Type 2 fuzzy multisets and its applications in decision making problems

Article type: Research Article

Authors: Paul, Jaya^* | John, Sunil Jacob

Affiliations: Department of Mathematics, National Institute of Technology, Calicut, India

Correspondence: [*] Corresponding author. Jaya Paul, Department of Mathematics, National Institute of Technology, Calicut 673 601, India. Tel.: 9447822023; E-mail: [email protected].

Abstract: The purpose of this paper is to introduce the concept of type 2 fuzzy multiset by integrating the type 2 fuzzy set and multiset models. Basic set operations of union, intersection and complement are extended to type 2 fuzzy multisets and made a comparative study on various set theoretic laws satisfied by these operations with set theoretic operations on type 1 and type 2 fuzzy sets. The notion of (α, λ) cut set is defined and some properties of cut sets are studied. Furthermore, we investigate the decision making based on type 2 fuzzy multisets. By means of (α, λ) cut sets, we propose an adjustable approach to type 2 fuzzy multiset based decision making. Moreover, we introduce the weighted type 2 fuzzy multiset and examine its application to decision making. Finally, by means of some illustrative examples we show the validity of type 2 fuzzy multiset, weighted type 2 fuzzy multiset in decision making problems.

Keywords: Type 2 fuzzy multisets, cut fuzzy sets, choice value, weighted type 2 fuzzy multiset

DOI: 10.3233/IFS-151761

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 1, pp. 359-369, 2016