Set Pair Analysis Apply In Multiple Attribute Decision Making Problems

With the improvement of fuzziness and comprehensiveness of multi-attribute problems,it is more and more difficult to solve multi-attribute decision-making problems by using scientific and reasonable decision-making methods.Solving multi-attribute decision-making problems and improving decision-making benefits have important practical significance.Based on this,the paper expounds the development history of multi-attribute decision-making problems,describes some progress made by relevant scholars,and analyses the feasibility of set pair analysis for solving multi-attribute decision-making problems.Based on this,a multi-attribute decision-making model with connection number and Fisher optimal partition method is proposed to determine the optimal reservoir normal water level scheme,and a multi-attribute dynamic decision-making model with subtraction set pair potential is proposed to optimize the construction scheme of water conservancy projects with time dimension.The following achievements have been achieved in this paper:(1)The Fisher optimal partition method is used to determine the grade partition number of a single decision-making index and the threshold of the standard partition.The relevant theory of set pair analysis is used to select the appropriate ternary connection number to optimize the scheme of normal reservoir water level.The decision-making method given in this paper is reasonable and reliable in the division of decision-making grade and the determination of decision-making grade standard threshold.The decision-making results obtained are scientific and effective.(2)The decision-making results of CNF-MADM model are consistent with those of TOPSIS method,and there are some local differences.CNF-MADM decision model can solve the problem of "reverse order" in TOPSIS method,and make the decision result scientific and effective.(3)The decision results obtained by CNF-MADM model are consistent with those obtained by traditional set pair analysis,and there are local differences.CNF-MADM decision-making model can solve the problem that the traditional set pair analysis method is difficult to determine the coefficient of difference,which leads to the fluctuation of decision-making results,making the decision-making results scientific and effective.(4)Using the weights of the decision-making indexes of Monte Carlo stochastic simulation,the results of 20 000 stochastic simulations show that the probability that alternative 4 becomes the optimal scheme is 84.7%,and that alternative 5 becomes the optimal scheme is 15.3%.It shows that alternative 4(normal storage level is 608 m)has a better ability to determine the final reservoir normal storage level.High reliability and stability.(5)On the basis of studying set pair analysis,the adjoint function of connection number is used to solve the dynamic multi-attribute decision-making problem.After recognizing the shortage of pair potential of division set,the pair potential of subtraction set is used to solve the dynamic multi-attribute decision-making problem.The pair potential of subtraction set is applied to the optimization of dynamic hydraulic engineering schemes including time dimension.The results show that the decision results obtained by using subtraction set pair potential in this case are consistent with those obtained by using the mature projection pursuit model.It shows that the application of subtraction set pair potential in dynamic multi-attribute decision-making is feasible,the decision results are scientific and reasonable,and the operation process is simple and easy to implement.In summary,the decision-making model based on set pair analysis can effectively solve the static and dynamic multi-attribute decision-making problems,and the calculation process is concise and operable,which provides some reference for multi-attribute decision-making management.