TY - CHAP UR - http://lib.ugent.be/catalog/pug01:8129549 ID - pug01:8129549 LA - eng TI - Additive generators based on generalized arithmetic operators in interval-valued fuzzy and Atanassov's intuitionistic fuzzy set theory PY - 2016 SN - 9783319263021 SN - 9783319263014 SN - 1434-9922 PB - Cham AU - Deschrijver, Glad UGent 001995006575 801001452431 AU - Kerre, Etienne AU - Angelov, Plamen editor AU - Sotirov, Sotir editor AB - In this paper we investigate additive generators in Atanassov's intuitionistic fuzzy and interval-valued fuzzy set theory. Starting from generalized arithmetic operators satisfying some axioms we define additive generators and we characterize continuous generators which map exact elements to exact elements in terms of generators on the unit interval. We give necessary and sufficient condition under which a generator actually generates a t-nporm and we show that the generated t-norm belongs to particular classes of t-norms depending on the arithmetic operators involved in the defintion of the generator. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 8129549 | ||
005 | 20170102095645.0 | ||
008 | 161027s2016------------------------eng-- | ||
020 | a 9783319263021 | ||
020 | a 9783319263014 | ||
022 | a 1434-9922 | ||
024 | a 1854/LU-8129549 2 handle | ||
024 | a 10.1007/978-3-319-26302-1_10 2 doi | ||
040 | a UGent | ||
245 | a Additive generators based on generalized arithmetic operators in interval-valued fuzzy and Atanassov's intuitionistic fuzzy set theory | ||
260 | a Cham, Switzerland b Springer c 2016 | ||
520 | a In this paper we investigate additive generators in Atanassov's intuitionistic fuzzy and interval-valued fuzzy set theory. Starting from generalized arithmetic operators satisfying some axioms we define additive generators and we characterize continuous generators which map exact elements to exact elements in terms of generators on the unit interval. We give necessary and sufficient condition under which a generator actually generates a t-nporm and we show that the generated t-norm belongs to particular classes of t-norms depending on the arithmetic operators involved in the defintion of the generator. | ||
598 | a B2 | ||
700 | a Deschrijver, Glad u UGent 0 001995006575 0 801001452431 0 975407443034 9 F5FEAC1A-F0ED-11E1-A9DE-61C894A0A6B4 | ||
700 | a Kerre, Etienne u WE02 0 801000205272 9 F358CFA4-F0ED-11E1-A9DE-61C894A0A6B4 | ||
700 | a Angelov, Plamen e editor | ||
700 | a Sotirov, Sotir e editor | ||
650 | a Mathematics and Statistics | ||
653 | a additive generator | ||
653 | a t-norm | ||
653 | a Atanassov's intuitionistic fuzzy set | ||
653 | a interval-valued fuzzy set | ||
773 | t Imprecision and uncertainty in information representation and processing : new tools based on intuitionistic fuzzy sets and generalized nets g Imprecision and uncertainty in information representation and processing : new tools based on intuitionistic fuzzy sets and generalized nets. 2016. Springer. 332 p.137-157 q 332:<137 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/8129549/file/8129562 z [ugent] y additive.pdf | ||
920 | a chapter | ||
Z30 | x WE 1 WE02 | ||
922 | a UGENT-WE |
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