On Generalized Fuzzy Multisets and their Use in Computation

TL;DR

This paper introduces generalized fuzzy multisets and hybrid sets, exploring their properties and applications in computational models like fuzzy P systems, advancing the theoretical foundation of fuzzy set theory in computation.

Contribution

It presents a new framework for L-multi-fuzzy and L-fuzzy hybrid sets and extends fuzzy P systems, offering a unified approach to fuzzy multiset processing in computation.

Findings

Defined L-multi-fuzzy and L-fuzzy hybrid sets with their properties

Extended fuzzy P systems to incorporate these new structures

Demonstrated the usefulness of these structures in mechanical multiset processing

Abstract

An orthogonal approach to the fuzzification of both multisets and hybrid sets is presented. In particular, we introduce L-multi-fuzzy and L-fuzzy hybrid sets, which are general enough and in spirit with the basic concepts of fuzzy set theory. In addition, we study the properties of these structures. Also, the usefulness of these structures is examined in the framework of mechanical multiset processing. More specifically, we introduce a variant of fuzzy P systems and, since simple fuzzy membrane systems have been introduced elsewhere, we simply extend previously stated results and ideas.