Solution Of Fuzzy Programming Research Articles

Fuzzy programming method for multi-objective optimal allocation of sediment resources and the cooperative bargaining: a case study in Weishan irrigation area, China.

The optimal allocation of sediment resources needs to balance three objectives including ecological, economic, and social benefits so as to realize sustainable development of sediment resources. This study aims to apply fuzzy programming and bargaining approaches to solve the problem of optimal allocation of sediment resources. Firstly, Pareto-optimal solutions of multi-objective optimization were introduced, and the multi-objective optimal allocation model of sediment resources and fuzzy programming model was constructed. Then, from the perspective of multiplayer cooperation, the optimal allocation model of sediment resources was transformed into a game model by using Nash bargaining, and Nash bargaining solution was obtained as the optimal equilibrium strategy. Finally, the influence of different disagreement utility points and bargaining weights on the results was discussed, and the results of Nash bargaining and fuzzy programming methods were compared and analyzed. Results corroborate that Nash bargaining can achieve the cooperative optimization of multiple objectives with competitive relationship and obtain satisfactory scheme. Disagreement utility points and bargaining weights have a certain impact on the optimization results. The solution of fuzzy programming is close to that of Nash bargaining, which provides different ideas for multi-objective optimization problem.

Fuzzy optimum design of aseismic structures

AbstractIt was pointed out in our previous paper that there exists a vast amount of fuzzy information in both objective and constraint functions of optimum design of structures. Then the idea of fuzzy optimum design of structures was first proposed and the problem with fuzzy allowable intervals of the physical variables (structural responses and sizes) could be solved via the α‐level cut approach.In this paper, the procedure of fuzzy optimum design of aseismic structures is further developed. For this purpose, the concepts and definitions of fuzzy predictive earthquake intensity, fuzzy response spectrum and fuzzy structural response are given. A solution of the programming problems with generalized fuzzy constraints (including both fuzzy constraint functions and their fuzzy allowable intervals) is put forward; one of its special cases is the χ‐level cut solution in Reference 1. The satisfaction degree of a fuzzy constraint function to its fuzzy allowable interval is defined, by which the problem considered is transformed into a series of non‐fuzzy programmings. Then, a series of optimum points can be obtained which make up the solution of the fuzzy programming.As the solution of fuzzy programming contains not one but a series of optimum points, a two‐step approach is presented to the fuzzy optimum design of aseismic structures. The first step is to find out the set of minimum cost design points corresponding to different design levels. In the second step, both construction cost and earthquake‐caused loss expectation in the service life of the structure are traded off to find the optimum design level as well as a corresponding optimum design scheme.