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Abstract: The aim of this paper is to investigate the multiple attribute decision making problems with intuitionistic fuzzy information, in which the information about attribute weights is incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional gray relational analysis (GRA) method, by which the attribute weights can be determined. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. Then, based on the traditional GRA method, calculation steps for solving intuitionistic fuzzy multiple attribute decision-making problems with incompletely known weight information are given. Furthermore, we have extended the above results to an interval-valued intuitionistic fuzzy environment and developed modified GRA method for interval-valued intuitionistic fuzzy multiple attribute decision-making with incompletely known attribute weight information. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. [Copyright &y& Elsevier]

Abstract: To study the problem of multiple attribute decision making in which the decision making information values are triangular fuzzy number, a new group decision making method is proposed. Then the calculation steps to solve it are given. As the key step, a new operator called fuzzy induced ordered weighted harmonic mean (FIOWHM) operator is proposed and a method based on the fuzzy weighted harmonic mean (FWHM) operator and FIOWHM operators for fuzzy MAGDM is presented. The priority based on possibility degree for the fuzzy multiple attribute decision making problem is proposed. At last, a numerical example is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate. [ABSTRACT FROM AUTHOR]

In this paper, we propose an uncertain linguistic hybrid geometric mean (ULHGM) operator, which is based on the uncertain linguistic weighted geometric mean (ULWGM) operator and the uncertain linguistic ordered weighted geometric (ULOWG) operator proposed by Xu [Z. S. Xu, "An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations", Decision Support Systems41 (2006) 488–499] and study some desirable properties of the ULHGM operator. We have proved both ULWGM and ULOWG operators are the special case of the ULHGM operator. The ULHGM operator generalizes both the ULWGM and ULOWG operators, and reflects the importance degrees of both the given arguments and their ordered positions. Based on the ULWGM and ULHGM operators, we propose a practical method for multiple attribute group decision making with uncertain linguistic preference relations. Finally, an illustrative example demonstrates the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: With respect to multiple attribute decision making problems with intuitionistic fuzzy information, some operational laws of intuitionistic fuzzy numbers, score function and accuracy function of intuitionistic fuzzy numbers are introduced. An optimization model based on the maximizing deviation method, by which the attribute weights can be determined, is established. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. We utilize the intuitionistic fuzzy weighted averaging (IFWA) operator to aggregate the intuitionistic fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one(s) according to the score function and accuracy function. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. [Copyright &y& Elsevier]