Interval-valued Intuitionistic Fuzzy Group Decision Research Articles

A programming-based algorithm for interval-valued intuitionistic fuzzy group decision making

Interval-valued intuitionistic fuzzy preference relations (IVIFPRs) are powerful to express the uncertain preferred and non-preferred judgments of decision makers simultaneously. After reviewing previous researches about IVIFPRs, we find that several limitations exist. Especially, previous methods are insufficient to address inconsistent and incomplete cases. Considering these issues, this paper first analyzes the limitations of the previous consistency concepts for IVIFPRs and then introduces a new one that avoids the disadvantages of previous ones. 0–1 mixed programming models are built for judging the multiplicative consistency of IVIFPRs. Subsequently, several multiplicative consistency-based 0–1 mixed programming models are constructed for determining missing values that can address the situation where ignored objects exist. For group decision making, a distance measure on IVIFPRs is defined, by which the weights of the decision makers are derived. Meanwhile, a consensus index is offered. A multiplicative consistency and consensus based algorithm to group decision making with IVIFPRs is proposed. Finally, two practical decision-making problems are offered to show the application of the new algorithm, and theoretical and numerical analysis of several related methods is made.

Soft computing based on maximizing consensus and fuzzy TOPSIS approach to interval-valued intuitionistic fuzzy group decision making

Multi-attribute group decision making (MAGDM) is an important research topic in decision theory. In recent decades, many useful methods have been proposed to solve various MAGDM problems, but very few methods simultaneously take them into account from the perspectives of both the ranking and the magnitude of decision data, especially for the interval-valued intuitionistic fuzzy decision data. The purpose of this paper is to develop a soft computing technique based on maximizing consensus and fuzzy TOPSIS in order to solve interval-valued intuitionistic fuzzy MAGDM problems from such two aspects of decision data. To this end, we first define a consensus index from the perspective of the ranking of decision data, for measuring the degree of consensus between the individual and the group. Then, we establish an optimal model based on maximizing consensus to determine the weights of experts. Following the idea of TOPSIS, we calculate the closeness indices of the alternatives from the perspective of the magnitude of decision data. To identify the optimal alternatives and determine their optimum quantities, we further construct a multi-choice goal programming model based on the derived closeness indices. Finally, an example is given to verify the developed method and to make a comparative analysis.

The selection of technology forecasting method using a multi-criteria interval-valued intuitionistic fuzzy group decision making approach

Technological forecasting is a tool for organizations to develop their technology strategies. The quality of forecasting is extremely important for the accuracy of the results and in turn company future. Therefore a proper selection methodology of forecasting technique that considers the characteristics of technology and resources needed such as cost, time is essential. On the other hand, although many forecasting techniques are available, there is a high uncertainty in choosing the most appropriate technique among a set of available techniques. In this paper interval valued intuitionistic fuzzy technique for order preference by similarity to ideal solution (TOPSIS) method is proposed for the solution of technological forecasting technique selection problem. The proposed method includes seven selection criteria and twelve forecasting technique alternatives. The methodology is applied for 3D TV technology. The results revealed that Fisher Pry method is found as the most appropriate method for forecasting since it has the highest closeness coefficient.

Deriving decision maker’s weights based on distance measure for interval-valued intuitionistic fuzzy group decision making

The purpose of this paper is to develop a new approach for measuring the decision makers’ weights in group decision making setting, in which the decision information, provided by multiple decision makers, is expressed in interval-valued intuitionistic fuzzy numbers. There are two key issues being addressed in this approach. The first one is to develop an ideal decision of group, which is the mean of group decision. The second one is to select the similarity measure between each individual decision and the ideal decision according to the idea of the TOPSIS of Hwang and Yoon (1981). A numeric example is also given to clarify the developed approach and to demonstrate its effectiveness.

A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS

An extension of TOPSIS, a multi-criteria interval-valued intuitionistic fuzzy decision making technique, to a group decision environment is investigated, where inter-dependent or interactive characteristics among criteria and preference of decision makers are taken into account. To get a broad view of the techniques used, first, some operational laws on interval-valued intuitionistic fuzzy values are introduced. Based on these operational laws, a generalized interval-valued intuitionistic fuzzy geometric aggregation operator is proposed which is used to aggregate decision makers’ opinions in group decision making process. In addition, some of its properties are discussed. Then Choquet integral-based Hamming distance between interval-valued intuitionistic fuzzy values is defined. Combining the interval-valued intuitionistic fuzzy geometric aggregation operator with Choquet integral-based Hamming distance, an extension of TOPSIS method is developed to deal with a multi-criteria interval-valued intuitionistic fuzzy group decision making problems. Finally, an illustrative example is used to illustrate the developed procedures.

A method based on distance measure for interval-valued intuitionistic fuzzy group decision making

In this paper we introduce some relations and operations of interval-valued intuitionistic fuzzy numbers and define some types of matrices, including interval-valued intuitionistic fuzzy matrix, interval-valued intuitionistic fuzzy similarity matrix and interval-valued intuitionistic fuzzy equivalence matrix. We study their properties, develop a method based on distance measure for group decision making with interval-valued intuitionistic fuzzy matrices and, finally, provide an illustrative example.