into type-1 and type-2 forms. In this paper, we introduce a novel probabilistic generation model for evaluating fuzzy relational coefficients as relational indicators. The proposed model adopts a structure in which the relational principle of “true implies true, false implies false” is probabilistically propagated. Using the vectors generated by this method, we quantitatively assess the directionality and strength of fuzzy relational coefficients and examine their validity as indicators of relational structure.