VIKOR Method with Triangular Intuitionistic Fuzzy Numbers

doi:10.12005/orms.2015.0151

Abstract

Abstract: The aim of this paper is to extend VIKOR method which is a compromise ranking approach for multiple attribute decision making (MADM) problems for intuitionistic fuzzy multi-attributes analysis. VIKOR method with triangular intuitionistic fuzzy numbers is researched for solving MADM problems in which the ratings of alternatives are expressed with triangular intuitionistic fuzzy numbers and the weights are real numbers. Firstly, a ranking method for triangular intuitionistic fuzzy numbers is proposed based on preference index. Secondly, according to the basic idea of VIKOR method, the steps of VIKOR method with triangular intuitionistic fuzzy numbers are given, and then the compromise solution is obtained under the condition of acceptable advantage and acceptable stability in decision making. Finally, the third party logistics providers selection example verifies the effectiveness and feasibility of the proposed method when the weight of maximum group utility equals 0.5.

Key words: Multi-attribute decision making, Triangular intuitionistic fuzzy number, VIKOR method, Ideal solution

摘要： 针对备选方案的属性值为三角直觉模糊数且权重为实数的多属性决策问题,研究了三角直觉模糊数型VIKOR方法。首先,本文提出了一种基于偏好指标的三角直觉模糊数排序方法;其次,根据VIKOR方法的基本思想,提出了求解三角直觉模糊数型VIKOR方法的步骤,并在可接受优势和决策过程的稳定条件下对备选方案进行排序,得到折衷解;最后,在最大群体效用权重为0.5的情况下,用第三方物流服务商选择为例说明了该方法的有效性和可行性。

关键词: 多属性决策, 三角直觉模糊数, VIKOR方法, 理想解

CLC Number:

C934

SUN Hong-xia,LI Yu. VIKOR Method with Triangular Intuitionistic Fuzzy Numbers[J]. Operations Research and Management Science, 2015, 24(4): 288-294.

孙红霞, 李煜. 三角直觉模糊数型VIKOR方法[J]. 运筹与管理, 2015, 24(4): 288-294.

References

[1] Opricovic S. Multi-criteria optimization of civil Engineering systems[J]. Faculty of Civil Engineering, Belgrade, 1998, 2(1): 5-21.
[2] Opricovic S, Tzeng G H. Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS[J]. European Journal of Operational Research, 2004, 156(2): 445-455.
[3] Büyükzkan G, Ruan D. Evaluation of software development projects using a fuzzy multi-criteria decision approach[J]. Mathematics and Computers in Simulation, 2008, 77(5): 464-475.
[4] Sayadi M K, Heydari M, Shahanaghi K. Extension of VIKOR method for decision making problem with interval numbers[J]. Applied Mathematical Modelling, 2009, 33(5): 2257-2262.
[5] 孙红霞, 张强. 区间数型模糊 VIKOR 方法[J]. 模糊系统与数学, 2011, 25(5): 122-128.
[6] Sanayei A, FaridMousavi S, Yazdankhah A. Group decision making process for supplier selection with VIKOR under fuzzy environment[J]. Expert Systems with Applications, 2010, 37(1): 24-30.
[7] 苏志欣, 王理, 夏国平.区间数动态多属性决策的VIKOR扩展方法[J]. 控制与决策, 2010, 25(6): 836-840.
[8] Park J H, Cho H J, Kwun Y C. Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information[J]. Fuzzy Optimization and Decision Making, 2011, 10(3): 233-253.
[9] 张市芳,刘三阳, 秦传东, 等. 动态三角模糊多属性决策的 VIKOR 扩展方法[J]. 计算机集成制造系统, 2012, 18(1): 186-191.
[10] Wan S P, Wang Q Y, Dong J Y. The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers[J]. Knowledge-Based Systems, 2013, 52: 65-77.
[11] Zhang N, Wei G. Extension of VIKOR method for decision making problem based on hesitant fuzzy set[J]. Applied Mathematical Modelling, 2013, 37(7): 4938-4947.
[12] Shu M H, Cheng C H, Chang J R. Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly[J]. Microelectronics Reliability, 2006, 46(12): 2139-2148.
[13] 张茂军, 南江霞, 李登峰, 李延喜. 带有三角直觉模糊数的多属性决策的TOPSIS[J]. 运筹与管理, 2012, 21(5): 96-101.

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