TY - JOUR
T1 - On dependencies and independencies of fuzzy implication axioms
AU - Shi, Yun
AU - Van Gasse, Bart
AU - Ruan, Da
AU - Kerre, Etienne E.
N1 - Score=10
PY - 2009/12/21
Y1 - 2009/12/21
N2 - A fuzzy implication, commonly defined as a two-place operation on the unit interval, is an extension of the classical binary implication. It plays important roles in both mathematical and applied sides of fuzzy set theory. Besides the basic axioms, there are many potential fuzzy implication axioms, among which eight are widely used in the literature. Different fuzzy implications satisfying different subgroups of these eight axioms can be found. However, certain interrelationships exist between these eight axioms. But the results remain incomplete. This paper aims to lay bare the interrelationships between these eight axioms. The result is instrumental to propose a classification of fuzzy implications.
AB - A fuzzy implication, commonly defined as a two-place operation on the unit interval, is an extension of the classical binary implication. It plays important roles in both mathematical and applied sides of fuzzy set theory. Besides the basic axioms, there are many potential fuzzy implication axioms, among which eight are widely used in the literature. Different fuzzy implications satisfying different subgroups of these eight axioms can be found. However, certain interrelationships exist between these eight axioms. But the results remain incomplete. This paper aims to lay bare the interrelationships between these eight axioms. The result is instrumental to propose a classification of fuzzy implications.
KW - Fuzzy implication
KW - Fuzzy implication axioms
KW - Fuzzy logic operators
KW - S-implication
KW - R-implication
UR - https://ecm.sckcen.be/OTCS/llisapi.dll/overview/38913744
U2 - 10.1016/j.fss.2009.12.003
DO - 10.1016/j.fss.2009.12.003
M3 - Article
SN - 0165-0114
VL - 161
SP - 1388
EP - 1405
JO - Fuzzy sets and systems
JF - Fuzzy sets and systems
IS - 10
ER -