0384236 - ÚI 2013 RIV NL eng J - Journal Article
Běhounek, Libor
Graded properties of unary and binary fuzzy connectives.
Fuzzy Sets and Systems. Roč. 202, 1 September (2012), s. 1-41. ISSN 0165-0114. E-ISSN 1872-6801
R&D Projects: GA ČR GPP103/10/P234
Grant - others:WWTF(AT) MA07-016
Institutional research plan: CEZ:AV0Z10300504
Keywords : fuzzy connectives * graded properties * Fuzzy Class Theory * logic-based fuzzy mathematics * defects of mathematical properties
Subject RIV: BA - General Mathematics
Impact factor: 1.749, year: 2012

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.
Permanent Link: http://hdl.handle.net/11104/0213947