Scalarization of Type-1 Fuzzy Markov Chains

Abstract

This paper presents a method to transform Fuzzy Markov chains into Crisp Markov chains by means of an equivalence matrix derived from the concept of Scalar cardinality of a fuzzy set. This proposal is a linear transformation of the fuzzy space into a probability space.

In this paper, a finite-state Fuzzy Markov Chain is transformed into a crisp Markov chain by a linear operator. It is a projection of the fuzzy space into a probability space which allows to compare them one another.