Entropy of Dynamical Systems on Interval-Valued Intuitionistic Fuzzy Sets

Abstract

In this work, we introduce the concepts of Shannon entropy and conditional entropy of experiments in the interval-valued intuitionistic fuzzy case, and study the basic properties of the information measures. Subsequently, by means of the suggested notion of entropy of partitions, we define the entropy of a dynamical system on interval-valued intuitionistic fuzzy sets (IVIF). A version of the Kolmogorov–Sinai theorem on generators for dynamical systems on the IVIF is proved. It is shown that this entropy is an invariant under isomorphisms of interval-valued intuitionistic fuzzy dynamical systems; thus, we obtain a tool for distinguishing some non-isomorphic interval-valued intuitionistic fuzzy dynamical systems. The proposed measure can be used as a measure of information of experiment whose outcomes are interval-valued intuitionistic fuzzy events.