zbMATH — the first resource for mathematics

Van Melle’s combining function in MYCIN is a representable uninorm: An alternative proof. (English) Zbl 0928.03060
Summary: Recently, A. Tsadiras and K. Margaritis [ibid. 93, 263-274 (1998)] have shown that the function implemented in the expert system MYCIN for combining certainty factors is a uninorm. In this paper, we present a compact alternative to the given direct and lengthy proof, based on the construction of representable uninorms by means of an additive generator. Consequently, we show that van Melle’s combining function is a representable uninorm. In fact, it is a rescaled version of the representable uninorm on the unit interval constructed from the algebraic product and the probabilistic sum.

03E72 Theory of fuzzy sets, etc.
68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
Full Text: DOI
[1] Buchanan, B.; Shortliffe, E., Rule-based expert systems, ()
[2] Dombi, J., Basic concepts for the theory of evaluation: the aggregative operator, European J. oper. res., 10, 282-293, (1982) · Zbl 0488.90003
[3] Duda, R.; Hart, P.; Nilsson, N., Subjective Bayesian methods for rule-based inference systems, (), 1075
[4] Fodor, J.; Yager, R.; Rybalov, A., Structure of uniforms, Internat. J. uncertainty, fuzziness knowledge-based systems, 5, 411-427, (1997) · Zbl 1232.03015
[5] Hájek, P., Combining functions for certainty factors in consulting systems, Internat. J. man-Mach. studies, 22, 59, (1985) · Zbl 0567.68055
[6] Hájek, P.; Havránek, T.; Jiroušek, R., Uncertain information processing in expert systems, (1992), CRC Press Boca Raton
[7] Klement, E.-P.; Mesiar, R.; Pap, E., On the relationship of associative compensatory operators to triangular norms and conorms, Internat. J. uncertainty, fuzziness knowledge-based systems, 4, 129-144, (1996) · Zbl 1232.03041
[8] Mesiar, R.; Píš, P., Fuzzy model of inexact reasoning in medicine, Comput. methods. progr. biomed., 30, 1-8, (1989)
[9] Schweizer, B.; Sklar, A., Probabilistic metric spaces, (1983), Elsevier New York · Zbl 0546.60010
[10] Tsadiras, A.; Margaritis, K., The MYCIN certainty factor handling function as uninorm operator and its use as a threshold function in artificial neurons, Fuzzy sets and systems, 93, 263-274, (1998)
[11] Yager, R.; Rybalov, A., Uninorm aggregation operators, Fuzzy sets and systems, 80, 111-120, (1996) · Zbl 0871.04007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.