Two Kinds Of Fuzzy Programming Model Based On Utility

Along with the increasing of the complexity of modern society,fuzzy programming has become an unavoidable question in many fields,such as the resource allocation,the production planning and optimization decision.It is also the widespread attention research in today’s academic circles and application fields.The fuzzy programming methods at this stage are usually the ones which discuss the optimal value or solution for a certain decision background.However,due to the fact that the fuzzy phenomenon has no clear boundary,the decision demanding is not severe in the processing of fuzziness.And with different consciousness of decision-makers integrated into the problems,the theory optimal solution is likely nonexistent in many practical problems.At this moment,in a certain range of allowable deviation,the solutions are the satisfaction ones in a fuzzy sense.In addition,when processing the programming problem with fuzzy constraints,the condition of decision results meeting the constraints also plays an important role,which reflects the reliability of the decision result to a certain extent.Consequently,the discussion of fuzzy satisfaction solutions and constraints’ comprehensive satisfaction degree in this article has theoretical and realistic significance.For the fuzzy programming problem with fuzzy constraints,we mainly do the following work: 1)at first,for the problems with single fuzzy constraint,we give its basic model,and analyze the characteristics and disadvantages of two common methods.Then we propose a satisfactory decision criterion,and give a quantification strategy to describe the decision consciousness(that is the level utility function).Based on this function and the fuzzy statistics,we establish a representation method of utility frequency and a fuzzy programming model based on utility frequency(denoted by BUF-FPM).Finally,combined with a concrete case,we analyze the feasibility of this method.2)When the quantity of decision variables and fuzzy constraints increases,there may be some function relationships among different variables.For this situation,we establish a computation model of comprehensive satisfaction degree which can balance the constraints’ weights.Then under the new decision environment determined by the above model,we can conduct the second stage programming.That is the two-stage fuzzy programming model based on the comprehensive satisfaction degree(denoted by BCSD-TFPM).After that,we make a further discussion of the feasible region embodied in triangular fuzzy number.Theoretical analysis and practical calculation results show that the proposed models has good structure,and can enrich the existing fuzzy programming theory and methods to a certain extent.