Abstract
This paper deals with the problem of synthesizing by conjunction a finite set of rules \(\mu_{i} \longrightarrow(1\leq i \leq n)\) into a single one \(\mu_{1} . \mu{2}...\mu{n} \longrightarrow \sigma_{1} . \sigma{2}...\sigma{n}\), and depending on the conditional’s representation. It is proven that, among the usual five types of fuzzy conditionals, the problem is only solved by the Mamdani-Larsen’s type min-conditionals.
This paper is partially supported by the Foundation for the Advancement of Soft Computing (Asturias, Spain), and CICYT (Spain) under grant TIN2008-06890-C02-01.
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Trillas, E., Alsina, C. (2012). From Leibniz’s Shinning Theorem to the Synthesis of Rules through Mamdani-Larsen Conditionals. In: Trillas, E., Bonissone, P., Magdalena, L., Kacprzyk, J. (eds) Combining Experimentation and Theory. Studies in Fuzziness and Soft Computing, vol 271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24666-1_18
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DOI: https://doi.org/10.1007/978-3-642-24666-1_18
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