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In the evolution of scientific theories, concern with uncertainty is almost invariably a concomitant of maturation. This is certainly true of the evolution· of physics, economics, operations research, communication sciences, and a host of other fields. And it is true of what has been happening more recently in the area of artificial intelligence, most notably in the development of theories relating to the management of uncertainty in knowledge-based systems. In science, it is traditional to deal with uncertainty through the use of probability theory. In recent years, however, it has become increasingly clear that there are some important facets of uncertainty which do not lend themselves to analysis by classical probability-based methods. One such facet is that of lexical elasticity, which relates to the fuzziness of words in natural languages. As a case in point, even a simple relation X, Y, and Z, expressed as if X is small and Y is very large then between Z is not very small, does not lend itself to a simple interpretation within the framework of probability theory by reason of the lexical elasticity of the predicates small and large.

Inhaltsverzeichnis

Frontmatter

1. Measures of Possibility and Fuzzy Sets

Abstract
The material in this book is based on a nontraditional approach to the imprecise and the uncertain. The basic concept is the measure of possibility. The object of this introduction is to provide motivation and context, to define measures of possibility, and to present basic notions necessary for understanding the later chapters. It appeals considerably to results contained in the authors’ theses [3, 24], among other references.
Didier Dubois, Henri Prade

2. The Calculus of Fuzzy Quantities

Abstract
This chapter gives methods of calculation for expressions containing imprecise quantities, represented by possibility distributions on the real numbers. These methods are in complete agreement with what is commonly called interval analysis, of which they constitute an extension to the case of weighted intervals. Their usefulness is illustrated by some examples at the end of the chapter. Moreover, fuzzy quantities will enter extensively in Chapters 3, 5, and 6. In essence, the calculus of fuzzy quantities constitutes a refinement of sensitivity analysis, which thereby acquires nuance, and this without great increase in the amount of calculation required. The calculus of fuzzy quantities can replace the calculus of random functions (cf. Papoulis [21]) when this proves too intractable, though of course with more or less loss of information according to the type of problem. A more detailed account of the theoretical part of this chapter may be found in Ref. 27. An introductory text is Ref. 28.
Didier Dubois, Henri Prade

3. The Use of Fuzzy Sets for the Evaluation and Ranking of Objects

Abstract
In an article that has since become a classic [4], Bellman and Zadeh proposed the theory of fuzzy sets as a conceptual framework for problems of choice with multiple criteria. The main contribution of that article was to emphasize that objectives and constraints can be represented by fuzzy sets which subsume elements of subjective preference. In this framework, the aggregation of criteria can be viewed as a problem of combining fuzzy sets by means of fuzzy set-theoretic operations. A number of articles—among which we may cite Fung and Fu [14], Yager [31, 33, 34], Zimmerman and Zysno [35, 36, 37], and Dubois and Prade [7, 11]—have been concerned with the axiomatic or practical determination of these aggregative operations. This question is the subject of the first part of this chapter, which summarizes a more detailed survey [38].
Didier Dubois, Henri Prade

4. Models for Approximate Reasoning in Expert Systems

Abstract
In the expert systems of artificial intelligence, the facts and/or the rules to be represented may often be uncertain or imprecise.
Didier Dubois, Henri Prade

5. Heuristic Search in an Imprecise Environment, and Fuzzy Programming

Abstract
The aim of artificial intelligence is to mimic, by machine, operations that the human mind can readily achieve, though we may not know exactly how. For example, understanding messages, making plans of action, analyzing situations, adapting a general mode of behavior to particular circumstances…. In all these activities the human being may have to take account of imprecise and uncertain information. However, this aspect of human intelligence has hitherto been relatively little studied in artificial intelligence.
Didier Dubois, Henri Prade

6. Handling Incomplete or Uncertain Data and Vague Queries in Database Applications

Abstract
One often has to handle data that are far from precise and certain. In fact, the value of an attribute of an object may be completely unknown, incompletely known (i.e., only a subset of possible values of the attribute is known), or uncertain (e.g., a probability or possibility distribution for its value is known). In addition, the attribute may not be applicable to some of the objects being considered and, in certain cases, we may not know whether the value even exists, or whether it is simply not known.
Didier Dubois, Henri Prade

Backmatter

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