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Recently, the TODIM method has been used to solve multiple attribute decision making (MADM) problems. The interval-valued Pythagorean fuzzy sets (IVPFSs) are useful tools to depict uncertainty of the MADM. In this paper, we will extend the TODIM method to the MADM with the interval-valued Pythagorean fuzzy numbers (IVPFNs). Firstly, the definition, comparison and distance of IVPFNs are briefly introduced, and the steps of the classical TODIM method for MADM problems are presented. Then, the extended classical TODIM method is proposed to deal with MADM problems with the IVPFNs, and its significant characteristic is that it can fully consider the decision makers' bounded rationality which is a real action in decision making. Furthermore, we develop the concept of the q-rung interval-valued orthopair fuzzy sets (q-RIVOFSs) and extend the TODIM method to q-RIVOFNs. Finally, a numerical example is proposed and a comparative analysis is given. [ABSTRACT FROM AUTHOR]

Abstract: With respect to 2-tuple linguistic multiple attribute group decision making problems with incomplete weight information, some basic concepts and operational laws of 2-tuple linguistic variables are introduced. An optimization model based on the maximizing deviation method, by which the attribute weights can be determined, is established. According to the traditional ideas of grey relational analysis (GRA), the optimal alternative(s) is determined by calculating the linguistic degree of grey relation of every alternative and 2-tuple linguistic positive ideal solution and 2-tuple linguistic negative ideal solution. It is based on the concept that the optimal alternative should have the largest degree of grey relation from positive ideal solution and the smallest degree of grey relation from the negative ideal solution. The method has exact characteristic in linguistic information processing. It avoided information distortion and losing which occur formerly in the linguistic information processing. Finally, a numerical example is used to illustrate the use of the proposed method. The result shows the approach is simple, effective and easy to calculate. [ABSTRACT FROM AUTHOR]

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]

Abstract: With respect to multiple attribute group decision-making problems with linguistic information of attribute values and weight values, a group decision analysis is proposed. Some new aggregation operators are proposed: the extended 2-tuple weighted geometric (ET-WG) and the extended 2-tuple ordered weighted geometric (ET-OWG) operator and properties of the operators are analyzed. Then, A method based on the ET-WG and ET-OWG operators for multiple attribute group decision-making is presented. In the approach, alternative appraisal values are calculated by the aggregation of 2-tuple linguistic information. Thus, the ranking of alternative or selection of the most desirable alternative(s) is obtained by the comparison of 2-tuple linguistic information. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

With respect to linguistic multiple attribute group decision making problems with incomplete weight information, a new method is proposed. In the method, the 2-tuple linguistic representation developed in recent years is used to aggregate the linguistic assessment information. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional technique for order performance by similarity to ideal solution, by which the attribute weights can be determined. Then, the optimal alternative(s) is determined by calculating the shortest distance from the 2-tuple linguistic positive ideal solution, and on the other side, the farthest distance of the 2-tuple linguistic negative ideal solution. The method has exact characteristic in linguistic information processing. It avoided information distortion and losing, which occur formerly in the linguistic information processing. Finally, a numerical example is used to illustrate the use of the proposed method. The result shows the approach is simple, effective, and easy to calculate. [ABSTRACT FROM AUTHOR]