Results 231 to 240 of about 113,183 (266)
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A characterization of the Hamacher family of t-norms
Fuzzy Sets and Systems, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fodor, János C., Keresztfalvi, Tibor
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2000
The aim of this chapter is to provide the reader with a collection of parameterized families of t-norms which we think are interesting from various points of view. We have chosen this compact form of presentation in order to simplify the search for specific examples.
Erich Peter Klement +2 more
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The aim of this chapter is to provide the reader with a collection of parameterized families of t-norms which we think are interesting from various points of view. We have chosen this compact form of presentation in order to simplify the search for specific examples.
Erich Peter Klement +2 more
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T-norms in subtractive clustering and backpropagation
International Journal of Intelligent Systems, 2010Summary: The tuning of a fuzzy model is discussed in the context of choices made between different t-norms. The effects of the choice is illustrated by looking at two fuzzy models initially generated, respectively, by grid partition and a novel variant of subtractive clustering. The new variant of subtractive clustering introduced in the paper is based
Andrea Mesiarová-Zemánková +1 more
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2000
We have already seen that there is a strict (pointwise) order relationship (1.5) between the four basic t-norms T M, T P, T L, and T D, and that each t-norm lies between the two extremes T M and T D (see (1.4)). It is also clear that the pointwise comparison of two t-norms is a partial order.
Erich Peter Klement +2 more
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We have already seen that there is a strict (pointwise) order relationship (1.5) between the four basic t-norms T M, T P, T L, and T D, and that each t-norm lies between the two extremes T M and T D (see (1.4)). It is also clear that the pointwise comparison of two t-norms is a partial order.
Erich Peter Klement +2 more
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2000
For the rather general class of all t-norms, which includes non-continuous t-norms and even t-norms which are not Borel measurable, no universal representation theorems exist so far. In fact, such a characterization of arbitrary t-norms would be closely related to the solution of the famous, still unsolved general associativity functional equation.
Erich Peter Klement +2 more
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For the rather general class of all t-norms, which includes non-continuous t-norms and even t-norms which are not Borel measurable, no universal representation theorems exist so far. In fact, such a characterization of arbitrary t-norms would be closely related to the solution of the famous, still unsolved general associativity functional equation.
Erich Peter Klement +2 more
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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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2000
When we introduced several important families of t-norms in Chapter 4, we mentioned already (without proof) that all these families are continuous with respect to the parameter, i.e., that we have pointwise convergence of the t-norms if the corresponding parameters converge (some of these statements are trivial, some of them follow directly from [Dombi
Erich Peter Klement +2 more
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When we introduced several important families of t-norms in Chapter 4, we mentioned already (without proof) that all these families are continuous with respect to the parameter, i.e., that we have pointwise convergence of the t-norms if the corresponding parameters converge (some of these statements are trivial, some of them follow directly from [Dombi
Erich Peter Klement +2 more
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2000
Generalizing the inverse of a bijective function, we consider the pseudo-inverse of monotone functions from [0, 1] to [0, 1]. Introducing a construction similar to the one given in [Schweizer & Sklar 1983, Theorem 5.2.1] with the help of the so-called quasi-inverses, we state a rather general method to construct new t-norms from known t-norms using the
Erich Peter Klement +2 more
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Generalizing the inverse of a bijective function, we consider the pseudo-inverse of monotone functions from [0, 1] to [0, 1]. Introducing a construction similar to the one given in [Schweizer & Sklar 1983, Theorem 5.2.1] with the help of the so-called quasi-inverses, we state a rather general method to construct new t-norms from known t-norms using the
Erich Peter Klement +2 more
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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 \([
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Convex combinations of strict t-norms
Soft Computing, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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