Abstract
Recently, the new operation ∆ was introduced over intuitionistic fuzzy sets and some of its properties were studied. Here, new additional properties of this operations are formulated and checked, providing an analogue to the De Morgan’s Law (Theorem 1), an analogue of the Fixed Point Theorem (Theorem 2), the connections between the operation ∆ on one hand and the classical modal operators over IFS Necessity and Possibility, on the other (Theorems 3 and 4). It is shown that it can be used for a de-i-fuzzification. A geometrical interpretation of the process of constructing the operator ∆ is given.
Highlights
Intuitionistic Fuzzy Sets (IFS) were introduced in 1983 in [1] as extensions of L
The present paper is devoted to the new operation 4 introduced over IFSs in [5], where some of its properties were studied
It is shown that the new operation is useful for realization of the de-i-fuzzification procedure, discussed in [6], which aims to provide a tool for transformation of a given IFS to a fuzzy set by analogy with the existing procedures for de-fuzzification in fuzzy sets theory that transform a fuzzy set to a crisp set
Summary
Intuitionistic Fuzzy Sets (IFS) were introduced in 1983 in [1] as extensions of L. In [3,4], a lot of operations, relations, and operators are introduced over IFSs (see [3,4]) and their properties are studied. IFSs are one of the most useful type of fuzzy sets. As it is mentioned in [4], it is important to search new operations over IFS and to search for real applications for them. The present paper is devoted to the new operation 4 introduced over IFSs in [5], where some of its properties were studied.
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