The Experts below are selected from a list of 87945 Experts worldwide ranked by ideXlab platform
Hua-wen Liu - One of the best experts on this subject based on the ideXlab platform.
-
The Distributivity Equations of Semi-Uninorms
International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 2019Co-Authors: Hua-wen Liu, Witold PedryczAbstract:Distributivity between two operations is a property posed many years ago — that is especially interesting in the framework of logical connectives because of its applications to fuzzy logic and approximate reasoning as their applications. Since semi-uninorms have been used in these topics, the study of the Distributivity between two semi-uninorms becomes of particular interest that calls for thorough studies. The Distributivity between two semi-uninorms, which are non-commutative and non-associative uninorms, has been developed only in the cases when both semi-uninorms are examples of very special classes of semi-uninorms. On the other hand, in general, the Distributivity does not rely on the commutativity and associativity. The objective of this work is twofold. The first one is to show new solutions to Distributivity equations for semi-uninorms. The second one is to check whether the results concerning the Distributivity between two uninorms are valid for semi-uninorms. We investigate the Distributivity involving two semi-uninorms when only one semi-uninrom lies in the most studied classes of semi-uninorms, achieving the above two objectives simultaneously.
-
the Distributivity equations of semi uninorms
International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 2019Co-Authors: Hua-wen Liu, Witold PedryczAbstract:Distributivity between two operations is a property posed many years ago — that is especially interesting in the framework of logical connectives because of its applications to fuzzy logic and appr...
-
the Distributivity equation for uninorms revisited
Fuzzy Sets and Systems, 2018Co-Authors: Hua-wen Liu, Daniel Ruizaguilera, Juan Vicente Riera, Joan TorrensAbstract:Abstract The Distributivity equation has been widely studied involving different classes of aggregation functions from t-norms and t-conorms to uninorms, nullnorms and generalizations of them. It is important in the framework of logical connectives because of its applications in fuzzy logic and approximate reasoning as well as in image processing. Since uninorms have been used in these topics, the study of the Distributivity between two uninorms becomes specially interesting. In a recent paper by the same authors the already known solutions were compiled and completed when the first uninorm is in any of the most studied classes of uninorms and the second uninorm is anyone. In this paper we want to achieve this study by focusing on the reverse direction, that is, for the cases when the second uninorm lies in any of the most studied classes of uninorms and the first one is any uninorm. We show along the paper that this new point of view leads to many new solutions.
-
on Distributivity equations for uninorms over semi t operators
Fuzzy Sets and Systems, 2016Co-Authors: Wenwen Zong, Hua-wen LiuAbstract:Recently, Drygaź generalized nullnorms and t-operators and introduced semi-t-operators by eliminating commutativity from the axioms of t-operators. Distributivity equations were investigated in families of certain operations (e.g. triangular norms, conorms, uninorms and nullnorms (or called t-operators)). In this paper, we give out the solutions of Distributivity equations for uninorms over semi-t-operators. Previous results about Distributivity equations for uninorms over nullnorms can be obtained as corollaries.
-
the Distributivity equations for semi t operators over uninorms
Fuzzy Sets and Systems, 2016Co-Authors: Wenwen Zong, Hua-wen Liu, Peijun XueAbstract:Recently the Distributivity equation was discussed in families of certain operations (e.g. triangular norms, conorms, uninorms and nullnorms (or called t-operators)). In this paper we describe the solutions of Distributivity for semi t-operators over uninorms. Previous results about Distributivity for nullnorms over uninorms can be obtained as a corollary.
Feng Qin - One of the best experts on this subject based on the ideXlab platform.
-
on the Distributivity equations between uni nullnorms and overlap grouping functions
Fuzzy Sets and Systems, 2021Co-Authors: Tinghai Zhang, Feng QinAbstract:Abstract The Distributivity equations between different binary aggregation functions have become an interesting and vast research field since Aczel studied them. This paper is mainly devoted to solving the Distributivity equations between uni-nullnorms and overlap (grouping) functions. The sufficient and necessary conditions for the Distributivity equations between them are obtained, and during the process, the full characterization of any idempotent uni-nullnorm is given.
-
Distributivity and conditional Distributivity for uni-nullnorms
Fuzzy Sets and Systems, 2019Co-Authors: Gang Wang, Feng QinAbstract:Abstract The Distributivity and conditional Distributivity of a uninorm over a continuous t-conorm is an open problem posed by Klement in the Linz Seminar 2000 closing session. After this, the study of Distributivity and conditional Distributivity between two aggregation operators become specially interesting. In this work, we continue investigating the same topic for uni-nullnorms, then the full characterization of all pairs ( F , G ) satisfying Distributivity and conditional Distributivity is given, where F is a uni-nullnorm, G is a t-norm, or a t-conorm, or a uninorm from U min and U max .
-
left and right Distributivity equations for semi t operators and uninorms
Fuzzy Sets and Systems, 2017Co-Authors: Pawel Drygaś, Feng Qin, Ewa RakAbstract:Abstract Recently, the Distributivity equation for different kind of operators has become a focus of research as the crucial tool in the numerous applications as utility and optimization theory, or integration theory. The main purpose of this paper is to study the Distributivity equations between two special classes of aggregation operators namely, semi-t-operators and uninorms. Without the commutativity assumption of semi-t-operators it is necessary to consider the left and the right Distributivity conditions separately. In both cases, the obtained solutions are significantly different.
-
Distributivity between semi uninorms and semi t operators
Fuzzy Sets and Systems, 2016Co-Authors: Feng QinAbstract:The problem of Distributivity was posed many years ago and it has been investigated for families of certain operations, such as t-norms, t-conorms, uninorms, and nullnorms. In this study, we continue the investigation of this same topic by focusing on semi-uninorms and semi-t-operators, which are generalizations of uninorms and t-operators that are obtained by omitting commutativity and associativity, and commutativity, respectively. The results obtained provide the full characterizations, except for a special subcase, and we extend the previous results regarding Distributivity between uninorms and nullnorms, as well as between semi-uninorms and semi-nullnorms. Moreover, we propose a more reasonable method for obtaining a proof to demonstrate the Distributivity between semi-uninorms and semi-t-operators.
-
Distributivity between semi t operators and mayor s aggregation operators
Information Sciences, 2016Co-Authors: Feng Qin, Yaming WangAbstract:The problem of Distributivity was first posed over forty years ago and it has been investigated for families of certain operations such as t-norms, t-conorms, uninorms, and nullnorms. In this paper, we investigate this topic further by focusing on Mayor's aggregation operators and semi-t-operators, which generalize the t-operators by omitting commutativity. The results that we obtain are complete and extend previous results concerning Distributivity between Mayor's aggregation operators and semi-nullnorms.
Ewa Rak - One of the best experts on this subject based on the ideXlab platform.
-
left and right Distributivity equations for semi t operators and uninorms
Fuzzy Sets and Systems, 2017Co-Authors: Pawel Drygaś, Feng Qin, Ewa RakAbstract:Abstract Recently, the Distributivity equation for different kind of operators has become a focus of research as the crucial tool in the numerous applications as utility and optimization theory, or integration theory. The main purpose of this paper is to study the Distributivity equations between two special classes of aggregation operators namely, semi-t-operators and uninorms. Without the commutativity assumption of semi-t-operators it is necessary to consider the left and the right Distributivity conditions separately. In both cases, the obtained solutions are significantly different.
-
Distributivity equations in the class of semi t operators
Fuzzy Sets and Systems, 2016Co-Authors: Pawe Dryga, Ewa RakAbstract:Recently, the Distributivity equations have been discussed in families of certain operations (e.g., triangular norms, conorms, uninorms, and nullnorms). In this study, we present the solutions to Distributivity between semi-t-operators. Previous results related to the Distributivity between nullnorms and between semi-t-operators and semi-nullnorms can be obtained as simple corollaries.
-
Distributivity equation in the class of 2 uninorms
Fuzzy Sets and Systems, 2016Co-Authors: Pawe Dryga, Ewa RakAbstract:This paper is mainly devoted to solving the functional equation of Distributivity between aggregation operators with 2-neutral element. Our investigations are motivated by the couple of distributive logical connectives and their generalizations used in fuzzy set theory e.g., triangular norms, conorms, uninorms, nullnorms and implications. One of the recent generalizations covering both uninorms and nullnorms are 2-uninorms, which form a class of commutative, associative and increasing operators on the unit interval with an absorbing element separating two subintervals having their own neutral elements. In this work the Distributivity of two binary operators from the class of 2-uninorms is considered. In particular, all possible solutions of the Distributivity equation for the three defined subclasses of these operators depending on the position of its zero and neutral elements are characterized.
-
the Distributivity property of increasing binary operations
Fuzzy Sets and Systems, 2013Co-Authors: Ewa RakAbstract:Abstract This paper is mainly devoted to solving the functional equations of Distributivity and conditional Distributivity of increasing binary operations with the unit. Our investigations are motivated by distributive logical connectives and their generalizations used in fuzzy set theory. In particular, some assumptions (namely associativity and commutativity) and results about conditional Distributivity of uninorms and triangular norms and triangular conorms were simplified. Moreover, some other properties e.g. componentwise convexity (concavity) for special operations from the class of quasi-copulas is considered.
-
Distributivity between uninorms and nullnorms
Fuzzy Sets and Systems, 2008Co-Authors: Józef Drewniak, Paweł Drygaś, Ewa RakAbstract:Recently the Distributivity equation was investigated in families of certain operations (e.g. triangular norms, conorms, uninorms and nullnorms). Generally, the assumption of associativity is not necessary in consideration of Distributivity equation. Moreover, if we omit commutativity assumption, consideration of the left and right Distributivity conditions is reasonable. Previous results about Distributivity between uninorms and nullnorms can be obtained as simple corollaries.
Ivana Stajnerpapuga - One of the best experts on this subject based on the ideXlab platform.
-
left and right Distributivity equations in the class of semi t operators
Fuzzy Sets and Systems, 2019Co-Authors: Dragan Jocic, Pawel Drygaś, Ivana StajnerpapugaAbstract:Abstract The issue of Distributivity is crucial for many different theoretical areas such as the utility theory and the integration theory. Also, this problem is of high interest for modelling some practical situations from, e.g., fields of economics and social sciences. Thus, recently, the Distributivity equations have been studied for different classes of aggregation operators by a significant number of researchers. The focus of this paper in particular is on solving the left and the right Distributivity equations between semi-t-operators.
-
on the conditional Distributivity of continuous semi t operators over uninorms
Fuzzy Sets and Systems, 2018Co-Authors: Dragan Jocic, Ivana StajnerpapugaAbstract:Abstract The issue of conditional Distributivity, or how it is also called, restricted Distributivity, which is a form of relaxed Distributivity on the restricted domain, is crucial for many different areas such as utility theory and integration theory. The focus of this paper is on this specific form of Distributivity for a continuous semi-t-operator with respect to a continuous t-conorm and for a continuous semi-t-operator with respect to a uninorm of the form U min or U max with continuous underlying t-norm and t-conorm.
-
restricted Distributivity for aggregation operators with absorbing element
Fuzzy Sets and Systems, 2013Co-Authors: Dragan Joci, Ivana StajnerpapugaAbstract:The problem of restricted Distributivity, i.e., a form of relaxed Distributivity on the restricted domain, plays an important role in many different fields such as utility theory and integration theory. This paper considers the following two cases of restricted Distributivity: (i) a continuous nullnorm with respect to a continuous t-conorm and (ii) a continuous nullnorm with respect to a uninorm of the form U"m"i"n or U"m"a"x with continuous underlying t-norm and t-conorm.
Joan Torrens - One of the best experts on this subject based on the ideXlab platform.
-
the Distributivity equation for uninorms revisited
Fuzzy Sets and Systems, 2018Co-Authors: Hua-wen Liu, Daniel Ruizaguilera, Juan Vicente Riera, Joan TorrensAbstract:Abstract The Distributivity equation has been widely studied involving different classes of aggregation functions from t-norms and t-conorms to uninorms, nullnorms and generalizations of them. It is important in the framework of logical connectives because of its applications in fuzzy logic and approximate reasoning as well as in image processing. Since uninorms have been used in these topics, the study of the Distributivity between two uninorms becomes specially interesting. In a recent paper by the same authors the already known solutions were compiled and completed when the first uninorm is in any of the most studied classes of uninorms and the second uninorm is anyone. In this paper we want to achieve this study by focusing on the reverse direction, that is, for the cases when the second uninorm lies in any of the most studied classes of uninorms and the first one is any uninorm. We show along the paper that this new point of view leads to many new solutions.
-
on the Distributivity property for uninorms
Fuzzy Sets and Systems, 2016Co-Authors: Hua-wen Liu, Daniel Ruizaguilera, Vicente J Riera, Joan TorrensAbstract:Abstract Distributivity between two operations is a property that was already posed many years ago and that is especially interesting in the framework of logical connectives. For this reason, the Distributivity property has been extensively studied for several families of operations like triangular norms and conorms, some kinds of uninorms and nullnorms (also called t-operators) and even for some generalizations of them. In this paper we investigate the Distributivity equation involving two uninorms lying in any one of the most studied classes of uninorms, leading to many new solutions.
-
Distributivity and conditional Distributivity of a uninorm and a continuous t-conorm
IEEE Transactions on Fuzzy Systems, 2006Co-Authors: Daniel Ruiz, Joan TorrensAbstract:The open problem recalled by Klement in the Linz2000 closing session, related to Distributivity and conditional Distributivity of a uninorm and a continuous t-conorm, is solved for the most usual known classes of uninorms. From the obtained results, it is deduced that Distributivity and conditional Distributivity are equivalent for these cases. It is remarkable that solutions appear involving not only strict t-conorms but also ordinal sums of the maximum with a strict t-conorm. Conversely, the Distributivity of a t-conorm over a uninorm is also studied leading only to already known solutions. Moreover, the dual case of Distributivity and conditional Distributivity involving uninorms and continuous t-norms is also solved, proving again the equivalence of both kinds of distributivities
-
corrigendum corrigendum to the Distributivity condition for uninorms and t operators fuzzy sets and systems 128 2002 209 225
Fuzzy Sets and Systems, 2005Co-Authors: Margarita Mas, Gaspar Mayor, Joan TorrensAbstract:In this paper, the study of the Distributivity equation involving uninorms in U given in (Fuzzy Sets and Systems, 128 (2002) 209-225.) is revised. Two wrong propositions in the mentioned reference are corrected and their right versions are proved.
