Various fuzzy logics in fuzzy set theory are proposed up to now. We study one of fuzzy logics called Kleene's fuzzy logic. Kleene's fuzzy logic is reperesented by Kleene algebra and its generalization is DeMorgan algebra. In this paper, we research on the mathematical properties of Kleene algebra and DeMorgan algebra with centers.

View full abstract

In recent studies about fuzzy modeling, numerous automatic modeling attempts following all qualifications for precision, number of rules and learning times using neural networks have been made. Specifically, a fuzzy modeling using neural netowork deleting rules in learning and a fuzzy modeling with iterative generation mechanism of fuzzy inference rules are wellknown for showing good characters. This paper suggests generalization methods combing them of getting a fuzzy reasoning that have best number of rules after tuning and deleting rules and shows validity to it in numerical examples and in appilcation to the obstacle avoidance.

View full abstract

In this paper, possibilistic linear programming problems with possibility distribution coefficient are discussed. In these problems, uncertainety is included in each coefficient, so evaluation methods for the optimality are required. The evaluation methods have been proposed based on possibilty and necessity measures in conventional researches. But, the coefficients of an objective function have been treated independently as fuzzy numbers or intervals, therefore, the relation among each coefficient has not been considered. In this paper, the relation among coefficients with uncertainty is represented by a normal possiblity distribution. And two algorithms for the evaluations are proposed, which are shown to be deduced to quadratic and linear programming problems. Finally numerical examples are shown to demonstrate our algorithms.

View full abstract

In this paper, we formulate a new fuzzy integral of vector valued functinos. First, the map Φ : R^n→R characterizing any multi linear utility function is extended to the map Φ : V^n→R preserving Φ's properties. The extended map Φ is expressed as the canonical inner product between the direct sum of alternating tensor spaces, [○!+]^n_<γ=1>A^γ(V), and the direct sum of their dual spaces, [○!+]^n_<γ=1>A^γ(V^*). Naturally, the map Φ is identified with the Lebesgue integral representation because any measurable function and any measure can be defined by an element of [○!+]^n_<γ=1>A^γ(V) and an element of [○!+]^n_<γ=1>A^γ(V^*), respectively. Next, any such measure is expressed by a fuzzy measure derived from the map Φ because it is a monotone increasing function for each real variable. Consequently, this Lebesgue integral can be considered as an integral with respect to a fuzzy measure.

View full abstract

In this paper, by considering the experts' imprecise or fuzzy understanding of the nature of the parameters in the problem-formulation process, large-scale multiobjective block-angular linear programming problems involving fuzzy numbers are formulated. Through the use of the α-level sets of fuzzy numbers, an extended Pareto optimality concept, called the α-Pareto optimality is introduced. To generate a candidate for the satificing solution which is also α-Pareto optimal, decision maker is asked to specify the degree α and the reference objective values. It is shown that the corresponding α-Pareto optimal solution can be easily obtained by solving the minimax problems for which the Dantzig-Wolfe decomposition method is applicable. Then a linear programming-based interactive decision-making method for deriving a satisficing solution for the decision maker efficiently from an α-Pareto optimal solution set is presented.

View full abstract

In the shop of manufacturing industry, demands of market fluctuates heavily. So we must adjust distribution of workers according to the work load every month. That is, we must fill up a lack of manpower by overtime works and holiday attendace. This problem is usually formulated as a multiobjective integer programming. But, generally speaking, this formulation is intractable to solve the problem in the sense that its soltion procedure becomes complex and comparing suboptimal solutions with optimal solutinos are difficult. In turn this paper makes up the model based on the membership function of fuzzy sets, proposes a solution procedure, and clarifies its efficiency.

View full abstract

In the shop of manufacturing industry, demands of market fluctuates heavily.So we must adjust distribution of workers according to the work load every month.So we must fill up a lack of manpower by overtime works and holiday attendance. This problem is usually formulated as a multi objective integer programming. But, generally speaking, this formulation is intractable to solve the problem in the sense that its solution procedure becomes complex and comparing suboptimal solutions with optimal solutins are difficult. In turn this paper makes up the model based on the membership function of corresponding to the distribution ratio between regular workers and parttime workers, proposes a solutin procedure, and clarifies its efficiency.

View full abstract

The process of teaching-learning is generally divided into three phases of planning, executino and evaluation.Evaluation is the phase at which the learners' attainment of the learning objective, the teacher's teaching plan and its execution and others are evaluated. This phase requires a method mainly of analyzing the attainment order of test items on the basis of the learners' response patterns in the test items.So far we have developed the FIRS(Fuzzy Item Relational Structure) analysis by which the learning traits of respective learners and groups, as well as the common trait of the whole class, can be analyzed, with the data on the marks obtained in the test items having a value of [0,1]. In the present paper we give a short description of the FIRS analysis and then discuss in detail Procedure 2 in which a matrix of the learners' attainment order is calculated on the set of test items. Since the results obtained in the procedure may have a significant effect on later analysis, we devote an extended discussion to what influence the selection of a main membership function used to calculate the attainment order relation may have on the decision of the attainment order relation.

View full abstract

Most of conventional fuzzy controllers use the input-data-based functional reasoning and the simplified reasoning, so that they can not rationally design any parameter in the conclusion of the fuzzy reasoning by some ways. Therefore, it is not necessarily effective for shortening the computational time and reducing the number of learning parameters to realize such fuzzy reasonings as a fuzzy-neural network.In this paper, a fuzzy-neural network controller is proposed by applying a mean-value-based functional reasoning, in which the mean values are used in constructing a conclusion function when a Gaussian function is applied for the antecedent membership function. Since the initial values of any parameter except for the mean-values in the conclusion can be rationally designed as the parameters, which are independent of the control rules and represent a stable switching plane (or line) in the VSS control, the learning time and the number of learning parameters in the conclusion are shown to be reduced drastically, compared with those due to the input-data-based founctional reasoning and the simplified reasoning, in which the initial parameters in the conclusion depend on the control rules. The effectiveness of the proposed method is illustrated by computer simulations for the tracking control problem of a mobile robot with two independent drive wheels.

View full abstract

The increasing importance of fuel saving and conservation of natural environment in the world has been responsible for a revival of interest in so-called "natural energy". One of the most expected future natural energy is wind power. The wind power system has optimum operating point which extracts available maximum power from generator. Moreover, the wind power varies with time and is sparse. Therefore, the wind power system requires the maximum power point tracking control of generator to obtain electric energy as large as possible.This paper proposes the maximum power point tracing control of wind power system with step-down chopper by using fuzzy control to obtain the maximum output power from generator. This method only uses the output power information, and membership functions consist of duty factor α and output power. Therefore, this control method can track maximum power point without complicated calculatino and mathematical model.

View full abstract

An administrative district is considered a fuzzy set with respect to physical environment. For example, a multiple regression equation for predicting rice yield in Fukushima prefecture should be somewhat applicable to data in Ibaraki prefecture, a neighboring district. This principle yields the weighted least squares, which makes a multiple linear equation effective in predicting rice yield in both Fukushima and Ibaraki. Optimization of the weight using cross-validation substantially enhances the predictability of multiple regression. This method is associated with bias regression such as smoothing spline and ridge regression. However, there are some open problems : definition of fuzzy set in this methodology and applicatino to nonlinear regressino such as neural network.

View full abstract

This paper presents a new control method of a gas convector to make human beings fell comfortable just after the start of heating of a room. The new method controls the amount of overshoot of the room temperature. The fuzzy neural network is applied to acquire the control rules from the experimental data. The obtained control rules fit the feelings of human beings well.The proposed control rules are actually used for the controller of gas convectors.

View full abstract