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This paper describes an efficient computational algorithm for evaluating min-max operations and the derivatives of min-max functions, which are common computation problems in the training of many types of fuzzy neural networks. Analysis and simulation are used to assess the efficiency of the computational algorithm developed in this paper.

This is the first of a series of papers on factor space theory and its applications to fuzzy information processing. This paper focuses on the basics of factor spaces such as the meaning, operations of factors, etc. A new axiomatic definition of factor space and the notion of the description frame are given. This is followed by the development of the representation of concepts in a description space. Finally, the notion of factor sufficiency and the atomic factor space are introduced.

In this paper, a constructive theory is developed to establish the fact that we can build a fuzzy system to approximate any continuous function on a compact set within a prescribed error bound. Based on the theory, an algorithm is described that can actually construct a near minimum fuzzy system for a given function to a desired accuracy.

Research under the name of Neural Logic Networks is an attempt to integrate connectionist models and logic reasoning [8, 9]. With a Neural Logic Network, a simple neural network structure with suitable weight(s) can be used to represent a set of flexible operations, which offer increased possibilities in dealing with inference in real-world problem solving. They also possess useful properties in an extended logic system which is called Neural Logic . One of the important features of Neural Logic is that all its operations can be defined and realized by neural networks, which form Neural Logic Networks. As one part of the research on Neural Logic Networks, fuzzy neural logic programming has been proposed [6]. This paper introduces a Prolog-like inference system based on Neural Logic as an implementation of fuzzy neural logic programming. In this system, fuzzy reasoning is executed by the Neural Logic inference engine with incomplete or uncertain knowledge. The framework of the system and its inference mechanism are described.

Inference problems are one of the main research topics in the AI field. So far there have been proposed various inference systems some of which have been applied in various problems according to their feature. In particular, the concepts of inference channel and truth-valued flow inference (TVFI) (Wang, 1988) have been used in building fuzzy inference machines. In this paper, we discuss the basic concepts of TVFI channel lattice, background graph, the confidence degree of channels, and knowledge combination, etc.

This paper presents a novel fuzzy self-tuning PID control scheme for regulating industrial processes. The essential idea of the scheme is to parameterize a Ziegler-Nichols-like tuning formula by a single parameter α, then to use an on-line fuzzy inference mechanism to self-tune the parameter. The fuzzy tuning mechanism, with process output error and error rate as its inputs, adjusts α in such a way that it speeds up the convergence of the process output to a set-point y r , and slows down the divergence trend of the output from y r . A comparative simulation study on various processes, including a second-order process, processes with long dead-time and non-minimum phase processes, shows that the performance of the new scheme improves considerably, in terms of set-point and load disturbance responses, over the PID controllers well-tuned using both the classical Ziegler-Nichols formula and the more recent Refined Ziegler-Nichols formula.

In this paper, we present a detailed discussion on the design of a rule-adaptive fuzzy control system, along with simulation analysis demonstrating its usefulness in controlling plants of various dynamical natures. Conceived first by Wang, and further clarified in [8], the rule-adaptive fuzzy controller considered here generates the fuzzy control signal as a convex combination of the standard fuzzy inputs to the controller, the error and the error rate. Such a combination is automatically adjusted on-line in response to the varying control situations with certain updating scheme. This paper considers two different updating schemes. The first one is based on a fuzzy relationship, and is a revision of the rule presented in [11]. The present paper also proposes the second updating rule that is essentially a nonlinear differential equation. Both of the rules are applied to the simulations of several selected dynamical plants. The simulation results show that the controller is effective in controlling a wide range of dynamical plants. Especially, it shows better performance in controlling the plants found difficult to be controlled by the conventional means. The simulation also shows that the controller can be used to curb the effect of load disturbance in the control process.

By means of an index-represented rule mapping, the response g of a fuzzy controller is decomposed into two parts: f , the classical component and g − f , the nonlinear component, called pad. We intend to analyse the pad in order to know what the relation is between fuzzy and classical PID controllers. Fuzzy controllers mentioned here are defuzzified by the typical center of gravity method. In the 1-input case, we get that f − g = 0, which means that the fuzzy controller is exactly the same as the classical P-controller, whenever the rule mapping is simple (Definition 1.2) and the linguistic values are a binary family (Definition 4.1). In the 2-input case of error and error change for simple rule mapping and for simple linguistic values family (4.7), and perfectly for the WXYZ linguistic values family (Definition 6.1), the fuzzy controller can be viewed as a series connection of a classical PD controller and a 1 + pad-element. The describing function of a 1 + pad-element is very simple and fine, and ensures that such fuzzy controller will be stable if the PD controller is. The similar consequences are also obtained for the case of three inputs.

In this paper, a study of knowledge representation is presented based on factor spaces. Examples are presented to show the applications of factor spaces to the concepts of representation and pattern recognition. Some topics as approximate reasoning are studied also.

A new concept in statistics is presented here, called ‘Set-valued Statistics’, where a trial is a crisp or a fuzzy set. Some propositions concerning mathematical properties are given. The falling-shadow theory related to set-valued statistics is briefly discussed. An important application to the prediction of damage caused by earthquakes shows the efficiency of set-valued statistical data processing techniques. Earthquake-generated damage prediction plays an essential role in plan-making as a preparation for seismic disaster and the result of forecasting the number of severely damaged building structures (due to an expected strong motion in an urban area) by using the falling-shadow Bayes principle depicts good future prospects for its application.