On the Operation ∆ over Intuitionistic Fuzzy Sets

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 (Theore...

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Bibliographic Details
Main Authors: Lilija Atanassova, Piotr Dworniczak
Format: Article
Language:English
Published: MDPI AG 2021-06-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/9/13/1518
Description
Summary: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.
ISSN:2227-7390