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The Archimedean Property for t-Norms in Interval-Valued Fuzzy Set Theory

Fuzzy Sets and Systems, 2006
In this paper, the Archimedean property of t-norms on the lattice L^I is introduced, where L^I is the underlying lattice of interval-valued fuzzy set theory (R. Sambuc) and intuitionistic fuzzy set theory (K.T. Atanassov).
Glad Deschrijver
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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
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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
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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 ...
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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),\
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Dominance on Continuous Archimedean Triangular Norms and Generalized Mulholland Inequality

Fuzzy Sets and Systems, 2021
Milan Petrik
exaly  

Resolution of Composite Fuzzy Relation Equations Based on Archimedean Triangular Norms

Fuzzy Sets and Systems, 2001
Spyros G Tzafestas, Giorgos B Stamou
exaly  

Constructing new loss functions for machine learning using strict continuous Archimedean t-norms

2025 11th International Conference on Optimization and Applications (ICOA)
Mohamed Hssini, Mustapha Atraoui
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Some Issues on Intuitionistic Fuzzy Aggregation Operators Based on Archimedean t-Conorm and t-Norm

Knowledge-Based Systems, 2012
Meimei Xia, Xu Zeshui
exaly  

Smoothly Generated Archimedean Approximation of Continuous Triangular Norms

Fuzzy Sets and Systems, 1999
Endre Pap
exaly