Results 1 to 10 of about 329 (158)

Continuous Archimedean t-norms and their bounds

Fuzzy Sets and Systems, 2001
In this interesting paper the authors study upper and lower bounds in the class of continuous Archimedean t-norms. Using additive generators and the class of subadditive functions, the authors describe (in a constructive way) how to construct these bounds. Extensions and some applications are presented.
Vladimír Marko, Radko Mesiar
openaire   +1 more source

Fuzzy implications derived from additive generators of continuous Archimedean t-norms

International Journal of Intelligent Systems, 2012
One class of fuzzy implications is introduced by means of the additive generators of continuous Archimedean t-norms. Basic properties of these implications are discussed. These implications are shown to be different from the known (S,N)-, R-, QL-, and Yager's f- and g-implications. Several functional equations with fuzzy implications are investigated. ©
Huawen Liu, Zhen-Bo Li
openaire   +1 more source

Conditional distributivity for uni-nullnorms with continuous and Archimedean underlying t-norms and t-conorms

Journal of Intelligent & Fuzzy Systems, 2019
The conditional distributivity, also called restricted distributivity, is crucial for many different areas such as utility theory and integral theory. This is the because it weakens distributivity on the domain. This paper is focused on and fully characterizes the conditional distributivity for a uni-nullnorm with continuous and Archimedean underlying ...
Gang Wang, Feng Qin 0002, Wen-Huang Li
openaire   +1 more source

On the determination of left-continuous t-norms and continuous archimedean t-norms on some segments

Aequationes mathematicae, 2005
A \(t\)(riangular) norm is a function \(T:[0,1]^2\to [0,1]\) such that for all \(x,y,z\in [0,1]\) we have \(T(x,y)=T(y,x),\,T(T(x,y),z)=T(x,T(y,z)),\,T(x,1)=x\) and \(T(x,\cdot)\) is increasing. The author finds new sets of uniqueness for (continuous Archimedean and left continuous) \(t\)-norms. These sets of uniqueness are some vertical segments of \([
openaire   +2 more sources

The dominance relation in some families of continuous Archimedean t-norms and copulas

Fuzzy Sets and Systems, 2009
Recently, \textit{P. Sarkoci} [Aequationes Math. 75, No. 3, 201--207 (2008; Zbl 1148.26016)] has shown that the dominance relation is not transitive in the class of continuous t-norms. When applying triangular norms, mostly some special families are considered and then it is important to know whether the transitivity of the dominance relation holds in ...
openaire   +2 more sources

On two distributivity equations for fuzzy implications and continuous, Archimedean t-norms and t-conorms

Fuzzy Sets and Systems, 2013
Recently, we have examined the solutions of the following distributivity functional equation I(x,S"1(y,z))=S"2(I(x,y),I(x,z)), when S"1, S"2 are continuous, Archimedean t-conorms and I is an unknown function. In particular, between these solutions, we have shown that implication functions are among its solutions.
openaire   +1 more source

Distributivity of Implication Operations over T-Representable T-Norms Generated from Continuous and Archimedean T-Norms

2012
During previous IPMU 2010 conference we have started investigations connected with finding all solutions of the distributive equation of implications \(\mathcal{I}(x,\mathcal{T}_1(y,z)) = \mathcal{T}_2(\mathcal{I}(x,y),\mathcal{I}(x,z))\) over t-representable t-norms in interval-valued fuzzy sets theory, i.e., when t-representable t-norms \(\mathcal{T ...
openaire   +1 more source

The Equation I(S(x, y), z) = T(I(x, z), I(y, z)) for t-representable t-conorms and t-norms Generated from Continuous, Archimedean Operations.

2013
In this article we continue investigations presented at previous WILF 2011 conference which are connected with distributivity of implication operations over t-representable t-norms and t-conorms. Our main goal is to show the general method of solving the following distributivity equation \(\mathcal{I}(\mathcal{S}(x,y),z) = \mathcal{T}(\mathcal{I}(x,z),\
openaire   +2 more sources

Pseudo-uninorms with continuous Archimedean underlying functions

Fuzzy Sets and Systems, 2023
Andrea Mesiarová-Zemánková
exaly  

Solving max-Archimedean t-norm interval-valued fuzzy relation equations

Fuzzy Sets and Systems, 2022
Antika Thapar
exaly