Type-2 Multi-Fuzzy Sets and Their Applications in Decision Making

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.