Paul P. Wang

The lower and upper approximations in a fuzzy group

In this paper, we first point out that there are still some incomplete theorems in [11] although some authors have showed several incorrect statements in the literature. We then present the improved versions of the incomplete propositions.

Advances in fuzzy sets, possibility theory, and applications

Fuzzy Set Theory: Past, Present and Future.- Advances in Fuzzy Sets - An Overview.- A Survey of Some Aspects on the Research Work of Fuzzy Topology in China.- Some Properties of Fuzzy Convex Sets.- Non-standard Concepts in Fuzzy Topology.- The Spaces of Fuzzy Probability and Possibility.- An Algebraic System Generalizing the Fuzzy Subsets of a Set.- From the Fuzzy Statistics to the Falling Random Subsets.- On Fuzzy Relations and Partitions.- Fuzzy Set Structure with Strong Implication.- Inference Regions for Fuzzy Propositions.- Fuzzy Tree Grammar and Fuzzy Forest Grammar.- Fuzzy Production Rules: A Learning Methodology.- Decision Support with Fuzzy Production Systems.- Imprecision in Computer Vision.- Fuzzy Programming: Why and How? - Some Hints and Examples.- A Fuzzy, Heuristic, Interactive Approach to the Optimal Network Problem.- Application of Fuzzy Set Theory to Economics.- Use of Fuzzy Logic for Implementing Rule-Based Control of Industrial Processes.- A New Approach to Design of Fuzzy Controller.- Advanced Results on Applications of Fuzzy Switching Functions to Hazard Detection.- The Application of Fuzzy Set Theory to a Risk Analysis Model of Computer Security.- Fuzzy Models of Human Problem Solving.- A Concept of A Fuzzy Ideal for Multicriteria Conflict Resolution.- Appendix I: Fuzzy Set Research in Peoples Republic of China.- Author Index.

Computational Intelligence in Economics and Finance

Due to the ability to handle specific characteristics of economics and finance forecasting problems like e.g. non-linear relationships, behavioral changes, or knowledge-based domain segmentation, we have recently witnessed a phenomenal growth of the application of computational intelligence methodologies in this field. In this volume, Chen and Wang collected not just works on traditional computational intelligence approaches like fuzzy logic, neural networks, and genetic algorithms, but also examples for more recent technologies like e.g. rough sets, support vector machines, wavelets, or ant algorithms. After an introductory chapter with a structural description of all the methodologies, the subsequent parts describe novel applications of these to typical economics and finance problems like business forecasting, currency crisis discrimination, foreign exchange markets, or stock markets behavior.

Idle Channel Noise of Delta Modulation

The basic properties of idle channel noise in a delta modulation (Delta M) system are determined. Analytical results are used to predict the noise waveform that the decoder will receive as well as the power level of the received noise. Experimental and computational results are in good agreement.

An Absolute Stability Criterion for Delta Modulation

This paper concerns the absolute stability problem of the delta modulation system via the Popov-Tsypkin stability theorems for nonlinear sampled-data systems. Emphasis has been placed on the stability criterion for a speech communication system using the delta modulation technique where the system contains a reshaping network.

Soft modeling for a certain class of intelligent and complex systems

Abstract This paper proposes a three-level hierarchical mathematical model for intelligent and complex systems. Motivation, background, rationale, interpretations and potential applications are presented. Different visions from different schools of thought in various academic disciplines are illustrated in a block diagram. The concept of “soft-modeling”, representing a dramatic departure from conventional mathematical modeling, is also proposed. The characteristics, approach, types of mathematics used and the interpretations that will eventually lead to engineering realization and commercialization are also presented.

A bi-directional fuzzy logic theory: the generalized Knuth's triadic logic for information retrieval

Abs0-u-tandard logic only deals with true and false, i.e. (0, 1). Zadeh discovered a type of logic that can contain values in (0, 11 which is called fuzzy logic today. On the other hand, the many-valued logic was first studied by Lukasiewicz. He created a so-called triadic logic by adding a 1/2 into the binary set (0, 1). Knuth modified Lukasiewiczs triadic logic to {-1, 0, +1) rather than Lukasiewiczs (0, 1/2, 1). This paper will combine Fuzzy logic with Knuths {-1, 0, +l}, and focus on developing a bidirectional fuzzy logic theory applied to information retrieval with expert relevance feedback and document relevance computing.

On Pattern Recognition and Quality Control

The application of pattern recognition to quality control is shown. The well-known methodology of conventional quality control is described briefly to illustrate the philosophy of quality measurement. The advantages of adopting the pattern classification approach in quality control (or quality assurance) include on-line quality monitoring without much alteration of existing conventional systems, instant diagnosis of the production process, and ultimately, automatic feedback control of the overall manufacturing process through the development of a corrective control policy.

The optimality of variable sampling schemes for a digital encoder

Regardless of simplicity in both structure and hardware, conventional digital modulators such as delta modulation and its modified forms, etc., have not yet been proven efficient. This is primarily due to the large magnitude of the resultant quantized noise. This paper, by invoking the maximum principle of Pontryagin, presents a novel digital encoder with variable sampling. The design criteria chosen is minimization of integrated quantized noise power since the major challenge for an efficient digital modulator is reduction of quantized noise. As it turns out, the resultant optimal systems can be identified from the discrete control systems point of view as belonging to the second type of PFM (pulse frequency modulation). Several possible implementations of the systems are suggested and the expected quality of performance is also discussed and predicted. Finally, the comparison of the optimal system with the conventional existing system is included for immediate reference.

On the evaluation of the parameters of a nonlinear system

Diamessis proposed a new method for evaluating the parameters of a nonlinear system by successive integration with different upper limits of time. In this letter, a different approach is taken which makes use of the invalidity of the superposition property of the nonlinear system by varying the amplitudes of the input function.