Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Fuzzy Relational Systems: Foundations and Principles
Fuzzy Relational Systems: Foundations and Principles
Domination of aggregation operators and preservation of transitivity
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Aggregation operators: new trends and applications
Aggregation operators: new trends and applications
Domination of ordered weighted averaging operators over t-norms
Soft Computing - A Fusion of Foundations, Methodologies and Applications
On the difference between traditional and deductive fuzzy logic
Fuzzy Sets and Systems
Relations in Fuzzy Class Theory
Fuzzy Sets and Systems
Features of Mathematical Theories in Formal Fuzzy Logic
IFSA '07 Proceedings of the 12th international Fuzzy Systems Association world congress on Foundations of Fuzzy Logic and Soft Computing
Parametric characterization of aggregation functions
Fuzzy Sets and Systems
Relational compositions in Fuzzy Class Theory
Fuzzy Sets and Systems
Aggregation Functions: A Guide for Practitioners
Aggregation Functions: A Guide for Practitioners
From fuzzy logic to fuzzy mathematics: A methodological manifesto
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Similarity relations and fuzzy orderings
Information Sciences: an International Journal
On a Graded Notion of t-Norm and Dominance
ISMVL '10 Proceedings of the 2010 40th IEEE International Symposium on Multiple-Valued Logic
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The paper studies basic graded properties of unary and binary fuzzy connectives, i.e., unary and binary operations on the set of truth degrees of a background fuzzy logic extending the logic MTL of left-continuous t-norms. The properties studied in this paper are graded generalizations of monotony, Lipschitz continuity, null and unit elements, idempotence, commutativity, and associativity. The paper elaborates the initial study presented in previous papers and focuses mainly on parameterization of graded properties by conjunction-multiplicities of subformulae in the defining formulae, preservation of graded properties under compositions and slight variations of fuzzy connectives, the values of graded properties for basic connectives of the ground logic, and the dependence of the values on the ground logic. The results are proved in the formal framework of higher-order fuzzy logic MTL, also known as Fuzzy Class Theory (FCT). General theorems provable in FCT are illustrated on several semantic examples.