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Additive Generator
The Experts below are selected from a list of 174 Experts worldwide ranked by ideXlab platform
Yao Ouyang – 1st expert on this subject based on the ideXlab platform

On the migrativity of triangular subnorms
Fuzzy Sets and Systems, 2013CoAuthors: Limin Wu, Yao OuyangAbstract:The (@a,T)migrative triangular subnorms, where T stands for the three prototype triangular norms (namely the product, the Lukasiewicz tnorm 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.

a generalization of Additive Generator of triangular norms
International Journal of Approximate Reasoning, 2008CoAuthors: 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 pseudotnorms and tsubnorms are also discussed. Several illustrative examples are given.

On the convex combination of TD and continuous triangular norms
Information Sciences, 2007CoAuthors: 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 leftcontinuous tnorms which can be combined with each other are given.
Peter Viceník – 2nd expert on this subject based on the ideXlab platform

Strictly Increasing Additive Generators of the Second Kind of Associative Binary Operations
Tatra mountains mathematical publications, 2019CoAuthors: 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. 
On some algebraic and topological properties of generated bordercontinuous triangular norms
Fuzzy Sets and Systems, 2013CoAuthors: Peter ViceníkAbstract:In the class of all bordercontinuous triangular norms generated by strictly decreasing Additive Generators the following algebraic and topological properties are studied in detail: the continuity (leftcontinuity/rightcontinuity), the bordercontinuity, 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 bordercontinuous triangular norm are expressed in terms of properties of generated functions. Some relevant examples and counterexamples are indicated.

Additive Generators of bordercontinuous triangular norms
Fuzzy Sets and Systems, 2008CoAuthors: Peter ViceníkAbstract:The characterization of all Additive Generators of bordercontinuous triangular norms (conorms) is introduced. It is also shown that the pseudoinverse of the Cantor function is an Additive Generator with a dense set of all points of discontinuity in [0,1] yielding a bordercontinuous triangular conorm.
Radko Mesiar – 3rd expert on this subject based on the ideXlab platform

On Additive Generators of overlap functions
Fuzzy Sets and Systems, 2016CoAuthors: 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 tnorm T, we analyze the overlap functions which are obtained by the distortion of T by a pseudoautomorphism, showing that the Additive Generator pair of such overlap function may be given in terms of the considered pseudoautomorphism 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.

A generalization of the migrativity property of aggregation functions
Information Sciences, 2012CoAuthors: 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 @amigrativity 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 @aBmigrativity and Bmigrativity. 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 tnorms, strict tconorms and representable uninorms.

Metrics and TEqualities
Journal of Mathematical Analysis and Applications, 2002CoAuthors: 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 leftcontinuous. Furthermore, it is shown that to any leftcontinuous 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 ).