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The aim of this paper is to develop a new methodology for solving group decision making problems in which preference comparisons between alternatives are expressed with Atanassov's intuitionistic fuzzy (IF) preference relations. In this methodology, the generalized ordered weighted averaging (GOWA) operator is extended to develop the Atanassov's IF set (IFS) generalized ordered weighted averaging (IFSGOWA) operator, which can aggregate vague or imprecise information expressed with the Atanassov's IFSs. The Atanassov's IFSGOWA operator based methodology is further developed to solve group decision making problems with Atanassov's IF preference relations. A real example of the agroecological region assessment problem is used to illustrate the implementation and applicability of the proposed methodology. It is also shown that the obtained decision results could be affected by the choice of the parameter lambda and the nature of the weights. [ABSTRACT FROM AUTHOR]

The aim of this paper is to use the concept of extended linguistic variables to develop a new methodology for solving multiattribute group decision making problems under linguistic assessments. In this methodology, using the generalized induced ordered weighted averaging operator and extended linguistic variables, linguistic ratings of each alternative on all attributes for each decision maker are aggregated into a comprehensive assessment, which is not always a linguistic term in the linguistic term set designated a priori. Comprehensive assessments of each alternative on all decision makers are similarly aggregated into a comprehensive assessment of the alternative for the group. An optimal linguistic term in the linguistic term set which approaches the comprehensive assessment of each alternative for the group as close as possible is computed and an extended 2-tuple fuzzy linguistic representation is obtained for the alternative. The ranking order of alternatives for the group is generated according to the extended 2-tuple fuzzy linguistic representations. A numerical example is examined to demonstrate applicability and implementation process of the methodology proposed in this paper. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to study how to solve a type of matrix games with payoffs of triangular fuzzy numbers. In this paper, the value of a matrix game with payoffs of triangular fuzzy numbers has been considered as a variable of the triangular fuzzy number. First, based on two auxiliary linear programming models of a classical matrix game and the operations of triangular fuzzy numbers, fuzzy optimization problems are established for two players. Then, based on the order relation of triangular fuzzy numbers the fuzzy optimization problems for players are decomposed into three-objective linear programming models. Finally, using the lexicographic method maximin and minimax strategies for players and the fuzzy value of the matrix game with payoffs of triangular fuzzy numbers can be obtained through solving two corresponding auxiliary linear programming problems, which are easily computed using the existing Simplex method for the linear programming problem. It has been shown that the models proposed in this paper extend the classical matrix game models. A numerical example is provided to illustrate the methodology. [ABSTRACT FROM AUTHOR]