Optimization Of Interval-valued Functions Based On The Order Relation Of Interval Numbers

The complexity of the environment and the inherent subjective ambiguity of human thinking lead to the fact that the information obtained is often vague and uncertain.Therefore,how to solve the information uncertainty in practical optimization problems has been a difficult problem in modern optimization problems.Interval mathematics provides a relatively simple yet complete way to express the information inaccuracy,making the solution result stay within the required or given accuracy as much as possible.The key to solving the interval-valued optimization problem is to give the appropriate interval number sequence relationship.In this paper,we study the interval-valued optimization problems under three different interval number order relations and try to find the optimal solution of one or more interval-valued optimization problems under the uncertainty of the original information.First,based on the interval number order relations of fuzzy relations,and then considering the derivative nature and convexity of interval-valued functions,this paper further investigates the existence and existence conditions of optimal solutions for interval-valued optimization problems.The validity and accuracy of the given optimization conditions are proved by arithmetic examples.Second,based on the interval number order relationship defined by TOPSIS fuzzy decision model,this paper redefines the optimal solution of the interval-valued optimization problem.Under the newly given definition of optimal solution points,the existence of TOPSIS optimal solution points for interval-valued optimization problems and the corresponding optimization conditions are investigated.Similarly,practical examples are given in this paper,which show that the optimization conditions and conclusions given here are convenient and effective in solving practical problems.Finally,this paper extends the triangular fuzzy number order relation to general fuzzy numbers by combining the properties of fuzzy number intercepts and applying it to solve fuzzy linear programming problems.Compared with the original model,the model is more general,has a wider range of application and is simple to compute.A real investment problem is selected to validate the model,and numerical examples are used to illustrate the effectiveness of the model in practical applications.