NEUTROSOPHIC MAGDM BASED ON ENTROPIES OF DEGREES α, β AND R-NORM
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Abstract
Yager [1988] developed the ordered weighted averaging (OWA) operator and applied in decision making problems. Xu & Yager [2006] developed some geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionistic fuzzy hybrid geometric (IFHG) operator and gave an application of the IFHG operator to multiple attribute group decision making with intuitionistic fuzzy information. Xu [2007e] and Xu & Chen [2007a, 2007b] also developed some arithmetic aggregation operators for decision making problems. One important issue in the theory of ordered weighted averaging (OWA) operators is the determination of the associated weights. One of the first approaches, suggested in the literature is a special class of OWA operators having maximal Shannon entropy of the OWA weights for a given level of orness; algorithmically it is based on the solution of a constrained optimization problem. The MAGDM problems have investigated under neutrosophic fuzzy environment, and proposed an approach to handling the situations where the attribute values are characterized by NFSs, and the information about attribute weights completely unknown. The proposed approach first fuses all individual neutrosophic fuzzy decision matrices into the collective neutrosophic fuzzy decision matrix by using the NFOWA operator. Then the obtained attribute weights and the NFHA operator have used to get the overall neutrosophic fuzzy values of alternatives  In this paper, the proposed approach in this work not only can comfort the influence of unjust arguments on the decision results, but also avoid losing or distorting the original decision information in the process of aggregation. Thus, the proposed approach provides us an effective and practical way to deal with multi-person multi-attribute decision making problems, where the attribute values are characterized by NFSs and the information about attribute weights is partially known. The suitable alternative is selected through the algorithm from the given neutrosophic information in which the unknown weights are derived based upon normal distribution.
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