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On a class of operators for expert systems. (English) Zbl 0785.68087
This paper mainly deals with a class of connectives that modelize the propagation of uncertainty in expert systems when a finite set of linguistic terms (or “labels”) is considered.
Continuous De Morgan triplets are frequently used to model this propagation in the fuzzy sets approach. We introduce a new definition (“directed algebra”) in order to obtain similar properties to those of continuous De Morgan triplets, but now on a totally ordered finite set. It is proved that there exist \(2^ n\) different directed algebra structures on a totally ordered set of \(n+2\) elements. All these structures are described and it is proved that only one of them is Archimedean.
Reviewer: G.Mayor

MSC:
68T30 Knowledge representation
68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
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References:
[1] Alsina, J. Math. Anal. Appl. 93 pp 15– (1983)
[2] and , ”A new approach to connective generation in the framework of expert systems using fuzzy logic,” Proceedings of XVIIIth. International Symposium on Multiple-Value Logic, Palma de Mallorca, Computer Society Press, Washington, D. C. 1988, pp. 157–162.
[3] Approximate Reasoning Models (Ellis Horwood Limited, New York, 1990).
[4] ”Estudi de models matemàtics per a connectius en lògica multivaluada,” Ph.D. thesis, Palma de Mallorca Universitat de les Illes Balears, 1990.
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