Nearest fuzzy number of type L-R to an arbitrary fuzzy number with applications to fuzzy linear system

Iranian Journal of Numerical Analysis and Optimization

مقاله 9، دوره 13، شماره 3 - شماره پیاپی 26، آذر 2023، صفحه 532-552   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.79051.1187

نویسنده

S.M. Alavi^*

Department of Mathematics, Faculty of Basic Sciences, Arak Branch, Islamic Azad University, Arak, Iran.

چکیده

The fuzzy operations on fuzzy numbers of type L-R are much easier than general fuzzy numbers. It would be interesting to approximate a fuzzy number by a fuzzy number of type L-R. In this paper, we state and prove two significant application inequalities in the monotonic functions set. These inequalities show that under a condition, the nearest fuzzy number of type L-R to an arbitrary fuzzy number exists and is unique. After that, the nearest fuzzy number of type L-R can be obtained by solving a linear system. Note that the trapezoidal fuzzy numbers are a particular case of the fuzzy numbers of type L-R. The proposed method can represent the nearest trapezoidal fuzzy number to a given fuzzy number. Finally, to approximate fuzzy solutions of a fuzzy linear system, we apply our idea to construct a framework to find solutions of crisp linear systems instead of the fuzzy linear system. The crisp linear systems give the nearest fuzzy numbers of type L-R to fuzzy solutions of a fuzzy linear system. The proposed method is illustrated with some examples.

کلیدواژه‌ها

Fuzzy number of type L-R؛ Nearest trapezoidal fuzzy number؛ Shape function؛ Fuzzy approximation

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