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Start Over Subject ordinal sum

1. Construction methods for implications on bounded lattices

Creator:
Kesicioğlu, M. Nesibe
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
ordinal sum, bounded lattice, and implication
Language:
English
Description:
In this paper, the ordinal sum construction methods of implications on bounded lattices are studied. Necessary and sufficient conditions of an ordinal sum for obtaining an implication are presented. New ordinal sum construction methods on bounded lattices which generate implications are discussed. Some basic properties of ordinal sum implications are studied.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Distributivity of ordinal sum implications over overlap and grouping functions

Creator:
Pan, Deng and Zhou, Hongjun
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
ordinal sum, distributivity, fuzzy implication functions, overlap functions, and grouping functions
Language:
English
Description:
In 2015, a new class of fuzzy implications, called ordinal sum implications, was proposed by Su et al. They then discussed the distributivity of such ordinal sum implications with respect to t-norms and t-conorms. In this paper, we continue the study of distributivity of such ordinal sum implications over two newly-born classes of aggregation operators, namely overlap and grouping functions, respectively. The main results of this paper are characterizations of the overlap and/or grouping function solutions to the four usual distributive equations of ordinal sum fuzzy implications. And then sufficient and necessary conditions for ordinal sum implications distributing over overlap and grouping functions are given.
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public

3. On a special class of left-continuous uninorms

Creator:
Li, Gang
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
uninorm, internal operator, ordinal sum, residual implication, and triangular subnorm
Language:
English
Description:
This paper is devoted to the study of a class of left-continuous uninorms locally internal in the region A(e) and the residual implications derived from them. It is shown that such uninorm can be represented as an ordinal sum of semigroups in the sense of Clifford. Moreover, the explicit expressions for the residual implication derived from this special class of uninorms are given. A set of axioms is presented that characterizes those binary functions I:[0,1]2→[0,1] for which a uninorm U of this special class exists in such a way that I is the residual implications derived from U.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. On the construction of t-norms (t-conorms) by using interior (closure) operator on bounded lattices

Creator:
Aşıcı, Emel
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
t-norm, t-conorm, ordinal sum, and bounded lattice
Language:
English
Description:
Recently, the topic of construction methods for triangular norms (triangular conorms), uninorms, nullnorms, etc. has been studied widely. In this paper, we propose construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices by using interior and closure operators, respectively. Thus, we obtain some proposed methods given by Ertuğrul, Karaçal, Mesiar [15] and Çaylı [8] as results. Also, we give some illustrative examples. Finally, we conclude that the introduced construction methods can not be generalized by induction to a modified ordinal sum for t-norms and t-conorms on bounded lattices.
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public

5. On the constructions of t-norms and t-conorms on some special classes of bounded lattices

Creator:
Aşıcı, Emel
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
t-norm, ordinal sum, t-conorm, and bounded lattice
Language:
English
Description:
Recently, the topic related to the construction of triangular norms and triangular conorms on bounded lattices using ordinal sums has been extensively studied. In this paper, we introduce a new ordinal sum construction of triangular norms and triangular conorms on an appropriate bounded lattice. Also, we give some illustrative examples for clarity. Then, we show that a new construction method can be generalized by induction to a modified ordinal sum for triangular norms and triangular conorms on an appropriate bounded lattice, respectively. And we provide some illustrative examples.
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public

6. On the dominance relation between ordinal sums of conjunctors

Creator:
Saminger, Susanne, De Baets, Bernard, and De Meyer, Hans
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
conjuntor, copula, domimance, ordinal sum, quasi-copula, and t-norm
Language:
English
Description:
This contribution deals with the dominance relation on the class of conjunctors, containing as particular cases the subclasses of quasi-copulas, copulas and t-norms. The main results pertain to the summand-wise nature of the dominance relation, when applied to ordinal sum conjunctors, and to the relationship between the idempotent elements of two conjunctors involved in a dominance relationship. The results are illustrated on some well-known parametric families of t-norms and copulas.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

7. Remarks on two product-like constructions for copulas

Creator:
Durante, Fabrizio, Klement, Erich Peter, Quesada--Molina, José Juan, and Sarkoci, Peter
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
copula, ordinal sum, shuffle of Min, and concordance
Language:
English
Description:
We investigate two constructions that, starting with two bivariate copulas, give rise to a new bivariate and trivariate copula, respectively. In particular, these constructions are generalizations of the ∗-product and the ⋆-product for copulas introduced by Darsow, Nguyen and Olsen in 1992. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

8. Some methods to obtain t-norms and t-conorms on bounded lattices

Creator:
Çayli, Gül Deniz
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
t-norm, ordinal sum, t-conorm, and bounded lattice
Language:
English
Description:
In this study, we introduce new methods for constructing t-norms and t-conorms on a bound\-ed lattice L based on a priori given t-norm acting on [a,1] and t-conorm acting on [0,a] for an arbitrary element a∈L∖{0,1}. We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public