Some Applications Of Preference Relation In Decision Analysis

When a decision maker is faced with a specific problem with multiple alternatives and wants to make a choice,it is very important to give preference information of these alternatives.Only after careful and rigorous evaluation of the above information can rational decisions be made.As a kind of matrix,preference relation can express many decision-making information concisely and clearly.It is a very powerful decision-making tool.There are two kinds of preference relations:reciprocal judgment matrix and complementary judgment matrix.This paper mainly studies the following two aspects in turn:(1)Based on indirect weak transitivity,the method to obtain the weights of in-consistent reciprocal judgment matrix schemes is studied.In the process of decision analysis,the reciprocal judgment matrix given by decision-makers is often inconsis-tent.The common methods is to check the acceptable consistency ratio of reciprocal preference relation.If the ratio is less than or equal to 0.1,the reciprocal judgment matrix has acceptable consistency and can be used to calculate the alternative weight vector and rank alternatives.However,these common methods may lead to the con-tradiction between the sorting results and the order of the alternatives described by the original matrix elements.In order to overcome this defect,this paper proposes the indirect weak transitivity of the reciprocal judgment matrix.Based on the indirect weak transitivity,a consistent proxy reciprocal judgment matrix is constructed,which ensures that the priority order of alternatives described by the elements of the proxy reciprocal judgment matrix remains the same with that of alternatives described by the elements of the original reciprocal judgment matrix.More importantly,the proxy matrix is consistent.Therefore,the method to calculate the weight vector based on the proxy reciprocal judgment matrix can reduce the decision failure caused by the orig-inal inconsistent reciprocal judgment matrix method.At the same time,a modified method is proposed to obtain the weights of inconsistent reciprocal judgment matrix based on indirect weak transitivity.This method enhances the general applicability of the method of obtaining the weight of inconsistent reciprocal judgment matrix based on indirect weak transitivity.(2)The complementary judgment matrix based on dominance and its application in interval number comparison are studied.For more than two interval numbers,as long as there are two interval numbers with the same point value but different length,then the advantages and disadvantages of the two interval numbers obtained by com-parison with some possibility degree formulas must be equal,which is not in line with common sense.Moreover,the complementary judgment matrix constructed by the possibility degree formula often does not have consistency.Ranking interval numbers based on the weight vector of the complementary judgment matrix may lead to the contradiction between the ranking result and the order of interval numbers described by the elements of the original matrix.In order to solve this contradiction,this paper puts forward the interval number additive and multiplicative dominance formula re-spectively.By using the additive or multiplicative dominance,we can not only compare the advantages and disadvantages of any two interval numbers more reasonably,but also make the complementary judgment matrix constructed have the additive or mul-tiplicative consistency.The method of calculating the weight through the consistent complementary judgment matrix and further ranking the interval numbers can often ensure the reasonable ranking results.