Research On Metric And Aggregation Operators On Several Classes Of Neutrosophic Set

As a generalization of fuzzy set,neutrosophic set can accurately describe the uncertainty,inconsistent and discontinuous information.It has been widely used in pattern classification,decision analysis,medical diagnosis,ecological assessment,personnel assessment,and many other fields.Metric is an important topic in fuzzy theory including distance,entropy,similarity measure,correlation coefficient,and so on.Multiple attribute decision making is an important topic of the modern decision-making theory.The method of aggregation operators is important to deal with multiple attribute decision making.In the framework of neutrosophic sets,it is necessary for the researchers to study the theory of metric and aggregation operators urgently.In view of this,the dissertation systematically studies the metric and aggregation operators of the neutrosophic sets,and applies them to the decision making problems.The main work of this dissertation is as follows:1.A new method to construct entropy and similarity measure of interval-valued neutrosophic setsInterval-valued neutrosophic set(INS)is designed for some uncertain situations in which each element has different truth-membership function,indeterminacy-membership function and falsity-membership function and permits the functions to be expressed by interval values.Under the environment of INS,we give the formulas of entropy and similarity measure of interval-valued neutrosophic sets(INSs).First,we construct two single valued neutrosophic sets(SVNSs)by a known INS,and use the similarity measure of the two SVNSs to define the entropy of INS and give an example to show the effectiveness of the proposed method.Then we use two known INSs to construct a new INS,and propose a method to calculate similarity measure between the two INSs based on entropy of the new one.Finally,we apply the proposed similarity measure to the medical diagnosis problem and obtain the reasonable decision.The result shows that our method is effective and reasonable.The special construction methods reflect the relationship between entropy and similarity measure and give a new research method of entropy and similarity measure.2.Power aggregation operators of single valued neutrosophic sets and their use in multiattribute group decision makingThe SVNS is designed for some practical situations in which each element has truthmembership function,indeterminacy-membership function and falsity-membership function and these functions are expressed by exact numbers.In the framework of SVNS,we propose four kinds of power weighted operators and present some useful properties of these operators and discuss the relationships among them.Then,an approach to multi-attribute group decision making(MAGDM)is proposed by the above aggregation operators.Moreover,the developed method is applied to the investment problem,and consult is given to the decision-making person.Finally,some comparisons with other methods are made.The results show that our approach is effective in dealing with uncertain decision making problems.3.Correlated aggregation operators of single valued neutrosophic sets and their application in multi-attribute group decision makingUnder the environment of the SVNSs,the attributes are not independent,but exist correlations of each other which increase the difficulty of decision making.Correlated aggregation operators are an effective tool to solve the above problem.The fuzzy measure and Choquet integral are two important tools to construct the correlated aggregation operators.In view of the correlations among the decision information,we propose the single valued neutrosophic correlated averaging(SVNCA)aggregation operator and the single valued neutrosophic correlated geometric(SVNCG)aggregation operator,and further study their properties.Then,an approach of MAGDM is developed by the proposed aggregation operators.Finally,the developed approach is applied to the investment problem,and the result shows the validity and effectiveness of the proposed correlated aggregation operators in dealing with uncertain decision making problems.4.Hybrid aggregation operators of single valued neutrosophic hesitant sets and their application in multi-attribute decision makingThe single valued neutrosophic hesitant set(SVNHS)is a combination of SVNS and hesitant fuzzy set(HFS)that is designed for some incomplete,uncertain and inconsistent situations in which each element has a few different values designed by truth-membershiphesitant function,indeterminacy-membership-hesitant function and falsity-membershiphesitant function.Under the environment of SVNHS,based on the score function,accuracy function and certainty function of SVNHS,we give the laws to compare different SVNHSs.Then,we propose the ordered weighted aggregation operators and hybrid weightedaggregation operators and study their properties.Furthermore,a method of MADM is developed by the proposed hybrid aggregation operators.Finally,we use the method to the software evaluation,and the result shows that our approach is reasonable and effective.