As Similarity measure for fuzzy sets is one of the important research topics of fuzzy set theory, there are several methods to measure similarity between two fuzzy sets (FS), Intuitionistic fuzzy sets (IFS) and Intuitionistic fuzzy multi sets (IFMS). In this paper, the Normalized Hamming Similarity measure of Intuitionistic Fuzzy Multi sets (IFMS) is introduced. This new measure for IFMS is bas...

Abstract We show that recurrence conditions do not yield invariant Borel probability measures in the descriptive set-theoretic milieu, strong sense if a action of locally compact Polish group on standard space satisfies such condition but does have an orbit supporting measure, then there is set which measure.

We propose a new measure for analyzing the structural similarities among the cognitive maps of different decision makers. Upon interpreting the cognitive response elicitation process in the general framework of fuzzy set theory, we are able to develop the similarity measure from straightforward operations on fuzzy relational products. In addition to the mathematical analysis, we present visual ...

In this paper, we present two new methods for evaluating students’ answerscripts based on the similarity measure between vague sets. The vague marks awarded to the answers in the students’ answerscripts are represented by vague sets, where each element ui in the universe of discourse U belonging to a vague set is represented by a vague value. The grade of membership of ui in the vague set à is ...

In this paper, new similarity, inclusion measure and entropy between type-2 fuzzy sets corresponding to grades of memberships are proposed. We also create the relationships among these measures between type-2 fuzzy sets. Several examples are used to present the calculation of these similarity, inclusion measure and entropy between type-2 fuzzy sets. The comparison results show that the proposed...

We investigate measure-theoretic aspects of various notions of reducibility by applying analogs of Demuth’s Theorem in the hyperarithmetic and set-theoretic settings.

We study the problem of defining similarity measures on preferences from a decisiontheoretic point of view. We propose a similarity measure, called probabilistic distance, that originates from the Kendall’s tau function, a well-known concept in the statistical literature. We compare this measure to other existing similarity measures on preferences. The key advantage of this measure is its exten...