关于梯形模糊数排序的新方法  

A New Method for Sorting Trapezoidal Fuzzy Numbers

作　　者：刘万里 刘艺 LIU Wani;LIU Yi(School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450046,China;Basic Teaching Department,Zhengzhou Urban Construction Vocational College,Zhengzhou 452100,China)

机构地区：[1]郑州航空工业管理学院数学学院,河南郑州450046 [2]郑州城建职业学院基础教学部,河南郑州452100

出　　处：《郑州航空工业管理学院学报》2024年第4期106-112,共7页Journal of Zhengzhou University of Aeronautics

基　　金：河南省重点研发与推广专项(212102210552)。

摘　　要：关于模糊数排序的问题一直是模糊决策研究的热点。随着研究的深入,研究对象由区间模糊数发展到三角模糊数,进而又发展到梯形模糊数。文章提出一种新的梯形模糊数排序方法,该方法是基于两个梯形模糊数减法法则,通过定积分的运算给出可能度的概念,再利用可能度大小和布尔矩阵法对多个模糊数进行排序。最后通过算例显示该方法的可行性,并通过与近期文献的方法比较,显示其有效性和优效性。研究结果表明,该方法不仅能够比较不同类型的模糊数次序,而且计算简单、区分度强,所以应用范围广泛。The issue of the size of fuzzy numbers has always been a hot research topic.With the deepening of re-search,fuzzy numbers have evolved from interval numbers to triangular fuzzy numbers,and then to trapezoidal fuzzy numbers.This article proposes a new trapezoidal fuzzy number sorting method.This method is based on two trapezoi-dal fuzzy number subtraction rules,which provide the concept of possibility degree through definite integral opera-tion,and use the size of possibility degree and Boolean matrix method to sort multiple fuzzy numbers.The feasibility of this method is demonstrated through a numerical example,and its effectiveness and superiority are demonstrated through comparison with the recent literature method.This method can not only compare the order of different types of fuzzy numbers,but also has simple calculation,strong discriminative power,and broad application prospects.

关 键 词：梯形模糊数 可能度 布尔矩阵 排序 

分 类 号：O223[理学—运筹学与控制论] C159[理学—数学]