Solution Model And Optimal Value Interval Of Interval Number Linear Programming Under Uncertain Environment

The coefficients in traditional linear programming are all determined.In real life,because of the uncertainty and complexity of objective things and the limitation of human knowledge,people often can not give the exact attributes of information,but can only give a range of changes,which results in interval number linear programming.Interval number linear programming is easy to describe,simple and practical,and has attracted wide attention from scholars at home and abroad.With the maturity of interval number linear programming theory,it is gradually applied in management,economy and industry.Firstly,the ranking methods of interval numbers are summarized.Sorting methods are generally di,vided into two categories,one is qualitative method based on ordering relation-ship,the other is quantitative method based on probability or reliability.Compared with order relation,possibility degree can describe the relationship between interval numbers more clearly.By analyzing the definition of possibility degree,two new possibilities are proposed.Secondly,by definite transformation of the interval objective function and the interval constraints,the interval number linear programming problem is transformed into a deterministic linear programming problem whose optimal solution is called the satisfactory solution.Satisfactory solutions are obtained in different ways of deterministic transforma-tion,and the satisfactory solutions obtained by using the newly defined possibility degree for deterministic transformation are improved obviously.Finally,the optimal interval of interval number linear programming is discussed.Although the coefficients of interval number linear programming are not complet.ely determined,they are relatively determined.In this paper,the best and worst optimal values of interval number linear progra.mming are obtained according to the value of coefficients,and then the optimal value interval is obtained.All the optimal values are in the optimal value interval.In practice,it is NP-hard to find the optimal value interval of interval number linear programming with interval equality constraints.