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

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Alavi S.M.

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Journal Paper

Paper Information

Journal: IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION Year:2023 | Volume:13 | Issue:3 Page(s): 532-552

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Information Journal Paper

Title

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

Author(s)

Alavi S.M. | Issue Writer Certificate

Keywords

Fuzzy Number of type L-R

Nearest Trapezoidal Fuzzy Number

Shape Function

Fuzzy approximation

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.

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