An essay on name and extension of rule-given properties
In the crisp case, any non-empty set A of a universe X is a preordering's class under the material conditional →A. Then, the elements of A are to be considered as those of X satisfying the property of being the ”followers” of any a ε A; we could see A as a ”segment of the structure (X, →).
Based on this idea, it is studied the frequent case in which a vague or crisp predicate P is known through both a set of rules (representable by a fuzzy or crisp preorder) and by a crisp prototype. The paper shows how, on this hypothesis, the extension of P or the membership function of the (fuzzy or crisp, respectively) set labelled P is obtained.
Unable to display preview. Download preview PDF.
- RUSSELL, B., The Principles of Mathematics, Routledge and Kegan Paul, London (1903).Google Scholar
- TRILLAS, E., On Fuzzy Conditionals Generalizing the Material Conditional, IPMU'92; Advanced Methods in Artificial Intelligence, Eds. B. Bouchon-Meunier, L. Valverde and R.-Yager, 85–100. Lecture Notes in Computer Science, Springer-Verlag (1993).Google Scholar
- TRILLAS, E., On Logic and Fuzzy Logic, to be shortly published in Int. Jour. of Uncertainty, Fuzziness and Knowledge-Based Systems.Google Scholar
- TRILLAS, E., ALSINA, C. Logic: going farther from Tarski?, Fuzzy Sets and Systems 53, 1–13, (1993).Google Scholar
- TRILLAS, E., ALSINA, C. Some Remarks on Approximate Entailment, International Journal of Approximate Reasoning (6), 525–533, (1992).Google Scholar
- VALVERDE, L., On the structure of F-indistinguishability operators, Fuzzy Sets and Systems 17, 313–328 (1985).Google Scholar
- ZADEH, L.A., Fuzzy Sets, Information and Control 8, 338–353, (1965).Google Scholar