A construction method of semicopulas from fuzzy negations

Constructing implication functions from fuzzy negations

“…Studies on symmetry of subsets of [0, 1] were initially done in [19] and [20]. See also [1] for the following adapted definitions.…”

“…Let N be a fuzzy negation and let F N be given by equation (1). Then i) F N is a commutative and conjunctive aggregation function.…”

“…In [1] it is proved that there always exists an Idsymmetrical fuzzy negation N such that F N = F N , a N = a N , and the Id-symmetrical fuzzy negation N can be taken such that N(a N ) ≤ a N . Moreover, if F N is left-continuous, then N(a N ) = a N .…”

“…It is known that when N is Id-symmetrical, the corresponding F N is in fact a t-norm in many cases (see Theorem 28 in [1]), and it is left-continuous when so is N . In all of theses cases I N clearly satisfies (EP ) (see examples 18-i) and 18-ii))…”

On a New Class of Fuzzy Coimplications Derived from Generalizedh-Generators and Fuzzy Negations

“…Recently, lots of works have been done on application and theoretical research of fuzzy sets (for instance, Refs. 1,2,4,6,[24][25][26]. Especially, studies of fuzzy logical connectives, such as implications, coimplications, t-norms, t-conorms, uninorms, etc, have become one of the most important and interesting mathematical problems in fuzzy logic.…”