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## Filters

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Fuzzy Set-Theoretic Operators and Quantifiers
[chapter]

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. ...

##
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Fuzzy sets and formal logics

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. ...

##
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Behavioral analysis of aggregation functions
[chapter]

*
Aggregation Functions
*

Editors Printed by: Universitätsdirektion, Johannes Kepler Universität,

doi:10.1017/cbo9781139644150.011
fatcat:3agfaonbbfahvenz6ll56kc5vm
*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*. ...##
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ON SOME AXIOMATIC EXTENSIONS OF THE MONOIDAL T-NORM BASED LOGIC MTL: AN ANALYSIS IN THE PROPOSITIONAL AND IN THE FIRST-ORDER CASE
[article]

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. ...