On the Operation ? over Intuitionistic Fuzzy Sets

Lilija Atanassova and Piotr Dworniczak
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Lilija Atanassova: Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 2, 1113 Sofia, Bulgaria
Piotr Dworniczak: The Great Poland University of Social and Economics, ul. Surzyńskich 2, 63-000 Środa Wielkopolska, Poland

Mathematics, 2021, vol. 9, issue 13, 1-11

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.

Keywords: intuitionistic fuzzy operation; intuitionistic fuzzy operator; intuitionistic fuzzy set (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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