Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference

verfasst von: Michel Grabisch, Hung T. Nguyen, Elbert A. Walker

Verlag: Springer Netherlands

Buchreihe : Theory and Decision Library

Enthalten in: Professional Book Archive

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Über dieses Buch

With the vision that machines can be rendered smarter, we have witnessed for more than a decade tremendous engineering efforts to implement intelligent sys tems. These attempts involve emulating human reasoning, and researchers have tried to model such reasoning from various points of view. But we know precious little about human reasoning processes, learning mechanisms and the like, and in particular about reasoning with limited, imprecise knowledge. In a sense, intelligent systems are machines which use the most general form of human knowledge together with human reasoning capability to reach decisions. Thus the general problem of reasoning with knowledge is the core of design methodology. The attempt to use human knowledge in its most natural sense, that is, through linguistic descriptions, is novel and controversial. The novelty lies in the recognition of a new type of un certainty, namely fuzziness in natural language, and the controversality lies in the mathematical modeling process. As R. Bellman [7] once said, decision making under uncertainty is one of the attributes of human intelligence. When uncertainty is understood as the impossi bility to predict occurrences of events, the context is familiar to statisticians. As such, efforts to use probability theory as an essential tool for building intelligent systems have been pursued (Pearl [203], Neapolitan [182)). The methodology seems alright if the uncertain knowledge in a given problem can be modeled as probability measures.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

The advance of science and technology is due to the desire to improve existing knowledge and to address new problems that have arisen. At any stage in the history of science, solutions to new problems require new concepts and new tools. Mathematics is called upon to formulate precisely the new concepts involved and to provide the new tools required for solutions. The mathematical theory of probability is a typical example. It serves as the backbone for the theory of statistics. Statistical techniques invade other fields, such as engineering. In engineering problems in which uncertainty is often an important factor, one borrows many statistical techniques, these being the primary body of mathematical tools available for use in uncertainty. The uncertainty involved might be due to errors in measurements, or to the lack of certain and complete knowledge of the system under consideration. But in applying these techniques, one has to be in the domain of applicability of probability theory. The success with problems such as stochastic control, identification of systems, pattern recognition, filtering, and so on, is due to the fact that these areas are assumed to be in the domain of applicability of probability theory. The knowledge that comes from uncertain information is modeled by probability measures, and the techniques are those from statistical decision theory. And it should be noted that the logic used is always the classical two-valued logic.