SCALAR CARDINALITIES OF FINITE FUZZY SETS FOR t-NORMS AND t-CONORMS-Reference-Cited by-同舟云学术

SCALAR CARDINALITIES OF FINITE FUZZY SETS FOR t-NORMS AND t-CONORMS

Published:2003-10 Issue:05 Volume:11 Page:599-614
ISSN:0218-4885
Container-title:International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
language:en
Short-container-title:Int. J. Unc. Fuzz. Knowl. Based Syst.

Author:

CASASNOVAS J.¹,TORRENS J.¹

Affiliation:

1. Department of Mathematics and Computer Science, University of Balearic Islands, Crta. de Valldemossa, Km. 7.5, 07071 Palma de Mallorca, Spain

Abstract

An axiomatic approach to scalar cardinalities of finite fuzzy sets involving t-norms and t-conorms is presented. A characterization theorem for these cardinalities is proved and it is also proved that some standard properties remain true. On the other hand, properties like finite additivity, valuation property or finite subadditivity depend on the t-norm and the t-conorm.

Publisher

World Scientific Pub Co Pte Lt

Subject

Artificial Intelligence,Information Systems,Control and Systems Engineering,Software

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218488503002351

Reference5 articles.

1. An axiomatic approach to scalar cardinalities of fuzzy sets

2. A generalizing look at sigma counts of fuzzy sets

3. Triangular Norms

4. On the simultaneous associativity ofF(x, y) andx+y−F(x, y)

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