Research On The Ranking Relation Of Interval Number And Its Application In The Multiattribute Decision Making Of Interval Fuzzy Preference Relation

Multi-attribute decision making problem exists universally in human daily life and affects human’s daily life.Everyone has to make decisions,but with the progress of scientific social environment and technology,human thinking has decision-making problems become more and more complex.Decision making under uncertain environment is a hot topic in decision making,and it is widely used in management,economy,management and military fields.In the existing uncertain decision theory,some decision methods have weaknesses such as the resulting in the contradiction between the ranking result and the preference of the decision maker,which is the result of the decision information that do not keep the consistency in the decision process.Based on this,this paper has carried out a series of research on the ranking decision method of interval number,which has very important practical significance.This paper mainly studies the following two contents:(1)Under the uncertain decision problems,there is a kind of information expressed by interval numbers.Therefore,it is necessary to give a feasible ranking method of interval numbers.The common method is to use the possibility formula of interval number to compare the interval number in pairs,to construct the fuzzy preference relationship,and then to rank the interval numbers.In general,the constructed fuzzy preference relation cannot maintain(additive,multiplicative)consistency,so the commonly used processing method is to check whether the fuzzy preference relation has acceptable consistency,if not,adjust the fuzzy preference relation,if it has acceptable consistency,using fuzzy preference relation in the logical relationship between elements and weight optimization model is set up,and then make decisions by solving the optimization model.However,this approach can lead to decision errors(see Example1,2).In order to assurance the consistency of decision-making information,superiority degrees of comparing interval number are proposed in this paper.Then the properties of interval number superiority degrees are studied.It is proved that the fuzzy preference relation constructed by comparing interval numbers in pairs with interval numbers superiority formula is consistent,Another advantage is that this distance difference can be accurately described when comparing distances between multiple interval numbers.Next,we discuss the properties of interval number superiority degree.The fuzzy preference relation is constructed by comparing all interval numbers two by two and using the interval numbers superiority formula.This paper proves that the fuzzy preference relation constructed in this way is consistent,which ensures the consistency of decision information and rationality of decision result.(2)Interval number fuzzy preference relation plays an important role in decision analysis and has a wide range of application value.Faced with the choice of alternative schemes,the common method is to construct the preference relation of decision maker through pair comparison,and then rank the alternative schemes of preference relation.Because of the superiority of interval number fuzzy preference relation,it is necessary to present a feasible method with consistent interval number fuzzy preference relation has great advantages and convenience in expressing uncertain problems.In the process of decisionmaking,keeping the consistency of decision-making information is the premise of correct decision-making.Generally speaking,the interval number fuzzy preference relationship given by decision-makers is often inconsistent.It is well known that the interval number fuzzy preference inconsistency relation cannot be directly used in decision making.A new consistent interval number fuzzy preference relation is constructed to replace the inconsistent interval number fuzzy preference relation.If the alternative is not correct,it may lead to wrong decisions.This paper proposes an interval number fuzzy preference relation with indirect weak transitivity.It is proved that the additive and product consistent interval number fuzzy preference relations must have indirect weak transitivity,Then two new sorting algorithms are proposed to deal with the differences in inconsistent interval fuzzy preference relationships.Combining the sorting method proposed in comparison with the common sorting method,the effectiveness of the new method is demonstrated.On the basis of theoretical research,some examples of this method are given,and the feasibility of the method is demonstrated.At the same time,the method proposed in this paper is compared with the common methods,and the conclusion is drawn from the decision results.Thus,the advantages of the method proposed in this paper are proved,which can not only keep the consistency of the decision-making process,but also overcome the disadvantage that the general method may cause the ranking results inconsistent with the preference of the decision maker.