Isomorphisms between de Morgan triplets
Fuzzy Sets and Systems - Mathematics and Fuzziness, Part II
Fuzzy Sets and Systems
A first course in fuzzy logic
Fuzzy Sets and Systems
Weak uninorm aggregation operators
Information Sciences—Informatics and Computer Science: An International Journal
Remarks on uninorm aggregation operators
Fuzzy Sets and Systems
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
The functional equations of Frank and Alsina for uninorms and nullnorms
Fuzzy Sets and Systems
Uninorms in fuzzy systems modeling
Fuzzy Sets and Systems
Fuzzy Measure Theory
The distributivity condition for uninorms and t-operators
Fuzzy Sets and Systems
The structure of continuous uni-norms
Fuzzy Sets and Systems
On the reversibility of uninorms and t-operators
Fuzzy Sets and Systems - Mathematics
New triangular operator generators for fuzzy systems
IEEE Transactions on Fuzzy Systems
Towards a General Class of Operators for Fuzzy Systems
IEEE Transactions on Fuzzy Systems
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We give a new representation theorem of the negation based on the generator function of the strict operator. We study a certain class of strict monotone operators which build DeMorgan class with infinite negations. We show that the necessary and sufficient condition for this operator class is fc(x)fd(X) = 1, where fc(x) and fd(X) are the generator function of the conjunctive and disjunctive operators. In the second part of the article we examine the relationship between Dombi's aggregative operators, uninorms and strict, continuous t-norms and t-conorms. We show that the class of representable uninorms is equivalent to the class of those uninorms which are also aggregative operators. We give new representation theorems for strong negations, and discuss the correspondence between strong negations, aggregative operators and strict, continuous (logical) operators. We show that in this system the four operators (conjunction, disjunction, aggregation, negation) can be described using only one generator function.