Interval type-2 Fuzzy Markov Chains: An approach

Abstract

This paper introduces a new proposal to involve uncertainties in Fuzzy Markov Chains by using Interval Type-2 Fuzzy Sets (IT2 FS). A Type-1 Fuzzy Markov chain is an approach which uses Type-1 Fuzzy Sets (T1 FS) to describe the distributional behavior of a Discrete-Time Markov process, while the IT2 FS approach is an extension of its scope that allows to embed several T1 FS inside its Footprint of Uncertainty. In this paper, a finite state Fuzzy Markov Chain process is defined by an Interval Type-2 Fuzzy environment, finding their limiting properties and its Type-reduced behavior. To do so, two examples are provided.