Based on the introduction of some new concepts of semifoasible direction, Feasible Degree (FDl) of semifeasible direction,feasible degree (FD2) of illegal points'belonging to'feasible domain, etc, this paper proposed a new fuzzy method for formulating and evaluating illegal points and three new kinds of evaluation functions and developed a special Hybrid Genetic Algorithm (HGA) with penalty function and gradient direction! search for nonlinear rogramming problems. It uses mutation along the weighted gradient direction as its main operator and uses arithmetic combinatorial crossover only in the later generation process, Simulation of some examples show that this method is effective.

Considering that the demand requirementsare fuzzy demand in each period during the planning horizon, this paper focuses on a novel approach to modelling multi-product aggregate production planning (APP) problems with fuzzy demands and fuzzy capacities. The objective of the problem considered is to minimize the total costs of quadratic production costs and linear inventory holding costs. By means of formulation of fuzzy emand, fuzzy addition and fuzzy equation, the productioninventory balance equation in single stage and dynamic balance equation are formulated as soft equations in terms of a degree of truth, and interpreted as the levels of satisfaction with production and inventory plan in meeting market demands. As a result, the multi-product aggregate production planning problem with fuzzy demands and fuzzy capacities can be modelled into a fuzzy quadratic programming with fuzzy bjective and

ln this paper, a nonsymmetric model for a type of fuzzy nonlinear programming problems with penalty coefficients (FNLP-PC) is proposed. Based on a fuzzy optimal solution set and an optimal decision et, a satisfying solution method and a crisp optimal solution method with a GA for FNLP-PC is developed. Finally, the analysis of simulation results of an actual production problem example are also given.

The current models and methods for PLP are usually restricted on some special types and usually the same type of possibilistic distribution. This paper focuses on linear programming problems with general possibilistic resources (GRPLP) and linear programming problems with general possibilistic objective coe cients (GOPLP). By introducing some new concepts of the largest most possible point, the smallest most possible point, the most optimistic point and the most possible decision, a new approach for formulating possibilistic constraints through general possibilistic resources and a satisfactory solution method will be discussed in this paper. A most possible decision method for GRPLP and a dual approach for GOPLP will be proposed for solving complex industrial decision problems.

Quality function deployment (QFD) is becoming a widely used customer-oriented approach and tool in product design. Taking into account the "nancial factors and uncertainties in the product design process, this paper deals with a fuzzy formulation combined with a genetic-based interactive approach to QFD planning. By introducing new concepts of planned degree, actual achieved degree, actual primary costs required and actual planned costs, two types of fuzzy optimisation models are discussed in this paper. These models consider not only the overall customer satisfaction, but also the enterprise satisfaction with the costs committed to the product. With the interactive approach, the best balance between enterprise satisfaction and overall customer satisfaction can be obtained, and the preferred solutions under di!erent business criteria can be achieved through human}computer nteraction.