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Limit T-Norms as a Basis for the Construction of New T-Norms
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2001Transformation of the Minimum t-norm TM by means of a non-decreasing transformation φ of the unit interval [0, 1] yielding triangular norm is studied. Full characterization of such φ is given. In the same spirit, transformations of the Drastic product TD are studied.
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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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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
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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Fuzzy Sets and Systems, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fuzzy Sets and Systems, 1997
It is well known that t-norms and t-conorms are used very often in fuzzy set theory. Applications to practical problems require the use of the ``most appropriate'' t-norm or t-conorm. For this reason, the construction of new t-norms seems to be an important tool for the theory but also for the applications. We present in this paper two kinds of t-norms,
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It is well known that t-norms and t-conorms are used very often in fuzzy set theory. Applications to practical problems require the use of the ``most appropriate'' t-norm or t-conorm. For this reason, the construction of new t-norms seems to be an important tool for the theory but also for the applications. We present in this paper two kinds of t-norms,
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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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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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A method for constructing t-norms
Korean Journal of Computational & Applied Mathematics, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Smooth Convex t-Norms Do Not Exist
Proceedings of the American Mathematical Society, 1988A binary operation on [0,1] which is associative, commutative, nondecreasing in each place, and has 1 as a unit element is said to be a t-norm. An example of continuous convex t-norm is \(W(x,y)=Max(x+y-1,0),\) x,y\(\in [0,1]\). The authors prove that smooth convex t-norms do not exist.
Alsina, Claudi, Thomás, Maria S.
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