TY - CHAP UR - http://lib.ugent.be/catalog/pug01:3196768 ID - pug01:3196768 LA - eng TI - Implication functions in interval-valued fuzzy set theory PY - 2013 SN - 9783642356773 SN - 9783642356766 SN - 1434-9922 PB - Berlin AU - Deschrijver, Glad UGent 001995006575 801001452431 AU - Baczyński, Michał editor AU - Beliakov, Gleb editor AU - Bustince, Humberto editor AU - Pradera, Ana editor AB - Interval-valued fuzzy set theory is an extension of fuzzy set theory in which the real, but unknown, membership degree is approximated by a closed interval of possible membership degrees. Since implications on the unit interval play an important role in fuzzy set theory, several authors have extended this notion to interval-valued fuzzy set theory. This chapter gives an overview of the results pertaining to implications in interval-valued fuzzy set theory. In particular, we describe several possibilities to represent such implications using implications on the unit interval, we give a characterization of the implications in interval-valued fuzzy set theory which satisfy the Smets-Magrez axioms, we discuss the solutions of a particular distributivity equation involving strict t-norms, we extend monoidal logic to the interval-valued fuzzy case and we give a soundness and completeness theorem which is similar to the one existing for monoidal logic, and finally we discuss some other constructions of implications in interval-valued fuzzy set theory. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 3196768 | ||
005 | 20170102095611.0 | ||
008 | 130419s2013------------------------eng-- | ||
020 | a 9783642356773 | ||
020 | a 9783642356766 | ||
022 | a 1434-9922 | ||
024 | a 1854/LU-3196768 2 handle | ||
024 | a 10.1007/978-3-642-35677-3_4 2 doi | ||
040 | a UGent | ||
245 | a Implication functions in interval-valued fuzzy set theory | ||
260 | a Berlin, Germany b Springer c 2013 | ||
520 | a Interval-valued fuzzy set theory is an extension of fuzzy set theory in which the real, but unknown, membership degree is approximated by a closed interval of possible membership degrees. Since implications on the unit interval play an important role in fuzzy set theory, several authors have extended this notion to interval-valued fuzzy set theory. This chapter gives an overview of the results pertaining to implications in interval-valued fuzzy set theory. In particular, we describe several possibilities to represent such implications using implications on the unit interval, we give a characterization of the implications in interval-valued fuzzy set theory which satisfy the Smets-Magrez axioms, we discuss the solutions of a particular distributivity equation involving strict t-norms, we extend monoidal logic to the interval-valued fuzzy case and we give a soundness and completeness theorem which is similar to the one existing for monoidal logic, and finally we discuss some other constructions of implications in interval-valued fuzzy set theory. | ||
598 | a B2 | ||
700 | a Deschrijver, Glad u UGent 0 001995006575 0 801001452431 0 975407443034 9 F5FEAC1A-F0ED-11E1-A9DE-61C894A0A6B4 | ||
700 | a Baczyński, Michał e editor | ||
700 | a Beliakov, Gleb e editor | ||
700 | a Bustince, Humberto e editor | ||
700 | a Pradera, Ana e editor | ||
650 | a Mathematics and Statistics | ||
653 | a implication | ||
653 | a interval-valued fuzzy set | ||
773 | t Advances in fuzzy implication functions g Advances in fuzzy implication functions. 2013. Springer. 300 p.73-99 q 300:<73 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/3196768/file/3196770 z [ugent] y 03000073.pdf | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/3196768/file/3196772 z [open] y LIimpl_overviewb.pdf | ||
920 | a chapter | ||
Z30 | x WE 1 WE02 | ||
922 | a UGENT-WE |
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