Intuitionistic Trapezoidal Fuzzy Linguistic Frank Operator andIts Application in Decision Making

doi:10.12005/orms.2018.0081

Abstract

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

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

CLC Number:

C934

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.

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.

References

[1]Zadeh L A. The concept of a linguistic variable and its application to approximate reasoning[J]. Information sciences, 1975, 8(3): 199-249.
[2]Atanassov K. Intuitionistic fuzzy sets[J]. Fuzzy sets and Systems, 1986, 20(1): 87-96.
[3]Herrera F, Martínez L. A 2-tuple fuzzy linguistic representation model for computing with words[J]. IEEE Transactions on Fuzzy Systems, 2000, 8(6): 746-752.
[4]王坚强,李靖靖.多粒度直觉二元语义的多准则群决策方法[J].科技信息,2009,(33):8-9.
[5]Ju Y B, Liu X Y, Yang S H. Trapezoid fuzzy 2-tuple linguistic aggregation operators and their applications to multiple attribute decision making[J]. Journal of Intelligent & Fuzzy Systems, 2014, 27(3): 1219-1232.
[6]Xu Z S. Group decision making with triangular fuzzy linguistic variables[C]//International Conference on Intelligent Data Engineering and Automated Learning. Springer Berlin Heidelberg, 2007: 17-26.[7]王坚强,张忠.基于直觉梯形模糊数的信息不完全确定的多准则决策方法[J].控制与决策,2009,24(02):226-230.
[8]Yu Q, Hou F J, Zhai Y B, Du Y Q. Some hesitant fuzzy einstein aggregation operators and their application to multiple attribute group decision making[J]. International Journal of Intelligent Systems, 2015, 31: 722-746.
[9]于倩,侯福均,翟玉冰,杜玉琴.区间犹豫模糊ELECTER多属性决策方法及应用[J].运筹与管理,2015,24(6):17-24.
[10]Du Y Q, Hou F J, Zafar W, Yu Q, Zhai Y B. A novel method for multiattribute decision making with interval-valued pythagorean fuzzy linguistic information[J]. International Journal of Intelligent Systems, 2017.
[11]Frank MJ. On the simultaneous associativity of F(x, y) and x+y-F(x, y)[J]. Aequationes mathematicae. 1979, 19(1): 194-226.
[12]Zhang X, Liu P D, Wang Y. Multiple attribute group decision making methods based on intuitionistic fuzzy frank power aggregation operators[J]. Journal of Intelligent & Fuzzy System. 2015, 29(5): 2235-2246.
[13]Zhang Z M. Interval-valued intuitionistic fuzzy frank aggregation operators and their applications to multiple attribute group decision making[J]. Neural Computing and Applications. 2016, 1: 1-31.
[14]Ji P, Wang J Q, Zhang H Y. Frank prioritized bonferroni mean operator with single-valued neutrosophic sets and its application in selecting third-party logistics providers[J]. Neural Computing and Applications, 2016: 1-25.
[15]Qin J D, Liu X W, Pedrycz W. Frank aggregation operators and their application to hesitant fuzzy multiple attribute decision making[J]. Applied Soft Computing, 2016, 41: 428-452.
[16]Peng H G, Wang J Q, Cheng P F. A linguistic intuitionistic multi-criteria decision-making method based on the Frank Heronian mean operator and its application in evaluating coal mine safety[J]. International Journal of Machine Learning and Cybernetics, 2016: 1-16.
[17]Ju Y B, Yang S H. Approaches for multi-attribute group decision making based on intuitionistic trapezoid fuzzy linguistic power aggregation operators[J]. Journal of Intelligent & Fuzzy Systems, 2014, 27(2): 987-1000.
[18]杨尚洪.模糊多属性决策方法及在电网企业投资中的应用[D].北京理工大学,2015.