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On the Operation ∆ over Intuitionistic Fuzzy Sets

Author

Listed:
  • Lilija Atanassova

    (Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 2, 1113 Sofia, Bulgaria
    These authors contributed equally to this work.)

  • Piotr Dworniczak

    (The Great Poland University of Social and Economics, ul. Surzyńskich 2, 63-000 Środa Wielkopolska, Poland
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Lilija Atanassova & Piotr Dworniczak, 2021. "On the Operation ∆ over Intuitionistic Fuzzy Sets," Mathematics, MDPI, vol. 9(13), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1518-:d:584401
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