Abstract
In a real-life scenario, it is undoable and unmanageable to solve a decision-making problem with the single stand-alone decision-aid method, expert assessment methodology or deterministic approaches. Such problems are often based on the suggestions or feedback of several experts. Usually, the feedback of these experts are heterogeneous imperfect information collected from various more or less reliable sources. In this paper, we introduce the concept of multi-sets over type-2 fuzzy sets. We have tried to propose an extension of type-1 multi-fuzzy sets into a type-2 multi-fuzzy set (T2MFS). After defining T2MFS, we discuss the algebraic properties of these sets including set-theoretic operations such as complement, union, intersection, and others with examples. Subsequently, we define two distance measures over these sets and illustrate a decision-making problem which uses the idea of type-2 multi-fuzzy sets. Furthermore, an application of a medical diagnosis system based on multi-criteria decision making of T2MFS is illustrated with a real-life case study.
Highlights
According to Cantor, a set is a well-defined collection of distinct objects, but let us see what happens if we consider a collection of objects where one or some or all objects occur more than once
Afterwards, Yager [2] proposed a new and more generalized concept of multi-sets named as multi-fuzzy sets (MFS) which can deal with many real life problems with some degree of ease
We have tried to extend the concept of multi-fuzzy set theory to type-2 multi-fuzzy sets
Summary
According to Cantor, a set is a well-defined collection of distinct objects, but let us see what happens if we consider a collection of objects where one or some or all objects occur more than once. There are various mathematical tools such as fuzzy sets, rough sets, multi-sets, multi-fuzzy sets, intuitionistic fuzzy sets, and type-2 fuzzy sets to deal with uncertainties [22,23,24], there might be some physical problems where the primary membership function may have more than one secondary membership grade with the same or different values In those particular cases, the existing mathematical tools might not be adequate. Type-2 multi-fuzzy sets are supposedly a new approach which will be an extension of the existing concepts and shall be helpful to deal with problems related to uncertainties.
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