Calculation of centroid of high dimensional fuzzy number and application

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WANG G.; XU Y.

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Journal Paper

Paper Information

Journal: Iranian Journal of Fuzzy Systems Year:2021 | Volume:18 | Issue:6 Page(s): 29-44

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Information Journal Paper

Title

Calculation of centroid of high dimensional fuzzy number and application

Author(s)

WANG G. | XU Y. | Issue Writer Certificate

Keywords

Fuzzy numberQ2

fuzzy n−cell numberQ2

fuzzy n−ellipsoid numberQ2

centroid of high dimensional fuzzy numberQ2

fuzzy orderQ2

Abstract

In this paper, the conception of centroid of n-dimensional Fuzzy number is introduced via regarding its membership function as the density function on its support set, and some properties of it are obtained. Compared with the mean of the multi dimensional Fuzzy number, the centroid takes into account the overall relationship between the edge membership functions of the membership function of the multi dimensional Fuzzy number. Therefore, it can approximate (characterize) the Fuzzy number more objectively and reasonably than using the mean of the multi dimensional Fuzzy number. The most important work of this paper is that for two special kinds of multi dimensional Fuzzy numbers (fuzzy n-cell numbers and fuzzy n-ellipsoid numbers), we respectively give calculation formulas, which can be used conveniently in application since the formulas are based on a definite integral of the level set functions of the multi dimensional Fuzzy number on the unit interval [0; 1], rather than the multiple integral of the membership function of the multi dimensional Fuzzy number itself on its support set. Then, by using the calculation formulas, we obtain another special property of the centroid for fuzzy n-cell number and fuzzy n-ellipsoid number. Finally, as an example of application, by using the centroid of multi dimensional Fuzzy number, we define a fuzzy order on n-dimensional Fuzzy number space, which can be used to rank uncertain or imprecise multichannel digital information.

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APA: Copy

WANG, G., & XU, Y.. (2021). Calculation of centroid of high dimensional fuzzy number and application. IRANIAN JOURNAL OF FUZZY SYSTEMS, 18(6 ), 29-44. SID. https://sid.ir/paper/412590/en

Vancouver: Copy

WANG G., XU Y.. Calculation of centroid of high dimensional fuzzy number and application. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2021;18(6 ):29-44. Available from: https://sid.ir/paper/412590/en

IEEE: Copy

G. WANG, and Y. XU, “Calculation of centroid of high dimensional fuzzy number and application,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 18, no. 6 , pp. 29–44, 2021, [Online]. Available: https://sid.ir/paper/412590/en

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