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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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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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An extension of several properties for fuzzy t-norm and vague t-norm
Journal of Intelligent & Fuzzy SystemsRosenfeld defined a fuzzy subgroup of a given group as a fuzzy subset with two special conditions and Mustafa Demirci proposed the idea of fuzzifying the operations on a group through a fuzzy equality and a fuzzy equivalence relation. This paper mainly focuses on fuzzy subsets and vague sets of monoids with several extended algebraic properties ...
Wang, Haohao, Li, Wei, Yang, Bin
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Regular left-continuous t-norms
Semigroup Forum, 2008A triangular norm (t-norm) \(\odot\) can be determined by its \textit{translations} \(\lambda_a:[0,1]\to[0,1]\), \(x\mapsto x\odot a\), where \(a\in[0,1]\). They form the set \(\Lambda=\{\lambda_a: a\in[0,1]\}\) of (non-strictly) increasing, mutually commuting functions and for each \(a\in[0,1]\), \(\lambda_a\) is the unique element of \(\Lambda\) such
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Vector t-Norms With Applications
IEEE Transactions on Fuzzy Systems, 2017Some basic t-norms defined on [0, 1] are well known in many study areas and applications. However, more general extension of them into vector forms can be used in a lot of new decision-making realms. In this study, we first define preference vector on a linearly ordered set, which includes different special vectors that are mathematically equivalent ...
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