International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In this paper, we propose a new rule-based method to determine exactly all the widest solution sets of a max-min fuzzy relational equation. As they can be applied to many fields of fuzzy logic, fuzzy relational equations are of great importance; therefore, many researches have been carried out on the subject and many methods have already been proposed to solve the various kinds of fuzzy equations that can be defined, especially the so-called max-min equations. One of the main consequences of the use of the max and min operators is the non uniqueness of the solution. Indeed, when a max-min fuzzy equation has solutions, there are several solutions which can be grouped in intervals. However, most of the existing methods do not enable to calculate the widest solution sets only, often leading to calculate non-maximal solution sets, that is, solution sets included in wider sets. This often results in unnecessary calculations, requiring huge amounts of memory and time. The method we propose here enables to determine rapidly all the widest solution sets of a max-min equation, and those sets only. The use of symbol-valued matrices enables to define simple rules and makes the method very simple to apply.

In this paper, a class of fuzzy controllers is considered. The controllers are constructed by applying product-max-COA(Center Of Area) inference method. The membership functions of the antecedence and the consequence are triangular and singelton in shape, respectively. The class of fuzzy controllers can be expressed by an explicit form, i.e. the sum of a linear function and some nonlinear terms. The explicit form of the class of controllers is generalized for multiple inputs. Therefore, by the use of the explicit form, the analysis of the fuzzy control system can be performed with the use of nonlinear control theory.

It is relatively easy to create rough fuzzy rules for a target system. However, it is time-consuming and difficult to fine-tune them for improving their behavior. Meanwhile, in the process of fuzzy inference the defuzzification operation takes most of the inferencing time. In this paper, we propose a fuzzy neural network model which makes it possible to tune fuzzy rules by employing neural networks and reduces the burden of defuzzification operation. In addition, to show the applicability of the proposed model we perform an experiment and present its result.

Based on the Truth Value Flow Inference(TVFI) theory presented by P.Z.Wang, a fuzzy rule P → Q can be denoted as a fuzzy point in the X × Y domain, when a set of rules are given, the fuzzy points are joined together to become a "fuzzy mountain". Such mountain represents the causal relationship between X and Y. This paper describes an adaptation procedure so that the fuzzy mountain can be refined from past examples. Experimental result shows that after learning, the fuzzy relation approaches to the true but unknown causal mapping between X and Y.

A multivalued (fuzzy) recognition system was formulated by Mandal et. al. which is capable of handling various imprecise inputs and provides multiple class choices to any input. In the present article, an application of the recognition system for detecting road-like structures from Indian Remote Sensing satellite (IRS) imagery has been described. The concept of multiple choices of the recognition system is found to be quite useful here. The results are seen to agree well with the geographical maps when various image frames were considered as input.

In the conventional analysis of structural mechanics, the structural behaviour are determined in mathematical functions and based on idealized assumptions. But structural members do not behaviour as the description of the mathematical functions if the system is too complicated. Consequently, we don't have an appropriate methodology and an convenient algorithm to utilize.

If we identify the structural system with a fuzzy model, , where is the fuzzy relation, the procedure of the system identification will be simplified and the model can be quickly constructed 110 matter the style of nonlinear form and the orders.

In this paper, four composition operators (α, β, φ and t) will be used to derive fuzzy relations from given data and then applied to two interesting problems of structural mechanics for illustrating the reliability ty and efficiency of the theory of fuzzy model.

This paper shows that emphatic effects on fuzzy inference results are observed under product-sum-gravity method by using fuzzy control rules whose consequent part is characterized by a membership function whose grades are greater than 1. Suppressive effects are also realized by employing fuzzy control rules whose consequent part is characterized by a negative-valued membership function. It is shown that good control results are obtained by using the fuzzy control rules of emphatic and suppressive types.

This paper presents a new adaptive fuzzy control scheme that is formulated and constructed directly in the control objective space. The idea of the objective-centered for-mulism on the basis of decomposition of closed-loop response profile is clarified first followed by a detailed description of the scheme. Unlike the existing adaptive fuzzy control methods, the rules and the membership functions of the fuzzy controller in the new scheme are fixed and the adaptation is done on the input and output weighting factors of the fuzzy controller. A simulation analysis is conducted to evaluate the controller performance in regulating a structure-varying process, and to illustrate the advantage of the scheme in controlling plants that can not be easily handled by other control approaches.

This paper is devoted to the investigation of commutative implications on a complete lattice L. It is proved that the disjunctive normal form (DNF) of a linguistic composition * is included in the conjunctive normal form (CNF) of that *, i.e., DNF(*) ≤ CNF(*) holds, for a special family of t-norms, t-conorms and negations induced by commutative implications.

This paper presents a fast fuzzy c-means (FCM) clustering algorithm with two layers, which is a mergence of hard clustering and fuzzy clustering. The result of hard clustering is used to initialize the c cluster centers in fuzzy clustering, and then the number of iteration steps is reduced. The application of the proposed algorithm to image segmentation based on the two dimensional histogram is provided to show its computational efficience.

In this paper, the hysteresis characterization in fuzzy spaces is presented by utilizing a fuzzy learning algorithm to generate fuzzy rules automatically from numerical data. The hysteresis phenomenon is first described to analyze its underlying mechanism. Then a fuzzy learning algorithm is presented to learn the hysteresis phenomenon and is used for predicting a simple hysteresis phenomenon. The results of learning are illustrated by mesh plots and input-output relation plots. Furthermore, the dependency of prediction accuracy on the number of fuzzy sets is studied. The method provides a useful tool to model the hysteresis phenomenon in fuzzy spaces.