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A Quantitative Approach to Approximate Reasoning in Rule-based Expert Systems

  • Chapter
Expert System Applications

Part of the book series: Symbolic Computation ((1064))

Abstract

This paper is divided in two main parts. The first one deals with the modeling of uncertainty and imprecision, while the second one is devoted to deductive inferences and to the problem of combining items of information, in case of imprecision or uncertainty. Together with probability, different kinds of uncertainty measures (credibility and plausibility functions in the sense of Shafer, possibility measures in the sense of Zadeh and the dual measures of necessity) are introduced in a unified way. The more empirical proposal used in the MYCIN expert system for dealing with uncertainty is also closely considered. The modeling of imprecise or vague information by means of possibility distributions is presented. The relation between imprecision and uncertainty in terms of possibility and necessity is also discussed as well as the notion of a degree of truth and the truth-qualification of propositions. Then, in the framework of possibility theory the representation of imprecise or fuzzy “if ..., then ...” rules and their processing by means of a generalized modus ponens are studied in detail. The particular case of uncertain rules is addressed in the same setting, and some default reasoning issues are considered. Different problems of reasoning which are specific of the treatment of uncertain information, without being dependent on a particular approach, are pointed out. In particular, it is shown that the combination of uncertain or imprecise items of information provided by different reliable sources, is not always suitable. Lastly, the Dempster/Shafer rule of combination as well as a possibilistic rule are examined. On the whole a computational approach to approximate reasoning based on recently developed theoretical tools, is proposed.

This paper gathers, develops and unifies results previously presented in other papers by the author (Prade, 1983, 1985c, 1984b, 1985a,b).

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  1. Langages et Systèmes Informatiques, Université Paul Sabatier, 31062, Toulouse Cedex, France

    Henri Prade

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  1. Institute of Computer Science, Polish Academy of Sciences, PKiN, pok. 1050, Warsaw, Poland

    Leonard Bolc

  2. Computing Research Laboratory, New Mexico State University, P.O. Box 30001, Las Cruces, NM, 88003, USA

    Michael J. Coombs

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Prade, H. (1988). A Quantitative Approach to Approximate Reasoning in Rule-based Expert Systems. In: Bolc, L., Coombs, M.J. (eds) Expert System Applications. Symbolic Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83314-4_3

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