Atanassov’s intuitionistic fuzzy measure based on the Sugeno integral induced by (α, β)-cut

Atanassov's intuitionistic fuzzy sets (A-IFSs) are used to deal with that information, which is incomplete as well as imprecise. In this paper, we defined a similarity measure by using Sugeno integral and technique of (α, β)-cut. Hwang et al. [Hwang, Chao-Ming, et al. "A similarity measure of intuitionistic fuzzy sets based on the Sugeno integral with its application to pattern recognition." Information Sciences 189 (2012): 93-109.] defined Sugeno integral based similarity measure for the first time. But, in Hwang et al.'s similarity measure, only α-cut is utilized that neglected the contribution of non-membership function. The non-membership function plays an equal role in the A-IFS theory. Therefore, we proposed the Sugeno integral based similarity measure concerning both the (α, β)-cuts. We added one artificial constructed example to show that our proposal is different than to similarity measure defined by Hwang et al. Moreover, we added some more benchmark examples to show the efficacy of the proposed similarity measure.

I. Introduction

Zadeh in [1], introduced the basic structure of fuzzy sets (FSs) in 1965 to deal with that information, which involves uncertainty. Henceforth, a variety of higher-order of FSs, for example, Interval-valued fuzzy sets [5], Type-2 fuzzy sets [1], Atanassov intuitionistic fuzzy sets [2], Vague sets [6] etc. have been proposed by the different researcher to generalized the conventional FSs. Atanassov intuitionistic fuzzy sets (A-IFSs); initially has been extended by Atanassov [2] in 1986, which is a popular extension of the FS theory, used to describe objective reality more realistically and precisely.