An assignment model based on similarity measures of intuitionistic fuzzy sets

• Author: Lixandroiu D.
• Pages: 429-436

Bulletin of the Transilvania University of Braşov

Series V: Economic Sciences • Vol. 9 (58) No. 2 - 2016

An assignment model based on similarity

measures of intuitionistic fuzzy sets

Dorin LIXNDROIU1

Abstract: First, this paper presents some distance and similarity measures of intuitionistic

fuzzy sets. These similarity measures can be applied in models of multi-attribute decision.

We propose an assignment model based on similarity measures of intuitionistic fuzzy sets,

where the elements of sets are weighted. A numerical example is also given.

Key-words: Intuitionistic fuzzy sets, similarity measures, Distance measures, Assignment

model

1. Introduction

The notion of intuitionistic fuzzy sets (IFS), introduced by Atanasov (1986),

generalized the concept of fuzzy sets (FS) introduced by Zadeh (1965). The

measures of distance and similarity are used to estimate the degree of closeness

between two sets. In the models of multi-attribute decision, the distance and the

similarity between two IFS is very important (Lixndroiu and Lixndroiu, 2013).

Szmidt and Kacprzyk (2000), Hung and Yang (2004, 2008) show several

measures for the distance between two IFS and the way the associated similarity

measure is constructed. Li Qin and Olson (2007) make a comparative analysis of

different defined measures of similarity between two IFS. Xu (2007) develop some

similarity measures of IFS and define the notions of positive ideal IFS and negative

ideal IFS. These similarity measures are applied to multiple attribute decision

making based on intuitionistic fuzzy information.

This article presents some measures for the distance between two IFS and

the possibility of obtaining similarity measures. It is known that the two concepts of

distance and similarity are dual concepts.

In Ejegwa, Akubo, Joshua (2014) a model of allocation is built based on the

distance between two IFS, in which the elements have the same importance.

In this article, based on the measure of similarity between two IFS, which also

considers the weights of the elements, we build a weighted allocation model.

1 Transilvania University of Braşov, lixi.d@unitbv.ro