直觉梯形模糊语言Frank算子及其在决策中的应用

doi:10.12005/orms.2018.0081

运筹与管理 ›› 2018, Vol. 27 ›› Issue (4): 29-34.DOI: 10.12005/orms.2018.0081

直觉梯形模糊语言Frank算子及其在决策中的应用

翟玉冰¹, 侯福均¹, 杜玉琴², 于倩³

1.北京理工大学管理与经济学院,北京 100081;
2.中国社会科学院大学经济学院,北京 102488;
3.重庆科技学院工商管理学院,重庆 401331

收稿日期:2017-04-14 出版日期:2018-04-25
作者简介:翟玉冰(1989-),女,河南濮阳人,博士研究生,研究方向:多属性决策,收益管理;侯福均(1967-),男,河北三河人,副教授,博士生导师,研究方向:决策理论与方法,运筹与优化,不确定理论及应用。
基金资助:
国家自然科学基金资助项目(71571019)

Intuitionistic Trapezoidal Fuzzy Linguistic Frank Operator andIts Application in Decision Making

ZHAI Yu-bing¹, HOU Fu-jun¹, DU Yu-qin²,YU qian³

1.Beijing Institute of Technology, School of Management and Economics, Beijing, 100081, China;
2.University of Chinese Academy of Social Sciences, School of Economics, Beijing 102488 , China;
3.Chongqing University of Science, Technology School of Business Administration,Chongqing 401331 , China

Received:2017-04-14 Online:2018-04-25

摘要/Abstract

摘要： 本文在直觉梯形模糊语言集的基础上,引入了Frank算子,提出一组新的算子——直觉梯形模糊语言Frank集结算子,并将其应用到多属性决策中。首先,本文提出了直觉梯形模糊语言集Frank算子的表达式,并给出相应的运算规则。然后提出了直觉梯形模糊语言Frank加权算术平均(ITrFLFWA)算子、直觉梯形模糊语言Frank加权几何平均(ITrFLFWG)算子、直觉梯形模糊语言Frank广义加权平均(ITrFLGFWA)算子等,并证明了其具有幂等性、有界性、单调性等性质。最后,通过实例验证了直觉梯形模糊语言Frank算子可以有效解决直觉梯形模糊语言环境下的多属性决策问题。

关键词: 直觉梯形模糊语言集, Frank算子, 信息集成算子, 多属性决策

Abstract: Based on the set of intuitionistic trapezoidal fuzzy linguistic, this paper introduces the Frank operator and proposes a new set of operators-intuitionistic trapezoidal fuzzy linguistic Frank assembly operators, and applies it to multi-attribute decision-making. Firstly, we give the concept of the formula, the corresponding operation rules, the scoring function, the exact function and the size comparison method of the Frank operator in the intuitionistic trapezoidal fuzzy linguistic environment. Then we propose the intuitionistic trapezoidal fuzzy linguistic Frank weighted arithmetic(ITrFLFWA)operator, intuitionistic trapezoidal fuzzy linguistic Frank weighted geometric(ITrFLFWG)operator, intuitionistic trapezoidal fuzzy linguistic generalized Frank weighted average(ITrFLGFWA)operator, etc., and prove its properties such as idempotency, boundedness, monotonicity. Finally, the decision-making method of the based and integrated operator is given, and the decision of the investment bank is given, which proves the validity of the method we propose. This method can be widely used in various combinations of investment decisions, risk decisions, supplier selection, and so on.

Key words: intuitionistic trapezoidal fuzzy linguistic set, frank operator, information integration operator, multiple attribute decision making

中图分类号:

C934

翟玉冰, 侯福均, 杜玉琴, 于倩. 直觉梯形模糊语言Frank算子及其在决策中的应用[J]. 运筹与管理, 2018, 27(4): 29-34.

ZHAI Yu-bing, HOU Fu-jun, DU Yu-qin,YU qian. Intuitionistic Trapezoidal Fuzzy Linguistic Frank Operator andIts Application in Decision Making[J]. Operations Research and Management Science, 2018, 27(4): 29-34.

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直觉梯形模糊语言Frank算子及其在决策中的应用

Intuitionistic Trapezoidal Fuzzy Linguistic Frank Operator andIts Application in Decision Making

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