Type-2 fuzzy multiple attribute decision-making method based on entropy and risk attitude

doi:10.11772/j.issn.1001-9081.2016.09.2535

Journal of Computer Applications ›› 2016, Vol. 36 ›› Issue (9): 2535-2539.DOI: 10.11772/j.issn.1001-9081.2016.09.2535

Previous Articles Next Articles

Type-2 fuzzy multiple attribute decision-making method based on entropy and risk attitude

WANG Cuicui¹, YAO Dengbao², LI Baoping^1,3

1. Department of Foundation, Anhui Sanlian University, Hefei Anhui 230601, China;
2. School of Economics and Management, Southeast University, Nanjing Jiangsu 211189, China;
3. School of Mathematical Science, Anhui University, Hefei Anhui 230601, China

Received:2016-02-26 Revised:2016-04-11 Online:2016-09-08 Published:2016-09-10
Supported by:
This work is partially supported by the National Natural Science Foundation of China (71473036) and the Provincial Nature Science Research Key Project for Colleges and Universities of Anhui Province (KJ2016A250), the Natural Science Key Project of Anhui Sanlian University (kjzd2016001).

基于熵和风险态度的二型模糊多属性决策方法

王翠翠¹, 姚登宝², 李宝萍^1,3

1. 安徽三联学院基础部, 合肥 230601;
2. 东南大学经济管理学院, 南京 211189;
3. 安徽大学数学科学学院, 合肥 230601

通讯作者: 王翠翠
作者简介:王翠翠(1989-),女,安徽宿州人,助教,硕士,主要研究方向:二型模糊理论与应用;姚登宝(1987-),男,安徽合肥人,博士研究生,主要研究方向:金融工程与风险管理;李宝萍(1976-),女,安徽巢湖人,副教授,硕士,主要研究方向:模糊决策。
基金资助:
国家自然科学基金面上项目（71473036）；安徽省高等学校省级自然科学研究重点项目（KJ2016A250）；安徽三联学院校级自然科学重点项目（kjzd2016001）。

Abstract

Abstract: In order to deal with the type-2 fuzzy decision-making problem that the attribute weights are unknown, a decision-making method based on type-2 fuzzy entropy and decision-maker's risk attitude was proposed. Firstly, the axiomatic principles of type-2 fuzzy entropy were constructed by introducing fuzzy factor and hesitancy factor to measure the uncertainty of Type-2 Fuzzy Set (T2FS), and some formulas were also given based on different distance measures. Secondly, in order to decrease effects of decision results caused by uncertain information, a non-linear programming model combined with type-2 fuzzy entropy was constructed to determine the attribute weights. Meanwhile, a score function was proposed by considering decision-maker's risk attitude and the specific decision-making processes were also given. Finally, the feasibility of the proposed method was verified through an example analysis, and the flexibility of the proposed method was also been reflected by comparing with existed references.

Key words: Type-2 Fuzzy Set (T2FS), type-2 fuzzy entropy, risk attitude, score function, multiple attribute decision-making

摘要： 针对属性权重信息完全未知的二型模糊多属性决策问题，提出了一种基于二型模糊熵和决策者风险态度的决策方法。首先，为了准确测度二型模糊集（T2FS）的不确定性，通过引入模糊因子和犹豫因子建立了二型模糊熵的公理化准则，并基于距离测度给出了对应的计算公式。其次，为了减少整体不确定信息对决策结果的影响，结合二型模糊熵构建非线性规划模型来确定属性权重。同时，将决策者的风险态度引入二型模糊信息的得分函数中并给出具体的决策步骤。最后，通过实例分析验证了该决策方法的可行性，并与现有文献对比发现该决策方法更具有灵活性。

关键词: 二型模糊集, 二型模糊熵, 风险态度, 得分函数, 多属性决策

CLC Number:

TP18

WANG Cuicui, YAO Dengbao, LI Baoping. Type-2 fuzzy multiple attribute decision-making method based on entropy and risk attitude[J]. Journal of Computer Applications, 2016, 36(9): 2535-2539.

王翠翠, 姚登宝, 李宝萍. 基于熵和风险态度的二型模糊多属性决策方法[J]. 计算机应用, 2016, 36(9): 2535-2539.

References

[1] ZADEH L A. Fuzzy sets [J]. Information and Control, 1965, 8(3): 338-353.
[2] ATANASSOV K T. Intuitionistic fuzzy sets [J]. Fuzzy Sets and Systems, 1986, 20(1): 87-96.
[3] ATANASSOV K, GARGOV G. Interval valued intuitionistic fuzzy sets [J]. Fuzzy Sets and Systems, 1989, 31(3): 343-349.
[4] TORRA T. Hesitant fuzzy sets [J]. International Journal of Intelligent Systems, 2010, 25(6): 529-539.
[5] ZADEH L A. The concept of a linguistic variable and its application to approximate reasoning [J]. Information Sciences, 1975, 8(3): 199-249.
[6] AGVERO J R, VARGAS A. Calculating functions of interval type-2 fuzzy numbers for fault current analysis [J]. IEEE Transactions on Fuzzy Systems, 2007, 15(1): 31-40.
[7] GILAN S S, SEBT M H, SHAHHOSSEINI V. Computing with words for hierarchical competency based selection of personnel in construction companies [J]. Applied Soft Computing, 2012, 12(2): 860-871.
[8] MENDEL J M. Computing with words and its relationship with fuzzistics [J]. Information Sciences, 2007, 177(4): 988-1006.
[9] MENDEL J M, JOHN R I B. Type-2 fuzzy sets made simple [J]. IEEE Transactions on Fuzzy Systems, 2002, 10(2): 117-127.
[10] KARNIK N N, MENDEL J M. Operations on type-2 fuzzy sets [J]. Fuzzy Sets and Systems, 2001, 122(2): 327-348.
[11] MENDEL J M. Advances in type-2 fuzzy sets and systems [J]. Information Sciences, 2007, 177(1): 84-110.
[12] ZADEH L A. Probability measures of fuzzy events [J]. Journal of Mathematical Analysis and Applications, 1968, 23(2): 421-427.
[13] SZMIDT E, KACPRZYK J. Entropy for intuitionistic fuzzy sets [J]. Fuzzy Sets and Systems, 2001, 118(3): 467-477.
[14] HUNG W L, YANG M S. Fuzzy entropy on intuitionistic fuzzy sets [J]. International Journal of Intelligent Systems, 2006, 21(4): 443-451.
[15] MAO J, YAO D, WANG C. A novel cross-entropy and entropy measures of IFSs and their applications [J]. Knowledge-Based Systems, 2013, 48(2): 37-45.
[16] XU Z, XIA M. Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision-making [J]. International Journal of Intelligent Systems, 2012, 27(9): 799-822.
[17] ZHAO N, XU Z, LIU F. Uncertainty measures for hesitant fuzzy information [J]. International Journal of Intelligent Systems, 2015, 30(7): 818-836.
[18] HWANG C M, YANG M S, HUNG W L, et al. Similarity, inclusion and entropy measures between type-2 fuzzy sets based on the Sugeno integral [J]. Mathematical and Computer Modelling, 2011, 53(9/10): 1788-1797.
[19] HWANG C M, YANG M S, HUNG W L. On similarity, inclusion measure and entropy between type-2 fuzzy sets [J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2012, 20(3):433-449.
[20] TAKÁC Z. Inclusion and subsethood measure for interval-valued fuzzy sets and for continuous type-2 fuzzy sets [J]. Fuzzy Sets and Systems, 2013, 224(4): 106-120.
[21] 邓廷权,王占江,王培培,等.二型模糊集的模糊熵研究[J].控制与决策,2012,27(3):408-412.(DENG T Q, WANG Z J, WANG P P, et al. Study on fuzzy entropy of type-2 fuzzy sets [J]. Control and Decision, 2012, 27(3): 408-412.)
[22] GHORABAEE M K. Developing an MCDM method for robot selection with interval type-2 fuzzy sets [J]. Robotics and Computer-Integrated Manufacturing, 2016, 37(C): 221-232.
[23] CHEN T Y. An interval type-2 fuzzy technique for order preference by similarity to ideal solutions using a likelihood-based comparison approach for multiple criteria decision analysis [J]. Computers and Industrial Engineering, 2015, 85(C): 57-72.
[24] QIN J D, LIU X W. Multi-attribute group decision making using combined ranking value under interval type-2 fuzzy environment [J]. Information Sciences, 2015, 297(C): 293-315.
[25] YAO D, LIU X, ZHANG X, et al. Type-2 fuzzy cross-entropy and entropy measures and their applications [J]. Journal of Intelligent and Fuzzy Systems, 2016, 30(4): 2169-2180.

Type-2 fuzzy multiple attribute decision-making method based on entropy and risk attitude

基于熵和风险态度的二型模糊多属性决策方法

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 5

Recommended Articles

Metrics

[1]	XU Jun, ZHONG Yuansheng. Subjective trust model based on consumers' risk attitude [J]. Journal of Computer Applications, 2015, 35(11): 3166-3171.
[2]	TAO Yang ZHOU Kun. Network selection handover strategy based on context-awareness [J]. Journal of Computer Applications, 2014, 34(12): 3381-3386.
[3]	GAO Jianxin WU Xiaoping QIN Yanlin WANG Jiasheng. Multidimensional timing trust degree rank model based on multiple attribute decision-making [J]. Journal of Computer Applications, 2013, 33(03): 720-722.
[4]	WANG Cui-cui YAO Deng-bao MAO Jun-jun SUN Li. Intuitionistic fuzzy multiple attributes decision making method based on entropy and correlation coefficient [J]. Journal of Computer Applications, 2012, 32(11): 3002-3017.
[5]	GUO Kai-hong MU You-jing. Multiple attribute decision-making method with intervals based on possibility degree matrix [J]. Journal of Computer Applications, 2012, 32(01): 218-222.