Abstract
Decision making under uncertainty describes situations that consider a profound lack of knowledge, where the functional form is completely unknown, and often, the relevant input and output variables are unknown as well. Data, being the vital input of decision making, contain a dissimilar level of imprecision that necessitates different approaches for making a proper and legitimate decision. In this article, we propose the concept of the intuitionistic type-2 fuzzy set (IT2FS). Several arithmetic operations on IT2FS such as union, intersection, complement, containment, etc., are defined, and the related algebraic properties of IT2FS are also studied. Subsequently, we define two new operators, namely the necessity operator and the possibility operator, to convert an IT2FS into an ordinary T2FS, and then discuss some of their basic properties. Moreover, in this study, two distance measures, the Hamming distance and Euclidian distance of IT2FS, are proposed, and their applications are illustrated with an example.
Highlights
Uncertainty is an intrinsic feature of information
In spite of the existing works on interval type-2 intuitionistic fuzzy sets, in the literature, to the best of our knowledge, there does not exist any study on generalized the intuitionistic type-2 fuzzy set. To circumvent this gap in the literature, in this study, we introduce the concept of the generalized intuitionistic type-2 fuzzy set (IT2FS) whose type-1 membership is the ordinary fuzzy membership, and the resulting type-2 consists of both membership and non-membership as the intuitionistic fuzzy set
We present the following example to illustrate the properties of IT2FS as mentioned below
Summary
Uncertainty is an intrinsic feature of information. In many scientific and industrial applications, we make decisions in an environment with different kinds of uncertainty. Marasini et al [10] presented a study, where the intuitionistic fuzzy set was used for questionnaire analysis, with a focus on the construction of membership, non-membership, and uncertainty functions. Many researchers did many investigations on theoretical [26,27,28,29], as well as on various application domains [30,31,32,33,34] of T2FS Considering both intuitionistic fuzzy and type-2 fuzzy environments, Singh and Garg [35].
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