TY - JOUR UR - http://lib.ugent.be/catalog/pug01:624006 ID - pug01:624006 LA - eng TI - Characterizations of (weakly) Archimedean t-norms in interval-valued fuzzy set theory PY - 2009 JO - (2009) 4th International Summer School on Aggregation Operators SN - 0165-0114 PB - ELSEVIER SCIENCE BV AU - Deschrijver, Glad UGent 001995006575 801001452431 AB - In this paper we ﬁrst give characterizations of the class of continuous t-norms on L^I (where L^I is the lattice of closed subintervals of the unit interval) which satisfy the residuation principle and which are a natural extension of a t-norm on the unit interval and which satisfy one of the following conditions: the negation generated by their residual implication is involutive; they are (weakly) Archimedean; they are (weakly) nilpotent. We fully characterize the class of continuous t-norms on L^I which satisfy the residuation principle, which are a natural extension of a t-norm on the unit interval and which are weakly Archimedean. We construct a separate representation for the t-norms in this class which are weakly nilpotent and for those which are not weakly nilpotent. Finally we give a characterization of the continuous t-norms on L^I which satisfy the residuation principle, which are a natural extension of a t-norm on the unit interval and which are strict. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 624006 | ||
005 | 20161219154317.0 | ||
008 | 090511s2009------------------------eng-- | ||
022 | a 0165-0114 | ||
024 | a 000263661700007 2 wos | ||
024 | a 1854/LU-624006 2 handle | ||
024 | a 10.1016/j.fss.2008.08.004 2 doi | ||
040 | a UGent | ||
245 | a Characterizations of (weakly) Archimedean t-norms in interval-valued fuzzy set theory | ||
260 | b ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS c 2009 | ||
520 | a In this paper we ﬁrst give characterizations of the class of continuous t-norms on L^I (where L^I is the lattice of closed subintervals of the unit interval) which satisfy the residuation principle and which are a natural extension of a t-norm on the unit interval and which satisfy one of the following conditions: the negation generated by their residual implication is involutive; they are (weakly) Archimedean; they are (weakly) nilpotent. We fully characterize the class of continuous t-norms on L^I which satisfy the residuation principle, which are a natural extension of a t-norm on the unit interval and which are weakly Archimedean. We construct a separate representation for the t-norms in this class which are weakly nilpotent and for those which are not weakly nilpotent. Finally we give a characterization of the continuous t-norms on L^I which satisfy the residuation principle, which are a natural extension of a t-norm on the unit interval and which are strict. | ||
598 | a A1 | ||
700 | a Deschrijver, Glad u UGent 0 001995006575 0 801001452431 0 975407443034 9 F5FEAC1A-F0ED-11E1-A9DE-61C894A0A6B4 | ||
650 | a Mathematics and Statistics | ||
653 | a interval-valued fuzzy set theory | ||
653 | a (weakly) Archimedean | ||
653 | a t-norm | ||
653 | a (weakly) nilpotent | ||
653 | a strict | ||
773 | t 4th International Summer School on Aggregation Operators g Fuzzy Sets Syst. 2009. ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS. 160 (6) p.778-801 q 160:6<778 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/624006/file/627045 z [ugent] y Deschrijver.pdf | ||
920 | a article | ||
Z30 | x WE 1 WE02 | ||
922 | a UGENT-WE |
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