When we consider a production planning problem, there may be many uncertainty factoras and multiple objectives.Fuzzy mathematical programming is a method considering these points, and various method have been proposed.In this paper, we consider the problem where there exists a relationship between variables and coefficients of the object function (for example, when the objective function is the sales, the coefficients, i.e. the prices are affected by production). We deal with the problem where the relationship is linear. In this case, the problem is a fuzzy multiobjective program with quadratic obgective functions. Even if we integrate these multiple objective functions by a certain method, the integrated problem still has multiple quadratic constraints. So it is very difficult to solve this program directly.In this paper, we propose a method for solving this problem. We approximately decompose variables and coefficients of the object function into interval constants, so that we may deal with a linear function.

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This paper introduces the simulation system that helps and suppotrs the parties concerned when they negotiate to make a decision. The negotiation model works by modifying the utility function for a compromise in the decision making process of the utility theory. The simulation method based on the fuzzy decision making is suggested to find out the solution or the compromising point that would satisfy both sides. In principal one party's concessive degree is decided by considering the opposite party's concessive degree and also the adherence to each arrtibyte. To find out the most appropriate concessive rule for a compromise out of a large number of those rules, tuning by genetic algorithm is practiced. And the paper discusses that the fuzzy rule is tuned in pracite by genetic algorithm and then the potimum rule is derived. As a concrete example of the simulation, group car buying decision is dealt with for showing its actual process and the results. All the results suggest that this method is expected to be very efficient in searching for a compromising point to avoid an explosion of combinations of solutions available.

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In this paper, job shop scheduling problems with fuzzy duedate and fuzzy processing time are formulated and a genetic algorithm which is suitable for solving the formulated problems is proposed. On the basis of the agreement index of fuzzy duedate and fuzzy completion time, the formulated fuzzy job shop scheduling problems are interpreted so as to maximize the minimum afreement index. For solving the formulated fuzzy job shop scheduling problems, a genetic algorithm is proposed ny incorporating the concept of similarity among individuals into the genetic algorithms using the Gantt chart. As illustrative numerical examples, both 6×6 and 10×10 job shop scheduling problems with fuzzy duedate and fuzzy processing time are considered, and the feasibility and effectiveness of the proposed method are demonstrated.

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The solid transportation problem(STP) is an extension of the classical transportation problem and often arises in public distruibution systems. In real-world situation, due to the complexity of the social and economic environment as well as some unpredictable factors such as weather, a common problem is the difficulty for determining the proper values of model parameters. One way of handing such uncertainty in decision making envirovement is fuzzy mathematical programming.In this paper, we propose the improvement of genetic algorithm which combine with the integral valed based on ranking fuzzy numbers method and transaction of competitive objectives. The proposed algorithm is incorporated with problem-specific knowledge and conductive to find out a set of Pareto optimal solutions in the criteria space based on decision maker degree of optimism. Finally, the computer simulation results show that the proposed algotithm is efficient for solving the fuzzy multiobjective STP.

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In this paper, we examine two kinds of voting schemes in fuzzy-rule-based classification systems. One is based on the voting by multiple fuzzy if-then rules in a single fuzzy classification system. The other is based on the voting by multiple fuzzy classification systems. First we describe the voting by multiple fuzzy if-then rules, which is used for the fuzzy reasoning in a single fuzzy-rule-based classification system. We also explain how the grade of certainty of each fuzzy if-then rule can be adjusted when the voting by fuzzy if-then rules is used for the fuzzy reasoning. Then we describe three voting methods for combining the classification results of multiple fuzzy classification systems : a perfect unison rule, a majority rule and a weighted voting rule. By computer simulations on real-world pattern classification problems such as iris data, appendicitis date and cancer date, we examine the performance of these voting methods. Simulation results show that the performance of the voting by multiple fuzzy classification systems is better than that of each individual classification system. The performance of the voting by multiple fuzzy classification systems is also compared with various results of other classification methods reported in the literature.

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A method for estimating and/or predicting the human psychological respones to the other different audio noise in the case of listening to an audio signal is proposed by using the fuzzy sets theory. Concretely, when the persons listening to an audio signal are exposed to the other external audio noise, the fuzzy relation between the sound pressure level of an audio signal and that of the other different audio noise is approximately given by the uni-variate membership function, the support of which is the signal to noise ratio.Next, a method for evaluating the psychological respones is proposed by using the concept of the fuzzy probability.Finally, the validity and the applicability of the proposed method are confirmed experimentally by applying it to the actually abserved data. The experimental results are good agreement with the theory.

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This paper describes an application of fuzzy logic control to nonlinear finite element analysis for hyper-elastic rubber-like materials. Since the accuracy and stability of the calculation and time consumption of the computer are largely affected according to increment parameters in the modelused in this kind of analysis, interpretation of the expertise and skill of a humman operator are frequently needed to perform the calculation process. Several parameters such as increments of contact force, etc. are modified by the fuzzy logic algorithm evaluating the results of analysis in each step of the calculation. In this paper, a concept of the caluculation analysis control is shownusing a simple model in which incorporates a pseudodamping force to stabilize the calculation performance, and a s an example, the present method is successfully applied to a rubber structure for the water seal of a dam gate.

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A model of residents' subjective evaluation for urban environment in Tokyo is developed. The model forms a two-level structure. The lower level model is a linear regression model that predicts the modes of subjective values of items of evaluation, such as sanitation or comfort, based on measurements of physical variables. The upper level model is a fuzzy model which aggregates the predicted values of items of evaluation to estimate comprehensive evaluation for urban invironment. Here, to take into accout local individualities, the area of Tokyo is partitioned into several local areas by a clustering for physical data, and the Choquet integral models are developed for individual local areas. The premise parts of the fuzzy model are constructed by using the clustering information, and the consequence parts are the respective Choquet integral models. The fuzzy measures in the Choquet integral models are identified by the convex quadratic programming techique and examined from the viewpoint of local individualities. The research is aimed at predicting comprehensive evaluation itself, and at the same time, structuring comprehensive evaluation of residents.

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From the viewpoint of practical reliability assurance, we often need to predict lifetimes, even when we do not have enough data during infant life. The authors propose a new method which utilizes experts' knowledge with a fuzzy reasoning, and study the prediction errors using failure date in accordance with the Weibull distribution.As a result, they show that the proposed method enables us to infer lifetimes based on one or a few infant life data without likelihood functions. Another new hybrid method which combines the fuzzy reasoning method with the maximum likelihood method is also proposed.

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