Comparison Between Fuzzy Number Sequences via Interactive Arithmetic J0 and Standard Arithmetic

Subject Areas : Transactions on Fuzzy Sets and Systems

Vinı`cius Francisco Wasques ^{1 *} , Nilmara de Jesus Biscaia Pinto ²

1 - Ilum School of Science, Brazilian Center for Research in Energy and Materials, Campinas, Brazil.
2 - Faculty of Applied Sciences, University of Campinas, Limeira, Brazil.

Received: 2024-10-31 Accepted : 2025-01-28 Published : 2025-02-13

Keywords: Interactive fuzzy numbers, Fuzzy number sequence, Fuzzy discrete equations, Sup-J extension principle.,

Abstract :

The focus of this work is to study sequences of interactive fuzzy numbers. The interactivity relation is associated with the concept of joint possibility distribution. In this case, the type of interactivity studied is linked to a family of joint possibility distributions (Jγ), in which the parameter γ intrinsically models levels of interactivity between the fuzzy numbers involved. Each element of the sequence of interactive fuzzy numbers is obtained through a discrete equation, and the arithmetic operations present in the equation are extended to this type of fuzzy number. Some simulations are performed to illustrate the behavior of the sequences, called interactive, and to compare them with the sequences obtained by other fuzzy arithmetic operations.

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