A tentative comparison of numerical approximate reasoning methodologies

doi:10.1016/S0020-7373(87)80026-3

International Journal of Man-Machine Studies

Volume 27, Issues 5–6, 12 November 1987, Pages 717-728

https://doi.org/10.1016/S0020-7373(87)80026-3 Get rights and content

Abstract

A critical discussion of approximate reasoning methods in artificial intelligence is proposed. The focus is on numerical approaches based on certainty factor, probability, possibility or evidence theory. The discussion is organized around three topics, namely knowledge representation, inductive versus deductive reasoning, and control strategies. The aim of the paper is to outline a tentative classification of emerging trends in uncertain reasoning, and to point out problems which are not solved yet or are sometimes overlooked by proponents of a single approach. The style of the paper is concise and assumes some familiarity of the reader with the referenced material.

References (48)

D. Dubois et al.
Ranking fuzzy numbers in the setting of possibility theory
Information Sciences
(1983)
J.H. Kim et al.
A computational model for causal and diagnostic reasoning in inference systems
G. Paass
Consistent evaluation of uncertain reasoning systems
R.R. Yager
Toward a theory of conjunctive variables
L.A. Zadeh
A theory of approximate reasoning
L.A. Zadeh
Syllogistic reasoning in fuzzy logic and its application to usuality and reasoning with dispositions
IEEE Transactions on Systems, Man and Cybernetics
(1985)
Special issue on non monotonie logic
Artificial Intelligence
(1980)
A. Bundy
Incidence calculus: a mechanism for probabilistic reasoning
Journal of Automated Reasoning
(1985)

M. Cayrol et al.

Fuzzy pattern matching

Kybernetes

(1982)

P. Chatalic et al.

An approach to approximate reasoning based on Dempster rule of combination

International Journal of Expert Systems

(1987)

P. Cheeseman

A method of computing generalized Bayesian probability values for expert systems

P.R. Cohen

D. Dubois et al.

Sur divers problèmes inhérents à l’automatisation des raisonnements de sens commun

D. Dubois et al.

Fuzzy logics and the generalized modus ponens revisited

Cybernetics and Systems

(1984)

D. Dubois et al.D. Dubois et al.

D. Dubois. et al.

Recent models of uncertainty and imprecision as a basis for decision theory: towards less normative frameworks

D. Dubois et al.

Possibilistic logic under matrix form

D. Dubois et al.

The principle of minimum specificity as a basis for evidential reasoning

D. Dubois et al.

Fuzzy numbers: an overview

D. Dubois et al.

Necessity measures and the resolution principle

IEEE Transactions Systems, Man and Cybernetics

(1987)

D. Dubois et al.

On incomplete conjunctive information

Cited by (10)

A linear programming framework for logics of uncertainty
1996, Decision Support Systems
Several logics for reasoning under uncertainty distribute “probability mass” over sets in some sense. These include probabilistic logic, Dempster-Shafer theory, other logics based on belief functions, and second-order probabilistic logic. We show that these logics are instances of a certain type of linear programming model, typically with exponentially many variables. We also show how a single linear programming package can implement these logics computationally if one “plugs in” a different column generation subroutine for each logic, although the practicality of this approach has been demonstrated so far only for probabilistic logic.
Bayesian logic
1994, Decision Support Systems
We combine probabilistic logic and Bayesian networks to obtain the advantages of each in what we call Bayesian logic. Like probabilistic logic, it is a theoretically grounded way of representing and reasoning with uncertainty that uses only as much probabilistic information as one has, since it permits one to specify probabilities as intervals rather than precise values. Like Bayesian networks, it can capture conditional independence relations, which are probably our richest source of probabilistic knowledge. The inference problem in Bayesian logic can be solved as a nonlinear program (which becomes a linear program in ordinary probabilistic logic). We show that Benders decomposition, applied to the nonlinear program, allows one to use the same column generation methods in Bayesian logic that are now being used to solve inference problems in probabilistic logic. We also show that if the independence conditions are properly represented, the number of nonlinear constraints grows only linearly with the number of nodes in a large class of networks (rather than exponentially, as in the general case).
Ignorance and uncertainty in reliability reasoning
1992, Microelectronics Reliability
A considerable ignorance is a typical aspect of any industrial reliability knowledge. A suitable reasoning algorithm is needed to evaluate a hypothesis (decision) uncertainty in spite of the massive ignorance. The evaluation of uncertainty in a reasoning path may be divided into two levels. The ‘local level’ concerns the uncertainty of individual knowledge items. The ‘topological level’ concerns the overall uncertainty. We describe here two novel algorithms for dealing with ignorance and/or uncertainty in reliability decision making and reasoning. One is based on an analogy with fluid/electric current flow through a network which is topologically identical to the reasoning path. The second idea is that the more identical knowledge items that are used in the deduction of two differing hypotheses, the closer the certainty values attached to the hypotheses. The final uncertainty associated with a hypothesis can be shown to satisfy Cox's axioms for a probability measure.
Multiple binary decision tree classifiers
1990, Pattern Recognition
Binary decision trees based on nonparametric statistical models of the data provide a solution to difficult decision problems where there are many classes and many available features related in a complex manner. Unfortunately, the technique requires a very large training set and is often limited by the size of the training set rather than by the discriminatory power of the features. This paper demonstrates that higher classification accuracies can be obtained from the same training set by using a combination of decision trees and by reaching a consensus using Dempster and Shafer's theory of evidence.
Commentary: Issues in knowledge-based decision support
1987, International Journal of Man-Machine Studies
Commentary: Cognitive engineering in complex and dynamic worlds
1987, International Journal of Man-Machine Studies

View all citing articles on Scopus

^†: A short and preliminary version of this paper is published in Proceedings of the 7th European Conference on Artificial Intelligence, Brighton, UK. July, 1986, Vol. 2, pp. 171–176.

View full text

A tentative comparison of numerical approximate reasoning methodologies†

Abstract

Information Sciences

IEEE Transactions on Systems, Man and Cybernetics

Special issue on non monotonie logic

Artificial Intelligence

Incidence calculus: a mechanism for probabilistic reasoning

Journal of Automated Reasoning

Fuzzy pattern matching

Kybernetes

An approach to approximate reasoning based on Dempster rule of combination

International Journal of Expert Systems

A method of computing generalized Bayesian probability values for expert systems

Sur divers problèmes inhérents à l’automatisation des raisonnements de sens commun

Fuzzy logics and the generalized modus ponens revisited

Cybernetics and Systems

Recent models of uncertainty and imprecision as a basis for decision theory: towards less normative frameworks

Possibilistic logic under matrix form

The principle of minimum specificity as a basis for evidential reasoning

Fuzzy numbers: an overview

Necessity measures and the resolution principle

IEEE Transactions Systems, Man and Cybernetics

On incomplete conjunctive information