The Experts below are selected from a list of 126 Experts worldwide ranked by ideXlab platform
Andrea Mesiarovazemankova - One of the best experts on this subject based on the ideXlab platform.
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characterization of n uninorms with continuous underlying functions via z Ordinal Sum construction
International Journal of Approximate Reasoning, 2021Co-Authors: Andrea MesiarovazemankovaAbstract:Abstract The n-uninorms with continuous underlying t-norms and t-conorms are characterized via the z-Ordinal Sum construction. We show that each n-uninorm with continuous underlying t-norms and t-conorms can be expressed as a z-Ordinal Sum of a countable number of Archimedean and idempotent semigroups with respect to the branching set A ∼ { z 1 , … , z n − 1 } , where the corresponding partial order has a tree structure.
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a note on decomposition of idempotent uninorms into an Ordinal Sum of singleton semigroups
Fuzzy Sets and Systems, 2016Co-Authors: Andrea MesiarovazemankovaAbstract:The idempotent uninorms are characterized by means of the Ordinal Sum of Clifford. It is shown that idempotent uninorms are in one-to-one correspondence with special linear orders on 0 , 1 . A connection between respective linear order on 0 , 1 and the characterizing multi-function of the uninorm is also investigated.
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Ordinal Sum construction for uninorms and generalized uninorms
International Journal of Approximate Reasoning, 2016Co-Authors: Andrea MesiarovazemankovaAbstract:Abstract The Ordinal Sum construction yielding uninorms is studied. A special case when all Summands in the Ordinal Sum are isomorphic to uninorms is discussed and the most general semigroups that yield a uninorm via the Ordinal Sum construction, called generalized uninorms, are studied.
Hua-wen Liu - One of the best experts on this subject based on the ideXlab platform.
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Distributivity of the Ordinal Sum Implications Over t-Norms and t-Conorms
IEEE Transactions on Fuzzy Systems, 2016Co-Authors: Wenwen Zong, Hua-wen LiuAbstract:Recently, Su and Liu have introduced a new class of fuzzy implications, called Ordinal Sum implications, and discussed some of their desirable properties, such as neutrality property, consequent boundary, exchange principle, etc. In this paper, we explore the class of Ordinal Sum implications with respect to distributivity. Necessary and sufficient conditions, under which Ordinal Sum implications are distributive over t-norms and t-conorms are given.
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on Ordinal Sum implications
Information Sciences, 2015Co-Authors: Aifang Xie, Hua-wen LiuAbstract:Abstract A new class of fuzzy implications, called Ordinal Sum implications, is introduced by means of the Ordinal Sum of a family of given implications, which is similar to the Ordinal Sum of t -norms (or t -conorms). Basic properties of Ordinal Sum implications are discussed. It is shown that the Ordinal Sum implication is really a new class, which is different from the known ( S , N ) -, R -, QL - and Yager’s f - and g -implications.
Lidong Wang - One of the best experts on this subject based on the ideXlab platform.
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Ordinal Sum of two binary operations being a t norm on bounded lattice
IEEE Transactions on Fuzzy Systems, 2021Co-Authors: Qin Zhang, Gul Deniz Cayli, Xu Zhang, Lidong WangAbstract:The Ordinal Sum of t-norms on a bounded lattice has been used to construct other t-norms. However, an Ordinal Sum of binary operations (not necessarily t-norms) defined on the fixed subintervals of a bounded lattice may not be a t-norm. Some necessary and sufficient conditions are presented in this paper for ensuring that an Ordinal Sum on a bounded lattice of two binary operations is, in fact, a t-norm. In particular, the results presented here provide an answer to an open problem put forward by Ertugrul and Yesilyurt [Ordinal Sums of triangular norms on bounded lattices, Inf. Sci., 517 (2020) 198-216].
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Characterizing an Ordinal Sum of two binary operations being a t-norm on bounded lattice
arXiv: General Mathematics, 2020Co-Authors: Qin Zhang, Xu Zhang, Lidong WangAbstract:This paper obtains some characterizations for the Ordinal Sum in the sense of Ertuǧrul and Yesilyurt of two binary operations (not necessarily $t$-norms) being increasing or a $t$-norm, answering an open problem posed by Ertuǧrul and Yesilyurt in [12].
Sandor Jenei - One of the best experts on this subject based on the ideXlab platform.
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a note on the Ordinal Sum theorem and its consequence for the construction of triangular norms
Fuzzy Sets and Systems, 2002Co-Authors: Sandor JeneiAbstract:In this paper, the well-known Ordinal Sum theorem of semigroups is generalized and applied to construct new families of triangular subnorms and triangular norms (t-norms). Among them one can find several new families of left-continuous t-norms too.
Radko Mesiar - One of the best experts on this subject based on the ideXlab platform.
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new types of Ordinal Sum of fuzzy implications
IEEE International Conference on Fuzzy Systems, 2017Co-Authors: Michal Baczynski, Anna Krol, Pawel Drygas, Radko MesiarAbstract:In this contribution new ways of constructing of Ordinal Sum of fuzzy implications are proposed. These methods are based on a construction of Ordinal Sums of overlap functions. Moreover, preservation of some properties of these Ordinal Sums of fuzzy implications are examined. Among others neutrality property, identity property, and ordering property are considered.
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Ordinal Sums and idempotents of copulas
Aequationes Mathematicae, 2010Co-Authors: Radko Mesiar, Carlo SempiAbstract:We prove that the Ordinal Sum of n-copulas is always an n-copula and show that every copula may be represented as an Ordinal Sum, once the set of its idempotents is known. In particular, it will be shown that every copula can be expressed as the Ordinal Sum of copulas having only trivial idempotents. As a by-product, we also characterize all associative copulas whose n-ary forms are n-copulas for all n.
