JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (1): 45-62.doi: 10.6040/j.issn.1671-9352.4.2023.0250

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Study on subtraction and division operations over picture fuzzy sets

MENG Weiwei, ZHENG Tingting*, LIU Junge, WU Xiaoyu   

  1. School of Mathematical Sciences, Anhui University, Hefei 230601, Anhui, China
  • Published:2025-01-10

Abstract: Aiming at the problem of the complete subtraction and division problems under picture fuzzy environments, the subtraction and division operations of PFNs(picture fuzzy numbers, PFNs)are defined by constructing equations for addition and multiplication. Based on the nearest distances, the optimal solution of the equation is derived in various situations, and more complete subtraction and division operation algorithms are obtained. The properties of the two newly defined operators and the mixed operation of addition and multiplication are analyzed in detail. The two improved operators are extended in a pointwise manner to the picture fuzzy set, and the essential properties are discussed. The applicability and feasibility of this operator is verified through numerical analysis.

Key words: picture fuzzy set, linear programming, subtraction operation, division operation, pattern recognition

CLC Number: 

  • TP391
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