Structure of Uninorms

1997 ◽  
Vol 05 (04) ◽  
pp. 411-427 ◽  
Author(s):  
János C. Fodor ◽  
Ronald R. Yager ◽  
Alexander Rybalov
Keyword(s):  
Representation Theorem ◽  
Unit Interval ◽  
Neutral Element ◽  
General Representation ◽  
Exhaustive Study

An exhaustive study of uninorm operators is established. These operators are generalizations of t-norms and t-conorms allowing the neutral element lying anywhere in the unit interval. It is shown that uninorms can be built up from t-norms and t-conorms by a construction similar to ordinal sums. De Morgan classes of uninorms are also described. Representability of uninorms is characterized and a general representation theorem is proved. Finally, pseudo-continuous uninorms are defined and completely classified.

scholarly journals Complex and distributional weights for sieved ultraspherical polynomials

1996 ◽  
Vol 19 (2) ◽  
pp. 229-242
Author(s):  
Jairo A. Charris ◽  
Felix H. Soriano
Keyword(s):  
Real Line ◽  
Representation Theorem ◽  
Contour Integral ◽  
General Representation ◽  
The Real ◽  
Ultraspherical Polynomials ◽  
Natural Range

Contour integral and distributional orthogonality of sieved ultraspherical polynomials are established for values of the parameters outside the natural range of orthogonality by positive measures on the real line. A general representation theorem for moment functionals is included.

The Relations between Implications and Left (Right) Semi-Uninorms on a Complete Lattice

2015 ◽  
Vol 23 (02) ◽  
pp. 245-261 ◽  
Author(s):  
Xiaoying Hao ◽  
Meixia Niu ◽  
Zhudeng Wang
Keyword(s):  
Complete Lattice ◽  
Unit Interval ◽  
Neutral Element ◽  
Order Property ◽  
Triangular Norms

Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we study the relations between implications and left (right) semi-uninorms on a complete lattice. We firstly investigate the left (right) semi-uninorms induced by implications, give some conditions such that the operations induced by implications constitute left or right semi-uninorms, and demonstrate that the operations induced by a right infinitely ∧-distributive implication, which satisfies the order property, are left (right) infinitely ∨-distributive left (right) semi-uninorms. Then, we discuss the residual operations of left (right) semi-uninorms and show that left (right) residual operators of strict left (right)-conjunctive left (right) infinitely ∨-distributive left (right) semi-uninorms are right infinitely ∧-distributive implications that satisfy the order property. Finally, we reveal the relationships between strict left (right)-conjunctive left (right) infinitely ∨-distributive left (right) semi-uninorms and right infinitely ∧-distributive implications which satisfy the order property.

scholarly journals Archimedean components of triangular norms

2005 ◽  
Vol 78 (2) ◽  
pp. 239-255 ◽  
Author(s):  
Erich Peter Klement ◽  
Radko Mesiar ◽  
Endre Pap
Keyword(s):  
Unit Interval ◽  
Neutral Element ◽  
Ordered Semigroup ◽  
Triangular Norms ◽  
Construction Methods

AbstractThe Archimedean components of triangular norms (which turn the closed unit interval into anabelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordinal sums and additive generators, new types of left-continuous triangular norms are constructed.

A General Representation Theorem for Sx

2015 ◽  
pp. 257-266
Author(s):  
Jeffrey Paris ◽  
Alena Vencovska
Keyword(s):  
Representation Theorem ◽  
General Representation
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