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Symmetry 2019, 11(2), 170; https://doi.org/10.3390/sym11020170

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

1
Department of Computer Science, Heritage Institute of Technology, Kolkata 700107, India
2
Department of Mathematics, National Institute of Technology, Durgapur 713209, India
3
Department of Computer Science and Engineering, National Institute of Technology, Durgapur 713209, India
4
Department of Logistics, University of Defence in Belgrade Military Academy, 11000 Belgrade, Serbia
*
Author to whom correspondence should be addressed.
Received: 30 December 2018 / Revised: 22 January 2019 / Accepted: 28 January 2019 / Published: 1 February 2019
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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. View Full-Text
Keywords: Multi-fuzzy sets; type-2 fuzzy sets; type-2 multi-fuzzy sets; distance measures; set operations Multi-fuzzy sets; type-2 fuzzy sets; type-2 multi-fuzzy sets; distance measures; set operations
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Kar, M.B.; Roy, B.; Kar, S.; Majumder, S.; Pamucar, D. Type-2 Multi-Fuzzy Sets and Their Applications in Decision Making. Symmetry 2019, 11, 170.

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