Search

In multiple attribute decision making (MADM) issues, the ambiguity, imprecision, and imperfection of assessment information may lead to inadequate decision-making results. However, the Z-number suggested by Zadeh in 2011 could somehow prevent this problem. For MADM issues with unknown attributes weights, an extended Distance from the Average Solution (EDAS) method is proposed under a mixture Z-number environment. In addition, the Criteria Importance Through Inter-criteria Correlation (CRITIC) method is used to estimate the weights of the criterion, which is easy to calculate and avoids subjective forecasts. A novel illustrative example is provided to demonstrate the feasibility, validity, and practicability of the presented method, and is compared with existing decision methods. The outcome indicates that the suggested method can solve complicated decision-making problems. [ABSTRACT FROM AUTHOR]

Recently, the TODIM (an acronym in Portuguese for Interactive Multi-criteria Decision Making) approach, which can characterize the decision makers’ psychological behaviors under risk, has been introduced to handle multiple attribute decision making (MADM) problems. The Pythagorean 2-tuple linguistic sets (P2TLSs) are useful tools to depict uncertainty in MADM. This paper use TODIM method to solve MADM with the Pythagorean 2-tuple linguistic numbers (P2TLNs). Firstly, the definition, comparison and distance of P2TLNs are briefly presented, and classical TODIM for MADM are introduced. Then, the extended classical TODIM method is proposed to deal with MADM problems with P2TLNs, and its important characteristic is to fully consider the decision makers’ bounded rationality which is a real action in MADM. Furthermore, we extend TODIM method to Pythagorean interval 2-tuple linguistic sets (PI2TLSs). Finally, a numerical example is proposed and a comparative analysis is also given. [ABSTRACT FROM AUTHOR]

In this study, we propose a spatial prisoner's dilemma game model with a 2-stage strategy updating rule, and focus on the cooperation behavior of the system. In the first stage, i.e., the pre-learning stage, a focal player decides whether to update his strategy according to the pre-learning factor β and the payoff difference between himself and the average of his neighbors. If the player makes up his mind to update, he enters into the second stage, i.e., the learning stage, and adopts a strategy of a randomly selected neighbor according to the standard Fermi updating rule. The simulation results show that the cooperation level has a non-trivial dependence osn the pre-learning factor. Generally, the cooperation frequency decreases as the pre-learning factor increases; but a high cooperation level can be obtained in the intermediate region of -3 < β < -1. We then give some explanations via studying the co-action of pre-learning and learning. Our results may sharpen the understanding of the influence of the strategy updating rule on evolutionary games. [ABSTRACT FROM AUTHOR]

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: 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 grey relational analysis (GRA) method, by which the attribute weights can be determined. 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. The degree of grey relation between every alternative and positive-ideal solution and negative-ideal solution are calculated. Then, a relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of grey relation to both the positive-ideal solution (PIS) and negative-ideal solution (NIS) simultaneously. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. [Copyright &y& Elsevier]

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]