Fuzzy sets (FSs) are an important tool to model uncertainty and vagueness. Entropy is being used measure the fuzziness within a fuzzy set (FS). These entropies find multicriteria decision-making. For measuring with TOPSIS techniques axiomatic definition of entropy for also given in this paper. The proposed provided satisfy all axioms. Several numerical examples presented compare existing entrop...

In the present communication, the existing measures of fuzzy entropy are reviewed. A generalized parametric exponential fuzzy entropy is defined.Our study of the four essential and some other properties of the proposed measure, clearly establishes the validity of the measure as an entropy. Keywords—fuzzy sets, fuzzy entropy, exponential entropy, exponential fuzzy entropy.

Given a fuzzy variable, what is the degree of difficulty of predicting the specified value that the fuzzy variable will take? Entropy provides a measure to characterize the fuzziness. Given some constraints, there are usually multiple compatible membership functions. Which membership function shall we take? The maximum entropy principle attempts to select the membership function that maximizes ...

Study about fuzzy entropy and similarity measure on intuitionistic fuzzy sets (IFSs) were proposed, and analyzed. Unlike fuzzy set, IFSs contains uncertainty named hesistancy, which is contained in fuzzy membership function itself. Hence, designing fuzzy entropy is not easy because of ununified entropy definition. By considering different fuzzy entropy definitions, fuzzy entropy is designed and...

fuzzy decision tree (fdt) classifiers combine decision trees with approximate reasoning offered by fuzzy representation to deal with language and measurement uncertainties. when a fdt induction algorithm utilizes stopping criteria for early stopping of the tree's growth, threshold values of stopping criteria will control the number of nodes. finding a proper threshold value for a stopping crite...

This paper denes and investigates the ergodic proper-ties of the entropy of a countable partition of a fuzzy dynamical sys-tem at different points of the state space. It ultimately introducesthe local fuzzy entropy of a fuzzy dynamical system and proves itto be an isomorphism invariant.

In the present paper, based on the concept of fuzzy entropy, an exponential intuitionistic fuzzy entropy measure is proposed in the setting of Atanassov’s intuitionistic fuzzy set theory. This measure is a generalized version of exponential fuzzy entropy proposed by Pal and Pal. A connection between exponential fuzzy entropy and exponential intuitionistic fuzzy entropy is also established. Some...

A fuzzy rough granular self-organizingmap (FRGSOM) involving a 3-dimensional linguistic vector and connection weights, defined in an unsupervised manner, is proposed for clustering patterns having overlapping regions. Each feature of a pattern is transformed into a 3-dimensional granular space using a π-membership function with centers and scaling factors corresponding to the linguistic terms l...

Fuzzy set theory which is a powerful tool for handling vague situations has advanced in a variety of ways and in many disciplines. Applications of this theory can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition and robotics. There have been a variety of fuzzy measures...