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On logical connectives for a fuzzy set theory with or without nonempty self‐contradictions
Author(s) -
Trillas E.,
Alsina C.,
Jacas J.
Publication year - 2000
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/(sici)1098-111x(200003)15:3<155::aid-int2>3.0.co;2-0
Subject(s) - infimum and supremum , contradiction , fuzzy logic , law of excluded middle , set (abstract data type) , context (archaeology) , mathematics , fuzzy set , computer science , fuzzy set operations , artificial intelligence , theoretical computer science , epistemology , discrete mathematics , philosophy , biology , programming language , paleontology
We show how noncontradiction and excluded‐middle laws can hold in a fuzzy logic where the concepts of contradiction and incompatibility are clearly distinguished. However, if we want to avoid self‐contradictions in fuzzy set theory then one needs to consider only fuzzy sets with supremum 1 and infimum 0. We clarify in this new context (on which the applications usually take place) which logical connectives make sense. ©2000 John Wiley & Sons, Inc.