毕达哥拉斯三角模糊数集成算子及其决策应用  

Pythagorean Triangular Fuzzy Numbers Aggregation Operators and Application to Decision Making

作　　者：何霞[1] 刘卫锋[1] 杜迎雪[1] HE Xia;LIU Wei-feng;DU Ying-xue(School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450015,China)

机构地区：[1]郑州航空工业管理学院数学学院,河南郑州450015

出　　处：《模糊系统与数学》2019年第2期128-138,共11页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金青年科学基金资助项目(11501525);航空科学基金资助项目(2016ZG55019);河南省高等学校重点科研项目(18A110032);郑州航院青年科研基金资助项目(2016113001)

摘　　要：将毕达哥拉斯模糊数与三角模糊数相结合,提出了毕达哥拉斯三角模糊数的概念,定义了其运算,研究了其运算规律,推广了直觉三角模糊数和毕达哥拉斯模糊数,并通过定义毕达哥拉斯三角模糊数的得分函数和精确函数,实现毕达哥拉斯三角模糊数的排序。然后,定义了毕达哥拉斯三角模糊数加权平均算子(PTFWA)和有序加权平均算子(PTFOWA)、毕达哥拉斯三角模糊数加权几何算子(PTFWG)和有序加权几何算子(PTFOWG)以及毕达哥拉斯三角模糊数混合平均算子(PTFHA)和混合几何算子(PTFHG),研究了它们的性质,并给出其计算公式。最后,提出了基于毕达哥拉斯三角模糊集成算子的决策方法,通过实例说明了其可行性。The concept of Pythagorean triangular fuzzy number (PTFN) is defined, which is one of the extensions of intuitionistic triangular fuzzy number and Pythagorean fuzzy number, and the operation of PTFN are introduced and the operations laws of PTFN are discussed. The concepts of the score and accuracy functions of PTFN are developed and a ranking method of comparing the magnitude of PTFNs is introduced. Then, Pythagorean triangular fuzzy numbers weighted averaging operator (PTFWA), Pythagorean triangular fuzzy numbers ordered weighted averaging operator (PTFOWA), Pythagorean triangular fuzzy numbers weighted geometric operator(PTFWG), Pythagorean triangular fuzzy numbers ordered weighted geometric operator ( PTFOWG ) and Pythagorean triangular fuzzy numbers hybrid averaging operator ( PTFHA), Pythagorean triangular fuzzy numbers hybrid geometric operator (PTFHG) are defined, and their natures of these operators are discussed, and the mathematical expressions of these operators are obtained by derivation. Lastly, an approach for decision making with Pythagorean triangular fuzzy aggregation operators is developed, and a practical example is provided to illustrate the practicality of the developed method.

关 键 词：毕达哥拉斯模糊集 毕达哥拉斯三角模糊数 集成算子 决策 

分 类 号：C934[经济管理—管理学] O223[理学—运筹学与控制论]