The Experts below are selected from a list of 174 Experts worldwide ranked by ideXlab platform
Yao Ouyang - One of the best experts on this subject based on the ideXlab platform.
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On the migrativity of triangular subnorms
Fuzzy Sets and Systems, 2013Co-Authors: Limin Wu, Yao OuyangAbstract:The (@a,T)-migrative triangular subnorms, where T stands for the three prototype triangular norms (namely the product, the Lukasiewicz t-norm and the minimum), are investigated in detail. The paper gives necessary and sufficient conditions under which a triangular subnorm with a continuous Additive Generator is (@a,T)-migrative with respect to any of the three prototype triangular norms.
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a generalization of Additive Generator of triangular norms
International Journal of Approximate Reasoning, 2008Co-Authors: Yao Ouyang, Jinxuan Fang, Zhenjiang ZhaoAbstract:This short note is devoted to the generalization of the concept of Additive Generators of triangular norms. The cases of pseudo-t-norms and t-subnorms are also discussed. Several illustrative examples are given.
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On the convex combination of TD and continuous triangular norms
Information Sciences, 2007Co-Authors: Yao Ouyang, Jinxuan Fang, Guiling LiAbstract:The problem of when T"@l@?(1-@l)T"D+@lT@l@?(0,1) is a triangular norm, where T"D is the drastic product and T is a continuous triangular norm, is studied. It is shown that T"@l cannot be a triangular norm when T is nilpotent. It is also shown that T"@l is a triangular norm if T is strict and its Additive Generator f satisfies f(@lx)=f(x)+f(@l) for all x@?[0,1]. The cases that T=T"M and T is the ordinal sum of continuous Archimedean summands are also discussed. Some left-continuous t-norms which can be combined with each other are given.
Peter Viceník - One of the best experts on this subject based on the ideXlab platform.
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Strictly Increasing Additive Generators of the Second Kind of Associative Binary Operations
Tatra mountains mathematical publications, 2019Co-Authors: Peter ViceníkAbstract:Abstract The class of strictly increasing Additive Generators of the second kind is defined and analyzed. Necessary and sufficient conditions for a binary operation generated by a strictly increasing Additive Generator of the second kind to be associative are introduced. The relation between the class of strictly increasing Additive Generators of the second kind of associative binary operations and the class of discrete upper Additive Generators of associative binary operations is revealed.
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On some algebraic and topological properties of generated border-continuous triangular norms
Fuzzy Sets and Systems, 2013Co-Authors: Peter ViceníkAbstract:In the class of all border-continuous triangular norms generated by strictly decreasing Additive Generators the following algebraic and topological properties are studied in detail: the continuity (left-continuity/right-continuity), the border-continuity, the conditional cancellation law, the cancellation law, the Archimedean Property, the diagonal property, the continuity on the diagonal and also the associative law. The relations among these properties are examined. A special attention is devoted to the set of all idempotent elements of generated functions and to the set of all points of discontinuity of an Additive Generator. The necessary and sufficient conditions for a generated function to be a border-continuous triangular norm are expressed in terms of properties of generated functions. Some relevant examples and counterexamples are indicated.
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Additive Generators of border-continuous triangular norms
Fuzzy Sets and Systems, 2008Co-Authors: Peter ViceníkAbstract:The characterization of all Additive Generators of border-continuous triangular norms (conorms) is introduced. It is also shown that the pseudo-inverse of the Cantor function is an Additive Generator with a dense set of all points of discontinuity in [0,1] yielding a border-continuous triangular conorm.
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Additive Generators of associative functions
Fuzzy Sets and Systems, 2005Co-Authors: Peter ViceníkAbstract:Associativity of a two place function T(x,y)=f^(^-^1^)(f(x)+f(y)) where f:[0,1]->[0,~] is a strictly monotone function andf^(^-^1^):[0,~]->[0,1] is the pseudo-inverse of f depends only on properties of the range of f. The following question is answered: what property of the range of an Additive Generator f is necessary and sufficient for associativity of the corresponding generated function T? We also introduce the characterization of all Additive Generators f of T with property T(...T(T(x"1,x"2),x"3),...,x"n)=f^(^-^1^)(f(x"1)+...+f(x"n)) for all [email protected]?N,n>=2 and for all x"1,...,x"[email protected]?[0,1]. Some constructions of non-continuous Additive Generators of associative functions are presented.
Radko Mesiar - One of the best experts on this subject based on the ideXlab platform.
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On Additive Generators of overlap functions
Fuzzy Sets and Systems, 2016Co-Authors: Graçaliz Pereira Dimuro, Benjamin Bedregal, Humberto Bustince, Maria José Asiain, Radko MesiarAbstract:In this paper we introduce the notion of Additive Generator pair for overlap functions. We also study how some of the properties that can be demanded to an overlap function can be expressed in terms of its Generator pair. In particular, given a continuous and positive t-norm T, we analyze the overlap functions which are obtained by the distortion of T by a pseudo-automorphism, showing that the Additive Generator pair of such overlap function may be given in terms of the considered pseudo-automorphism and the Additive Generator of T. Finally, we also consider the influence of the migrativity, homogeneity and idempotency properties for the overlap functions obtained by such distortion in terms of their respective Additive Generator pairs.
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A generalization of the migrativity property of aggregation functions
Information Sciences, 2012Co-Authors: Humberto Bustince, Radko Mesiar, B. De Baets, Javier Fernandez, Javier MonteroAbstract:This paper brings a generalization of the migrativity property of aggregation functions, suggested in earlier work of some of the present authors by imposing the @a-migrativity property of Durante and Sarkoci for all values of @a instead of a single one. Replacing the algebraic product by an arbitrary aggregation function B naturally leads to the properties of @a-B-migrativity and B-migrativity. This generalization establishes a link between migrativity and a particular case of Aczel's general associativity equation, already considered by Cutello and Montero as a recursive formula for aggregation. Following a basic investigation, emphasis is put on aggregation functions that can be represented in terms of an Additive Generator, more specifically, strict t-norms, strict t-conorms and representable uninorms.
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Metrics and T-Equalities
Journal of Mathematical Analysis and Applications, 2002Co-Authors: Bernard De Baets, Radko MesiarAbstract:Abstract The relationship between metrics and T -equalities is investigated; the latter are a special case of T -equivalences, a natural generalization of the classical concept of an equivalence relation. It is shown that in the construction of metrics from T -equalities triangular norms with an Additive Generator play a key role. Conversely, in the construction of T -equalities from metrics this role is played by triangular norms with a continuous Additive Generator or, equivalently, by continuous Archimedean triangular norms. These results are then applied to the biresidual operator E T of a triangular norm T . It is shown that E T is a T -equality on [0, 1] if and only if T is left-continuous. Furthermore, it is shown that to any left-continuous triangular norm T there correspond two particular T -equalities on F ( X ), the class of fuzzy sets in a given universe X ; one of these T -equalities is obtained from the biresidual operator E T T by means of a natural extension procedure. These T -equalities then give rise to interesting metrics on F ( X ).
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Fuzzy Days - Generated Connectives in Many Valued Logic
Lecture Notes in Computer Science, 1999Co-Authors: Radko MesiarAbstract:Many valued logic is based on the truth values range and the corresponding connectives of conjunction, disjunction, negation, implication, etc. Depending on the corresponding required properties, several relationships between MV connectives occur. So, e.g., de Morgan rules brings together conjunction, disjunction and negation; residuation relates conjunction and implication; negation is often required to be consistent with the corresponding implication; etc. On the other hand, up to the negation, all other mentioned connectives are binary operations and their real evaluation may be rather time consuming. Therefore a representation by means of (one argument) functions which are called Generators is considered. Recall such a wellknown representation of Archimedean continuous t-norms (as conjunctions on [0,1]) or t-conorms (as disjunctions on [0,1]) which is due to Ling [7] and in its general form was shown already by Mostert and Shields [9]. Note that the choice of an Additive Generator (which is strictly decreasing) of a continuous Archimedean t-norm T is unique up to a positive multiplicative constant. Further, if a continuous Archimedean t-norm T is generated by an Additive Generator f, then the dual t-conorm S, S(x, y) = 1 − T(1 − x, 1 − y) is generated by an Additive Generator g = f(1 − x). More, the corresponding residual implicator I is also defined by means of f, I(x, y) = f (−1)(max(0, f(y) − f(x))). See [2].
Zhenjiang Zhao - One of the best experts on this subject based on the ideXlab platform.
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a generalization of Additive Generator of triangular norms
International Journal of Approximate Reasoning, 2008Co-Authors: Yao Ouyang, Jinxuan Fang, Zhenjiang ZhaoAbstract:This short note is devoted to the generalization of the concept of Additive Generators of triangular norms. The cases of pseudo-t-norms and t-subnorms are also discussed. Several illustrative examples are given.
Alireza Nasr-isfahani - One of the best experts on this subject based on the ideXlab platform.
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Pure semisimple n-cluster tilting subcategories
Journal of Algebra, 2020Co-Authors: Ramin Ebrahimi, Alireza Nasr-isfahaniAbstract:Abstract From the viewpoint of higher homological algebra, we introduce pure semisimple n-abelian categories, which are analogs of pure semisimple abelian categories. Let Λ be an Artin algebra and M be an n-cluster tilting subcategory of Mod-Λ. We show that M is pure semisimple if and only if each module in M is a direct sum of finitely generated modules. Let m be an n-cluster tilting subcategory of mod-Λ. We show that Add ( m ) is an n-cluster tilting subcategory of Mod-Λ if and only if m has an Additive Generator if and only if Mod ( m ) is locally finite. This generalizes Auslander's classical results on pure semisimplicity of Artin algebras.
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Pure semisimple $n$-cluster tilting subcategories
arXiv: Representation Theory, 2019Co-Authors: Ramin Ebrahimi, Alireza Nasr-isfahaniAbstract:From the viewpoint of higher homological algebra, we introduce pure semisimple $n$-abelian category, which is analogs of pure semisimple abelian category. Let $\Lambda$ be an Artin algebra and $\mathcal{M}$ be an $n$-cluster tilting subcategory of $Mod$-$\Lambda$. We show that $\mathcal{M}$ is pure semisimple if and only if each module in $\mathcal{M}$ is a direct sum of finitely generated modules. Let $\mathfrak{m}$ be an $n$-cluster tilting subcategory of $mod$-$\Lambda$. We show that $Add(\mathfrak{m})$ is an $n$-cluster tilting subcategory of $Mod$-$\Lambda$ if and only if $\mathfrak{m}$ has an Additive Generator if and only if $Mod(\mathfrak{m})$ is locally finite. This generalizes Auslander's classical results on pure semisimplicity of Artin algebras.
