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Fuzzy Set-Theoretic Operators and Quantifiers [chapter]

János Fodor, Ronald R. Yager
2000 Fundamentals of Fuzzy Sets  
Note that we use the symbol := indicating that the item on its lefthand side is equal, by definition, to the already known item on its right-hand side.  ...  Since these extensions are mainly pointwisely defined, we review basic results on the underlying unary or binary operations on the unit interval such as negations, t-norms, t-conorms, implications, coimplications  ...  Acknowledgments The work of J. Fodor has been partially supported by the National Scientific Research Fund (OTKA) under grant T025163.  ... 
doi:10.1007/978-1-4615-4429-6_3 fatcat:obcyvr6pzfbttdlpmtlfjenyaa

Fuzzy sets and formal logics

Lluís Godo, Siegfried Gottwald
2015 Fuzzy sets and systems (Print)  
The paper discusses the relationship between fuzzy sets and formal logics as well as the influences fuzzy set theory had on the development of particular formal logics.  ...  Our focus is on the historical side of these developments.  ...  Godo acknowledges partial support by the Spanish projects EdeTRI (TIN2012-39348-C02-01) and 2014 SGR 118.  ... 
doi:10.1016/j.fss.2015.06.021 fatcat:jstlgpnzrze3pkikat2rcbeeh4

Behavioral analysis of aggregation functions [chapter]

Michel Grabisch, Jean-Luc Marichal, Radko Mesiar, Endre Pap
Aggregation Functions  
Editors Printed by: Universitätsdirektion, Johannes Kepler Universität, A-4040 Linz 2 Since their inception in 1979, the Linz Seminars on Fuzzy Set Theory have emphasized the development of mathematical  ...  Different to previous years, the scope of the seminar does not restrict to a single sub-topic of fuzzy set theory.  ...  The result helps us to determine a classification on the class of fuzzy implications.  ... 
doi:10.1017/cbo9781139644150.011 fatcat:3agfaonbbfahvenz6ll56kc5vm

ON SOME AXIOMATIC EXTENSIONS OF THE MONOIDAL T-NORM BASED LOGIC MTL: AN ANALYSIS IN THE PROPOSITIONAL AND IN THE FIRST-ORDER CASE [article]

M. Bianchi
2010
The first example of left-continuous t-norm was the one of Nilpotent Minimum, introduced in [Fod95] .  ...  It follows that the left-continuity plays a central role for the existence of the residuum: this is one of the reasons that render interesting the study of the class of left-continuous t-norms.  ...  The proof for SBL n ∀ is similar, and hence we only discuss the parts where the two proofs diverge. To check the validity of φ ∨ ¬(∀yP (y)) in V, note Theorem 8.6.6.  ... 
doi:10.13130/m-bianchi_phd2010-12-17 fatcat:7be646fehjayljwiwhmh3g2ha4