Research On Multi-attribute Decision-making Methods Based On Neutrosophic Numbers

Multiple attribute decision making(MADM)or multiple attribute group decision making(MAGDM)is an important branch of modern decision sciences.Its theory and method are widely applied to many areas,such as economics,management,engineering,military affairs,and so forth.Compared with fuzzy sets,intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets,simplified neutrosophic set,includes single-valued neutrosophic sets(SVNSs)and an interval neutrosophic sets(INSs)is very suitable for the expression of incomplete,indeterminate,and inconsistent information in actual applications.Therefore,SVNSs and IINSs are more flexible and practical when addressing fuzziness and uncertainty than traditional fuzzy sets,intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets.So,the fuzzy MADM problems arouse the academic circles enormous interest.Therefore,the research on MADM or MAGDM based on the neutrosophic sets has important theoretic significance and higher practical application.Thus,the purpose of this paper is to do a deep research on the MADM or MAGDM problems based on the neutrosophic sets under some situations.The detailed arrangement of this paper stands out as follows:(1)In this section,we extend the TODIM method to the MADM with the single-valued neutrosophic numbers(SVNNs).Firstly,the definition,characteristics,expectation,comparative method and distance of SVNNs are briefly introduced,and the steps of the classical TODIM method for MADM problems are presented.Then,on the basis of the classical TODIM method,the extended TODIM method is proposed to deal with MADM problems in which the attribute values are in the SVNNs,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 extend the above results to interval neutrosophic environment.Finally,a numerical example is proposed to verify the developed approach and its practicality and effectiveness.(2)In this section,we extend VIKOR(VIsekriterijumska optimizacija I KOmpromisno Resenje)method to the MAGDM with the SVNNs.Firstly,the basic concepts of SVNNs are briefly presented.The method firstly aggregates all individual decision makers' assessment information based on single-valued neutrosophic weighted averaging(SVNWA)operator,then,the extended classical VIKOR method is proposed to deal with MAGDM problems with the SVNNs.Furthermore,we have extended the above results to interval neutrosophic environment.The validity and stability of this method are verified by example analysis and sensitivity analysis,and its superiority is illustrated by the comparison with the existing method.(3)In this section,we investigate the single-valued neutrosophic multiple attribute decision making(MADM)problems with preference information on alternatives,some operational laws of single-valued neutrosophic numbers,score function and accuracy function of single-valued neutrosophic numbers are introduced.An optimization model based on the minimum 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 single-valued neutrosophic weighted averaging(SVNWA)operator to aggregate the single-valued neutrosophic 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.The method can sufficiently utilize the objective information,and meet decision makers' subjective preference,can be easily performed on computer.Furthermore,we have extended the above results to interval neutrosophic environment.Finally,an illustrative example for potential evaluation of emerging technology commercialization is given to verify the developed approach and to demonstrate its practicality and effectiveness.