Results 111 to 120 of about 12,827,475 (135)
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On the Determination of Left-Continuous t-Norms and Continuous Archimedean t-Norms on Some Segments
Aequationes Mathematicae, 2005A \(t\)(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 \([
Sándor Jenei
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Continuous Archimedean t-Norms and Their Bounds
Fuzzy Sets and Systems, 2001In 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
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Characterizations of Uni-Nullnorms With Continuous Archimedean Underlying t-Norms and t-Conorms
Fuzzy Sets and Systems, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feng Sun, Xue-ping Wang, Xiao-Bing Qu
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Reconstruction of Additive Generators From Partial Derivatives of Continuous Archimedean t-Norms
2010 40th IEEE International Symposium on Multiple-Valued Logic, 2010The paper shows a direct correspondence between the first partial derivatives of a continuous Archimedean triangular norm and the first derivatives of its additive generator. An explicit formula for the additive generator is obtained. Application of the result is demonstrated on the problem of convex combinations of strict triangular norms.
Mirko Navara +2 more
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2011 4th International Conference on Biomedical Engineering and Informatics (BMEI), 2011
In order to avoid combinatorial rule explosion in fuzzy reasoning, in this work we explore the distributive equation of implication I(T(x, y), z) = S(I(x, z), I(y, z)). In detail, by means of the sections of I, we give out the sufficient and necessary conditions of solutions for the distributive equation of implication I(T (x, y), z) = S(I(x, z), I(y ...
Feng Qin, Ping-Chong Yang
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In order to avoid combinatorial rule explosion in fuzzy reasoning, in this work we explore the distributive equation of implication I(T(x, y), z) = S(I(x, z), I(y, z)). In detail, by means of the sections of I, we give out the sufficient and necessary conditions of solutions for the distributive equation of implication I(T (x, y), z) = S(I(x, z), I(y ...
Feng Qin, Ping-Chong Yang
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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.
Michał Baczyński
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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.
Michał Baczyński
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A Note to the Addition of Fuzzy Numbers Based on a Continuous Archimedean T-Norm
Fuzzy Sets and Systems, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Characterizations of (Weakly) Archimedean t-Norms in Interval-Valued Fuzzy Set Theory
Fuzzy Sets and Systems, 2009 In this paper we first give characterizations of the class of continuous t-norms on L^I (where L^I is the lattice of closed subintervals of the unit interval) which satisfy the residuation principle and which are a natural extension of a t-norm on the ...
Glad Deschrijver
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Mathematica Slovaca, 2023
ABSTRACT The issue of distributivity of aggregation operators is crucial for many different areas such as fuzzy sets and fuzzy logic, pseudo-analysis and measure theory, and particulary in the decision making theory. The problem of distributivity of an operator form a special class of uni-nullnorms over a general uninorm is being ...
Jočić, Dragan, Štajner-Papuga, Ivana
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ABSTRACT The issue of distributivity of aggregation operators is crucial for many different areas such as fuzzy sets and fuzzy logic, pseudo-analysis and measure theory, and particulary in the decision making theory. The problem of distributivity of an operator form a special class of uni-nullnorms over a general uninorm is being ...
Jočić, Dragan, Štajner-Papuga, Ivana
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IEEE Transactions on Fuzzy Systems, 2021
Yager's q -rung orthopair fuzzy set is a generalization of fuzzy sets, whose prominent feature is that the q th power sum of the membership and the nonmembership degrees is equal to or less than one, and we call its core, an ordered pair, q -rung orthopair fuzzy number ( q -ROFN).
Zhenghai Ai +3 more
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Yager's q -rung orthopair fuzzy set is a generalization of fuzzy sets, whose prominent feature is that the q th power sum of the membership and the nonmembership degrees is equal to or less than one, and we call its core, an ordered pair, q -rung orthopair fuzzy number ( q -ROFN).
Zhenghai Ai +3 more
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