A transitive coupling problem discussed by Wakabayashi and Ouchi that arises in the embedding process of their method for fuzzy structural modeling. They also have considered the particular max and min solutions for the problem. The present paper aims at disclosing algebraic structure of the solution set for the problem based on a study of a generalized transitive coupling problem by the authors, whereby the followings are shown : ・the solution set is closed under scalar product, ・the solution set is closed under ∧-, ∨-operations, but not necessarily under ∨-, ∨-operations, ・if the solution set includes a solution which is different from the self-evident solution, the solution set has the carbinal number of continuum.Moreover, considering the relationship between the particular and the general solutions, the authors show that ・the min solutions decide whether the third inequality with α-product plays the role of a substaintial constrain or not, ・the min solutions are extremal in the solution set.

A multiset is a set-like entity which can contain repeated elements. Given a universal set, a multiset may be constructed by selecting elements of the universal set. Moreover an element of the universal set may be selected more than once. For example, let the universal set be X={a, b, c, d}, then A={a, a, b, b, b} is a multiset. the class of ordinary sets can be regarded as a subclass in the class of all multisets. Fuzzy multisets which are also called fuzzy bags have been studied by Yager who defined basic relations of inclusion and equality, and operations of union and intersection. However, his definitions are inappropriate, since the basic relations and operations are inconsistent with the corresponding relations and operations for ordinary fuzzy sets. In this paper, the basic relations of inclusion and equality, and the basic operatoins of union and intersection are newly defined using a grade sequence for each element of the universal set. Appropriateness of the new difinitions is shown by proving consistency with the ordinary fuzzy set relations and operations. Moreover and α-cut for fuzzy multisets is defined and the properties of the commutative law, the associative law, and the distributive law for fuzzy multisets are proved using the α-cut. Possible applications of fuzzy multisets are suggested.

In this paper, taking account of an information retrieval in connection with sensitive information such as fine arts, the authors discuss quantitative verifica-tion of synonymous relations among sensitive words in their thesaurus. For instance, the criticism or apprediation of fine art are often emotiona, subjective, and sensitive so that sensitive words are frequently used as keywords in the informa-tion retrieval. However, because a sensitive word has many complicate and fuzzy synonyms, it is inevitable to control the information retrieval by fuzzy thesaurus. In this paper, regarding a sensitive word as a fuzzy set of stimula-ting events, the authors formulate the experimental method to quantify the fuzzy synonymous relations among sensitive words by "a membership function" and "a coefficient of the synonymous relation". The characteristics of this method is to cellect subjective's reaction of sensitive workds to a series of stimulating events, and analyze those data to estimate the fuzzy synonymous relation among sensitive words. The results contributes to the fuzzy synonymous thesaurus of sensitive words to the sensitive information retrieval of a fuzzy database.

Ultrasonic motor is a new type motor and it has an excellent performance and many useful features. Its simplified mathematical model, has not been developed yet. Moreover, its speed characteristics vary with driving conditions. Therefore, it is important to identify the speed characteristics of ultrasonic motor on-line in order to achieve the high-performance control. In this paper, the authors dervie a mathematical model of ultrasonic motor and propose position control based on the model using adaptive control. Moreover, we propose precise position control of ultrasonic motor using on-line parameter identification algorithm (recursively least square method : RLSM) with variable forgetting factor based on fuzzy reasoning. The effectiveness of proposed control scheme is demonstrated by experiments.

The addition of adaptive functions into fuzzy control and the introduction of fuzzy adaptive law of adjustment of parameters into adaptive control are being done in the scope of the fuzzy adaptive control system. In this paper, firstly, we deal with the control rule from operator's point of view, experience and so on as a fixed control rule. Next, this paper proposes the Fuzzy Adaptive Control System (FACS) with predictive control which adapts to changes due to plant dynamics and external condition. Finally, a computer simulation of a road train drive control confirmed that the proposed FACS was effective.

In the previous paper, we proposed a digital acceleration control method for trajectory control of robot manipulator from a basic view point for motion process. However, there has been practical difficulties for the direct measurement of the velocity and acceleration of the robot manipulator. In this paper, we propose an estimating method of them based on fuzzy reasoning. A serial-drive robot manipulator is taken as an example to show the effectiveness of the proposed method.

A GA-based technique for reconstructing plane binary images from a minimal number of projections is presented ;its effectiveness is demonstrated by reconstructing two-dimensional objects from their one-dimensional coded images. The algorithm gets projection data from three different angles. An initial population of strings, each of which contains encoding of an image, is generated randomly. Typical as well as some new genetic operations are performed on every generation of a population to produce a new generation. Results obtained are compared to those obtained by one of the well known iterative algebraic reconstruction techniques, and it was found that the proposed evolutionary method is superior to the algebraic method when the number of projection directions is limited to three.

For generating or tuning fuzzy rules Gaussian-type membership functions in a fuzzy system model, it is well known to adopt the Neuro-Fuzzyl learning algorithm based on Gradient-descent method. In the learning algorithm, however, the number of tuning parameters increases quickly, as the number of input variables increases. Moreover, the representatoin of fuzzy rules after learning in the form of fuzzy rule table becomes difficult and the case of weak-firing occurs. In this paper, we propose a new learning approach for generating or tuning fuzzy rules, in order to improve the above problems. Further, we compare it with the conventional method several identified functions, and show that the proposed method is a useful tool for learning a fuzzy system model.

In some systems which involve human beings, such as management systems or social systems, there are cases that we have to treat the data including the haman vagueness. In this paper, these data are treated as fuzzy data, and its probabilities of occurrence are defined by membership functions and statistical models using the definition of Zadeh's probability of fuzzy events. As, also, a ariterion to select a statistical model, AIC (Akaike's Information Criterion) has been defined. However, we cannot obtain AIC directly for a statistical model using fuzzy data. In this papaer, we propose a method to method to select a proper statistical model using AIC from fuzzy data. Using this method, we can select a proper statistical model by selecting a proper distribution model for fuzzy data, and the method extends the area of application of AIC. Furthermore, to investigate the usefulness, our method is applied to the selection problems of parameters of normal distributions, and its usefulness is illustrated using computer simulation.

This paper focuses on behavior of system included personnel required as a constitutent elements and considers the dynamics of the system as the self-organization process in system. This system is constituted in three variables, interaction, cohesion and activity, and is identified as the self-organization model using non-linear differential equations. And this process which indicates the changes in the states of the system is analyzed through attractor by lyapunov spectrum. By considering the dynamics of the self-organization model applying the non-linear deterministic theory, we clarify that the self-organization process indicates chaotic complex behaviors.

Fuzzey Flexible Interpretive Structural Modeling (FISM/Fuzzy) is a fuzzy version of Flexible Interpretive Structural Modeling (FISM). The fuzzy transitive embedding is a problem of how to efficiently fill the fuzzy reachability matrix.To perform the fuzzy transitive embedding logicaly and effectively, a fuzzy partially filled reachability matrix (FPR-matrix) is proposed. While an FISM/fuzzy structural model is being developed, or after it has been developed, the developer may want to make changes in it. Procedure for changing a structural model with computer assistance is called "correction". Correction is key to FISM/fuzzy. This is becase developing a structural model is inherently a trial-and-error process.In this paper a correction theory and algorithm for FRR-matrix is proposed. Use of the algorithm makes it possible to do a flexible and an efficient modeling for complex and fuzzy systems.

The farm planning problem which is related to the whole farm management, in a fact-finding investigation of farm management→data arrangement→making plan→practice and evaluation, plays an improtant role in improving the management. The acientific and/or mathematical method at present however, can not deal with fuzzy logic subjectivity of the decision maker. Therefore, the present method obviously need a logical correction, sure there are many cases of unfitness and unsuitability. In present paper, we asumed that there were many fuzzy logic applications in the natural environment that affected the decision of farm manager. We studied the upland and beef mixed farming to determine if the fuzzy thory could be effectively applied in farm design. Also, we discussed the modeling of the fuzzy possibility problem, one application of fuzzy theory, as a method for the farm planning problem. First, we attempted to estimate the upland and beef mixed farming with a fuzzy problem which was considered in two directions : one is the fuzziness of the desired level for the goal and constraint of the decision maker and the other is the fuzziness of the coefficient of objective function and constraint conditin. Secondly, we discuss the positive analysis of upland beef mixed farming in Ketaka-cho, Tottori, as a concrete example that the fuzzy theory could be applied effectively with the various fuzzy logic applications in the decision making process of farm planning.

This paper focuses on the use of kernel method and projection pursuit regression for non-parametric probability density estimation. Direct application of the kernel method is not able to pick up characteristic features of multidimensional density function. The proposed projection projection pursuit regression method based on the eigen value problem is able to bypass the "curse of dimensionality" in mutidimensional density estimation.

The state vector separation type fuzzy control system of cart-pole system inculdes hard type and soft type. Hard type is a system making the state vector controller of pole system effective in all topological space of pole. As for soft type, this controller works only in the limitted handstand domain and hanging down domain effective for controlling, and 2 domain outside is a system to take in natural behavior of a pole as the non-control area. A problem of hardtype is that useless travelling of a cart is generated so that the controller tries hard in all topological space of pole. A merit of soft type is that useless travelling of a cart is not generated. Because the system stops controlling in an excessive state of work in order to permit naturally behaving of a pole, and performs efficient control for uprising and invertedly stabilizing the pole in limit area.This paper demonstrates effectiveness of soft type system by numerical simulation, and provides design knowledges on soft type fuzzy control system of cart-pole system.

As a kind of learning approach for a fuzzy system model, so-called the self-tuning method of fuzzy rules by Dalta rule proposed by H. Nomura et al. is well known. While the method has high generalization capability, the number of tuning parameters increases quickly for fuzzy system models with multiple-input variables and the shape of the fuzzy rule table is destroyed after the learning. Moreover, sometimes the case of a non-firing occurs for evaluating input data. To improve the above problems, we suggest a new tuning algorithm for learning fuzzy models based on the gradient descent method. In this learning algorithm, the number of tuning parameters is fixed in the learning process and the shape of fuzzy rule table never changes even after the learning. Furthermore, we compare the suggested method with the self-tuning method, and illustrate the efficiency of the suggested method for tuning fuzzy reles by means for several numerical examples.

An optimum decision on a production machine inspection period is difficult because there are some failures and large loss cost for maker, if period is too long, on the other hand there is no economial policy due to many machine stops and inspection labor costs, if the period is short, A model equation on the inspection period is studied in maintainability engineering, but some fuzzy elements as a failure distribution form and a repair time are involved in the model equation. In this paper those fuzzy elements are inferred with fuzzy reasoning, and the optimum inspection period is based on a model equation.

This paper presents a new method to correct color using pigments.The new method uses fuzzy linear programming and computer color matching support system which is used for color matching of ceramics and textures. We can obtain an economic pigments desigin using the new method.Simulations using pigments design datas of ceramics are done to demonstrate the usefulness of the new method.