Published : 2023-12-29

VECTORIAL MODEL OF ORDERED FUZZY NUMBERS (vOFN)

Abstract

In the article, the authors set themselves the task of redefining the Ordered Fuzzy Numbers calculus introduced by Witold Kosiński. The last decade of research contributed to the presented considerations. during which the authors often had to refute the accusations made by some researchers against this system of calculations on fuzzy numbers. Therefore, the article redefined the number of OFNs from a functional approach to a vector approach, creating vOFN (Vectorial Ordered Fuzzy Numbers). The authors presented a solution to the so-called incorrect OFN numbers, i.e. numbers with non-convex shapes. They solved the problem of comparing OFN numbers unsolved by Kosiński. They also eliminated the feature, which is incomprehensible to many researchers, of the increase in the degree of the polynomial functions of the rising and falling edges, which took place when performing the operations of the product and quotient of OFN numbers, which resulted in curvilinear graphs of the functions of these edges. Thanks to the redefinition, all the positive properties of OFN are preserved and the disadvantages are eliminated. The authors believe that thanks to the vOFN approach, this arithmetic will find even more applications as it is simple, reliable, unambiguous and extremely easy to implement.

Keywords:

fuzzy logic, fuzzy sets, OFN, vOFN



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Czerniak, J., Żak, A., & Marciniak, B. (2023). VECTORIAL MODEL OF ORDERED FUZZY NUMBERS (vOFN). Fides, Ratio Et Patria. Studia Toruńskie, (19), 272–296. https://doi.org/10.56583/frp.2559

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Akademia Zamojska
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fax 84 638 35 00
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