An application of soft computing technique in group decision making under interval-valued intuitionistic fuzzy environment

In this paper, we investigate the group decision making problem, in which the each decision maker (DM) provides his/her preferences over alternatives with respect to attributes in interval-valued intuitionistic fuzzy number. To determine the weights of DMs, inspired by the idea of TOPSIS technique, combining an optimistic coefficient, we first define a positive ideal decision as the average of all individual decisions and three negative ideal decisions, which have the maximum separations from the positive ideal decision. This method is suitable for cautious (avoiding risk) decision, since each negative ideal decision can effectively avoid a risk.By employing the derived weights of DMs, we aggregate all the individual decisions into a collective decision. After that, we aggregate all attribute values of each alternative of the collective decision into an overall evaluation of the alternative. Then rank all alternatives according to their score and accuracy degree and select the most desirable one.We compare this model with other methods and illustrate this method by a numerical example and a sensitivity analysis about the optimistic coefficient.     

TOPSIS with belief structure for group belief multiple criteria decision making

The technique for order performance by similarity to ideal solution(TOPSIS)is one of the major techniques in dealing with multiple criteria decision making(MCDM)problems, and the belief structure(BS)model has been used successfully for uncertain MCDM with incompleteness, impreciseness or ignorance. In this paper, the TOPSIS method with BS model is proposed to solve group belief MCDM problems. Firstly, the group belief MCDM problem is structured as a belief decision matrix in which the judgments of each decision maker are described as BS models, and then the evidential reasoning approach is used for aggregating the multiple decision makers' judgments. Subsequently, the positive and negative ideal belief solutions are defined with the principle of TOPSIS. To measure the separation from ideal solutions, the concept and algorithm of belief distance measure are defined, which can be used for comparing the difference between BS models. Finally, the relative closeness and ranking index are calculated for ranking the alternatives. A numerical example is given to illustrate the proposed method.     

基于TOPSIS的语言真值直觉模糊多属性决策

针对具有模糊语言值信息的多属性决策问题,结合传统的TOPSIS方法,提出了基于TOPSIS的语言真值直觉模糊多属性决策方法。在语言真值直觉模糊代数的基础上,用语言真值直觉模糊对来表达既有可比的又有不可比的模糊语言值信息,给出了语言真值直觉模糊对之间的归一化距离算法,并讨论了其相关性质。提出了语言真值直觉模糊正、负理想点,通过计算各方案属性值与正、负理想点之间的距离,得到各方案与理想点之间的相对贴近度,并根据相对贴近度的排序结果得到最优方案。实例说明该决策方法的合理性和有效性。     

多属性决策的模糊理想点法

讨论了属性值为三角模糊变量的多属性决策问题,提出了确定模糊正理想点和模糊负理想点的方法,给出了基于模糊正理想点和模糊负理想点对各方案进行排序的方法。给出算例验证了所提出的方法的有效性,并验证了不同方法所确定的模糊正理想点和模糊负理想点,会导致方案排序的改变。     

A note on the TOPSIS method in MADM problems with linguistic evaluations

The TOPSIS method, commonly known as the technique for order preference by similarity to ideal solutions, is one of the most popular approaches used in multi-attribute decision making (MADM). The fundamental procedure of the traditional TOPSIS method is rather straightforward, the ranking position of an alternative depends on its relative closeness to the positive ideal solution and the negative ideal solution, respectively. In order to encompass uncertain and ambiguous decision elements, an extension of the original TOPSIS method has been coined. With the help of fuzzy sets based TOPSIS, an overwhelming trend of fuzzy decision making applications has been witnessed. In the present work, however, it is found that the extended fuzzy TOPSIS method is unable to distinguish all the different alternatives under linguistic environment. Moreover, the undistinguishable alternatives are countless in quantity, and they have formed specific patterns with respect to the parameters of TOPSIS methods. To dampen this ranking ambiguity, we designed a set of supplemental methods to construct a revised TOPSIS approach with linguistic evaluations. Correspondingly, the sufficiency of the revised TOPSIS method to guarantee total orders has been proven. Furthermore, a numerical example concerning the production line improvement of a manufacturing company is demonstrated to validate the feasibility and supremacy of the proposed method. Finally, a series of further discussions are performed to shed some lights on the impacts caused by the changes of the alternative quantity, the attribute quantity, and the type of linguistic term.     

The effect of normalization norms in multiple attribute decision making models: a case study in gear material selection

The main objective of this paper is to evaluate the effect of different normalization norms within multiple attribute decision making (MADM) models. The application of the work is dedicated to gear material selection for power transmission. To this end, the general scheme of the decision model is first presented, with close attention to the context of material selection. Subsequently, the entropy method and technique for order preference by similarity to ideal solution (TOPSIS) are employed to weigh the selected failure criteria and to rank the selected material IDs, respectively. Finally, by the introduction of different norms to the solution algorithm, the effect of normalization formalism on the material selection using the MADM models is studied. A simple multiaxial strategy is also recommended from which safer engineering decisions may be attained.     

基于直觉梯形模糊TOPSIS的多属性群决策方法

提出一种改进的逼近理想解排序(TOPSIS)方法,即直觉梯形模糊TOPSIS多属性群决策方法。首先,应用直觉梯形模糊数形式表示方案属性偏好和属性权重信息且专家权重完全未知;然后,利用直觉梯形模糊数间距离测度和期望值及直觉梯形模糊加权平均算子来确定决策者权重信息和属性权重信息;进而给出直觉梯形模糊环境下方案优选的算法;最后,通过算例进一步说明了该直觉梯形模糊TOPSIS方法的有效性。     

Compromise ratio method for fuzzy multi-attribute group decision making

The aim of this paper is to develop a compromise ratio (CR) methodology for fuzzy multi-attribute group decision making (FMAGDM), which is an important part of decision support system. Owing to fuzziness being inherent in decision data and group decision making processes, the crisp values are inadequate to model real-life situations. In this paper, the weights of all attributes and the ratings of each alternative with respect to each attribute are described by linguistic terms which can be expressed in trapezoid fuzzy numbers. A fuzzy distance measure is developed to calculate difference between trapezoid fuzzy numbers. The compromise ratio method for FMAGDM is developed by introducing the ranking index based on the concept that the chosen alternative should be as close as possible to the ideal solution and as far away from the negative-ideal solution as possible simultaneously. The computation principle and procedure of the compromise ratio method are described in detail in this paper. Moreover the TOPSIS method which was developed for multi-attribute decision making (MADM) with crisp decision data is analyzed and extended to multi-attribute group decision making (MAGDM) under fuzzy environments. A comparative analysis of the compromise ratio method and the extended fuzzy TOPSIS method is illustrated with a numerical example, showing their similarity and some differences.     

Multiple-attribute decision making methods for plant layout design problem

The layout design problem is a strategic issue and has a significant impact on the efficiency of a manufacturing system. Much of the existing layout design literature that uses a surrogate function for flow distance or for simplified objectives may be entrapped into local optimum; and subsequently lead to a poor layout design due to the multiple-attribute decision making (MADM) nature of a layout design decision. The present study explores the use of MADM approaches in solving a layout design problem. The proposed methodology is illustrated through a practical application from an IC packaging company. Two methods are proposed in solving the case study problem: Technique for order preference by similarity to ideal solution (TOPSIS) and fuzzy TOPSIS. Empirical results showed that the proposed methods are viable approaches in solving a layout design problem. TOPSIS is a viable approach for the case study problem and is suitable for precise value performance ratings. When the performance ratings are vague and imprecise, the fuzzy TOPSIS is a preferred solution method.     

The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making

The technique for order preference by similarity to ideal solution (TOPSIS) method is a well-known compromising method for multiple criteria decision analysis. This paper develops an extended TOPSIS method with an inclusion comparison approach for addressing multiple criteria group decision-making problems in the framework of interval-valued intuitionistic fuzzy sets. Considering the relative agreement degrees and the importance weights of multiple decision makers, this paper presents a modified hybrid averaging method with an inclusion-based ordered weighted averaging operation for forming a collective decision environment. Based on the main structure of the TOPSIS method, this paper utilizes the concept of inclusion comparison possibilities to propose a new index for an inclusion-based closeness coefficient for ranking the alternatives. Additionally, two optimization models are established to determine the criterion weights for addressing situations in which the preference information is completely unknown or incompletely known. Finally, the feasibility and effectiveness of the proposed methods are illustrated by a medical group decision-making problem.