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Fuzzy Sets, Intuitionistic Fuzzy Sets: Separation of Generalized Interval-Valued Intuitionistic Fuzzy Sets

Monoranjan Bhowmik (Vidyasagar Teacher's Training College, India) and Madhumangal Pal (Vidyasagar University, India)

Source Title: Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices

DOI: 10.4018/978-1-5225-0914-1.ch001

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Abstract

In this chapter, we define four separations of generalized interval-valued intuitionistic fuzzy sets (GIVIFSs). In fact, all interval-valued Intuitionistic fuzzy sets (IVIFSs) are GIVIFSs but all GIVIFSs are not IVIFSs. Also, we studied some properties of the four separated subsets of GIVIFSs.

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Some Definitions And Properties

We present two fundamental operators ∨ and ∧ defined over fuzzy sets below:

On the interval [0,1] (where the fuzzy sets takes their elements) the following operations are defined for all x, y∈ [0,1]:

1.
x∨y = max (x, y),
2.
x∧y = min (x, y).

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Fuzzy Sets, Intuitionistic Fuzzy Sets: Separation of Generalized Interval-Valued Intuitionistic Fuzzy Sets

Abstract

Some Definitions And Properties

Complete Chapter List