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The measure of the similarity between intuitionistic fuzzy sets (IFSs) is an important topic in IFSs theory. In this paper, we propose two computational formulae for similarity measures on IFSs based on a quaternary function called intuitionistic fuzzy equivalence. We first propose the concept of intuitionistic fuzzy equivalence. Then we give a computational formula for intuitionistic fuzzy equivalencies (i.e., Eq. (1)), which is obtained from combining dissimilarity functions and fuzzy equivalencies. Based on Eq. (1), we obtain two computational formulae for similarity measures on IFSs. The first one is obtained by aggregating Eq. (1). The second one is obtained by respectively aggregating the numerator and the denominator of Eq. (1). We also examine some properties of the proposed similarity measures on IFSs. Finally, we make a comparison between the proposed similarity measures on IFSs and those existing ones in the literature through several counter-intuitive cases. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of an interval-valued fuzzy equivalence as an interval extension of the fuzzy equivalence. The partial orders between fuzzy equivalencies are studied. Three ways of constructing interval-valued fuzzy equivalencies from given fuzzy equivalencies and aggregation functions are provided. Some examples of interval-valued fuzzy equivalencies built by the proposed constructive methods are shown. The properties and structures of interval-valued fuzzy equivalencies are also studied. [ABSTRACT FROM AUTHOR]

In fuzzy neural networks, it is usual to perform rule matching by employing fuzzy similarity measures. A fuzzy similarity measure is reserved for a binary fuzzy relation. In fuzzy relational calculus, the notion of T -transitivity is indispensable because it is strongly related to the concept of a metric. In this study, we consider whether the two types of fuzzy similarity measures given by Li et al. (2014) [24] satisfy T L -transitivity. We also investigate the T L -transitivity of fuzzy equivalencies. [ABSTRACT FROM AUTHOR]

A similarity-based approximate reasoning methodology that requires the construction of fuzzy relations was proposed by Raha et al. [26] . This paper investigates properties of four inferred conclusions calculated by Raha's similarity-based approximate reasoning method. The relationships among the four inferred conclusions are examined. The monotonicity and the approximation property for similarity-based approximate reasoning methods are defined. Then the monotonicity and the approximation property of Raha's similarity-based approximate reasoning method are studied. [ABSTRACT FROM AUTHOR]