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The aim of this paper is to propose a new aggregation method to solve heterogeneous MAGDM problem which involves real numbers, interval numbers, triangular fuzzy numbers (TFNs), trapezoidal fuzzy numbers (TrFNs), linguistic values and Atanassov's intuitionistic fuzzy numbers (AIFNs). Firstly, motivated by the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS), we propose a new general method for aggregating crisp values, TFNs, TrFNs and linguistic values into AIFNs. Thus all the group decision matrices for each alternative which involves heterogeneous information are transformed into an Atanassov's intuitionistic fuzzy decision matrix which only contains AIFNs. To determine the attribute weights, a multiple objective Atanassov's intuitionistic fuzzy programming model is constructed and solved by converting it into a linear program. Subsequently, comparison analyses demonstrate that the proposed aggregated technology can overcome the drawbacks of existing methods. An example about cloud computing service evaluation is given to verify the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The ranking of intuitionistic fuzzy sets (IFSs) is very important for the intuitionistic fuzzy decision making. The aim of this paper is to propose a new risk attitudinal ranking method of IFSs and apply to multi-attribute decision making (MADM) with incomplete weight information. Motivated by technique for order preference by similarity to ideal solution (TOPSIS), we utilize the closeness degree to characterize the amount of information according to the geometrical representation of an IFS. The area of triangle is calculated to measure the reliability of information. It is proved that the closeness degree and the triangle area just form an interval. Thereby, a new lexicographical method is proposed based on the intervals for ranking the intuitionistic fuzzy values (IFVs). Furthermore, considered the risk attitude of decision maker sufficiently, a novel risk attitudinal ranking measure is developed to rank the IFVs on the basis of the continuous ordered weighted average (C-OWA) operator and this interval. Through maximizing the closeness degrees of alternatives, we construct a multi-objective fractional programming model which is transformed into a linear program. Thus, the attribute weights are derived objectively by solving this linear program. Then, a new method is put forward for MADM with IFVs and incomplete weight information. Finally, an example analysis of a teacher selection is given to verify the effectiveness and practicability of the proposed method. [ABSTRACT FROM AUTHOR]

Multi-attribute group decision making (MAGDM) has attracted more and more attention in many fields. Correspondingly, a number of usable methods have been proposed for various MAGDM problems, nevertheless, very few research focus on the aggregation techniques of intuitionistic fuzzy information. The aim of this paper is to aggregate decision information into interval-valued intuitionistic fuzzy numbers (IVIFNs) to solve heterogeneous MAGDM problem in which the decision information involves real numbers, interval numbers, triangular fuzzy numbers (TFNs) and trapezoidal fuzzy numbers (TrFNs). There are three issues being addressed in this paper. The first is to propose a new general method to aggregate the attribute value vector into IVIFNs under heterogeneous MAGDM environment utilizing the relative closeness in technique for order preference by similarity to ideal solution (TOPSIS). The second is to construct a multiple objective intuitionistic fuzzy programming model to determine the attribute weights. Borrowing the results of the former two issues, the last is to present a new method to solve heterogeneous MAGDM problem. A comparison analysis with existing method is conducted to demonstrate the advantages of the proposed method. Two examples are provided to verify the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: Triangular intuitionistic fuzzy numbers (TIFNs) are a special intuitionistic fuzzy set (IFS) on a real number set, which are very useful for decision makers (DMs) to depict their fuzzy preference information. In this work, we investigate multiple attribute group decision-making (MAGDM) problems in which the ratings of alternatives are expressed with TIFNs, and the weights of the attributes and DMs are completely unknown. Firstly, the crisp weighted possibility mean of TIFNs is defined, and the Hamming distance and Euclidean distance for TIFNs are defined based on Hausdorff distance. The triangular intuitionistic fuzzy weighted average (TIF-WA) operator is developed. Then, the weights of attributes are calculated by applying Shannon entropy measure and the weights of DMs are determined objectively combining the evidence theory with Bayes approximation. The individual decision matrixes for all DMs are aggregated into the group decision matrix by using the TIF-WA operator. Thereby, the classic Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method is extended for solving the MAGDM with TIFNs. Finally, the ranking order of alternative is given according to the closeness of alternative with respect to the ideal solution. The personnel selection example verifies the effectiveness of the proposed method. [Copyright &y& Elsevier]