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

Document Type : Research Article

Author

• S.M. Alavi

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

10.22067/ijnao.2023.79051.1187

Abstract

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.

Keywords

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

20.1001.1.24236977.2023.13.3.9.4

Main Subjects

• Numerical linear algebra and its applications

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