The Research On Multiple Criteria Group Decision-making Methods Based On Probability Multi-valued Neutrosophic Sets

Multi-criteria decision-making is widely used in politics,economy,culture,society,ecology and other aspects.Because of the uncertainty and fuzziness in the decision-making process,it is difficult for decision-makers to give quantitative or qualitative information accurately,so the fuzzy multi-criteria decision-making problems appears.Fuzzy sets emerge at the historic moment,which provides a reliable expression of mathematical information for multi-criteria decision-making.With the deepening of people's cognition,decisionmaking problems are becoming more and more complicated,leading to the emergence of inconsistent and discontinuous fuzzy information.Besides,decision-makers need to consider more and more factors when giving evaluation values,resulting in the appearance of the hesitancy information reflecting the uncertainty of decision-makers and the probability information reflecting the preference of decision-makers.As a kind of information form combining fuzzy mathematics and probability theory,probability multi-valued neutrosophic sets organically combine neutrosophic sets,hesitant fuzzy sets and probability preference,including three parts: hesitant probabilistic truth-membership degree,hesitant probabilistic indeterminacy-membership degree and hesitant probabilistic falsity-membership degree.It not only reflects the hesitancy degree of decision-makers,but also reflects the preference degree of decision-makers,describing the complex and uncertain information more comprehensively.At present,although the research of probability multi-valued neutrosophic sets has just started,it has been recognized by most experts and scholars,and the research prospect is broad.The existing research is mainly carried out from the basic theory of probability multivalued neutrosophic sets.No matter from the basic theory or method extension,we can conduct in-depth research on probability multi-valued neutrosophic sets to solve the realistic complex decision-making problems.Therefore,in order to enrich the research results of the probability multi-valued neutrosophic sets,this paper mainly studies from the following aspects on the basis of the original research:(1)Considering the outranking relation theory-based methods,this paper studies the multi-criteria group decision making PROMETHEE method based on probability multivalued neutrosophic sets.For this reason,we propose the basic operation rules of probability multi-valued neutrosophic numbers and the probability multi-valued neutrosophic weighted average operator to aggregate the individual decision-maker information.We propose the probability multi-valued neutrosophic generalized distance measure considering the risk attitude of decision-makers to calculate the deviation of any two unequal probability multivalued neutrosophic numbers,which is regarded as the independent variable of the preference function in the PROMETHEE method,so as to calculate the positive flows,negative flows and net flows of the alternatives,and then select the optimal one.(2)Considering the utility theory-based methods,this paper studies the probability multivalued neutrosophic sets-based multi-criteria group decision making ARAS method which considers the relationship between criteria.For this reason,we propose the probability multivalued neutrosophic entropy measure to calculate the expert weight information,and propose the probability multi-valued neutrosophic normalized weighted Bonferroni distance to construct a mathematical model to derive the associated criteria weight information.Furthermore,we propose the probability multi-valued neutrosophic sets-based multi-criteria group decision making ARAS method which considers the relationship between criteria.By comparing the utility function values between the given alternatives and the constructed ideal alternative,we can choose the best alternative.(3)Considering that most decision-makers are bounded rational,this paper studies the probability multi-valued neutrosophic multi-criteria group decision making TODIM method considering prospect theory.For this reason,we use the mathematical model to derive the weight information of experts and criteria,and apply the proposed probability multi-valued neutrosophic generalized distance measure to calculate the dominance degree of pairwise alternatives,so as to obtain the comprehensive ranking,which makes the decision-making closer to the reality.(4)Considering the risk aversion of decision-makers,this paper studies the improved probability multi-valued neutrosophic multi-criteria group decision making MABAC method considering regret theory.For this reason,we propose the probability multi-valued neutrosophic similarity measure to derive experts' weights,and propose the probability multi-valued neutrosophic likelihood which is used to improve the distance measure in traditional MABAC method and to act as the independent variable of perceived utility function in regret theory,so as to select the best alternative through the comparison of overall perceived utility values.This idea not only makes up for the shortcomings of traditional MABAC method,but also makes the decision-making results more scientific and reasonable,more in line with the reality.