Enumerative combinatorics
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
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
The functional equations of Frank and Alsina for uninorms and nullnorms
Fuzzy Sets and Systems
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
The distributivity condition for uninorms and t-operators
Fuzzy Sets and Systems
The modularity condition for uninorms and t-operators
Fuzzy Sets and Systems
The structure of continuous uni-norms
Fuzzy Sets and Systems
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
On the reversibility of uninorms and t-operators
Fuzzy Sets and Systems - Mathematics
Fuzzy Sets and Systems
Logic-based fuzzy networks: A study in system modeling with triangular norms and uninorms
Fuzzy Sets and Systems
Granular representation and granular computing with fuzzy sets
Fuzzy Sets and Systems
A new way to extend t-norms, t-conorms and negations
Fuzzy Sets and Systems
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In this paper we study binary operators on [0,1] which are associative, monotone non-decreasing in both variables and commutative (AMC) with neutral element. In this work, we generalize the concept of neutral element and this generalization gives rise to a new class of AMC binary operators on [0,1] called n-uninorms. n-Uninorms are denoted as U^n, where n comes from the generalization of the neutral element. We study the structure of n-uninorms. The structure resembles an ordinal sum structure made up of n uninorms. We characterize some special cases of them based on some continuity considerations and show that t-norms, t-conorms, uninorms and nullnorms (t-operators) are special cases of n-uninorms. We also show that given n there are n+1 classes of operators in U^n and each of them has many subclasses. We also study the Frank equation involving n-uninorms and show that we need to consider only n-uninorms for the study. Finally, we show that the total number of subclasses of operators in U^n follows the famous series called Catalan Numbers.