On the structural properties for the cross product of fuzzy numbers with applications

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Alikhani Robab

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Journal Paper

Paper Information

Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2020 | Volume:6 | Issue:23 Page(s): 95-109

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Title

On the structural properties for the cross product of fuzzy numbers with applications

Author(s)

Alikhani Robab | Issue Writer Certificate

Keywords

Cross product

Triangular fuzzy number

Fuzzy variable coefficients

Generalized differentiability

Linear fuzzy differential equations

Abstract

In the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’ s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. The main advantage is that this product preserves the shape of triangular or trapezoidal fuzzy numbers under multiplication and from computational point of view the Cross product is more applicable than the usual product. The above mentioned properties motivate us to use the Cross product in applications as a possible alternative of the product obtained by Zadeh's extension Principle. The aim of the present paper is to give an explicit formula for the Cross product of Triangular fuzzy numbers based on the scalar product of fuzzy numbers and then, explicit formulas for the length of Cross product of Triangular fuzzy numbers and fuzzy derivative of Cross product of triangular fuzzy functions. As an application, we apply the Cross product concept for the first order Linear fuzzy differential equations with Fuzzy variable coefficients and obtain its triangular solutions under Generalized differentiability. Finally, some examples are given to illustrate the theoretical results.

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APA: Copy

Alikhani, Robab. (2020). On the structural properties for the cross product of fuzzy numbers with applications. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 6(23 ), 95-109. SID. https://sid.ir/paper/951819/en

Vancouver: Copy

Alikhani Robab. On the structural properties for the cross product of fuzzy numbers with applications. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2020;6(23 ):95-109. Available from: https://sid.ir/paper/951819/en

IEEE: Copy

Robab Alikhani, “On the structural properties for the cross product of fuzzy numbers with applications,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 6, no. 23 , pp. 95–109, 2020, [Online]. Available: https://sid.ir/paper/951819/en

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