Structure of left-continuous triangular norms with strong induced negations
نویسنده
چکیده
This paper is the continuation of [11] where the rotation construction of left-continuous triangular norms was presented. Here the class of triangular subnorms and a second construction, called rotation-annihilation, are introduced: Let T1 be a left-continuous triangular norm. If T1 has no zero divisors then let T2 be a left-continuous rotation invariant t-subnorm. If T1 has zero divisors then let T2 be a left-continuous rotation invariant triangular norm. From each such pair (T1; T2) the rotation-annihilation construction produces a left-continuous triangular norm with strong induced negation. An infinite number of new families of such triangular norms can be constructed in this way, and this further extends our spectrum of choice for the proper triangular norm e.g. in probabilistic (statistical) metric spaces, or for logical and set theoretical connectives in non-classical logic, or e.g. in fuzzy sets theory and its applications. On the other hand, the introduced construction brings us closer to the understanding of the structure of these operations.
منابع مشابه
A characterization theorem on the rotation construction for triangular norms
The rotation construction for t-norms is introduced in (J. Appl. Non-Classical Logics 10 (2000) 83–92). In the present paper we characterize the widest class of operators with which the rotation construction results in left-continuous t-norms with involutive associated negations. c © 2002 Elsevier Science B.V. All rights reserved.
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ورودعنوان ژورنال:
- Journal of Applied Non-Classical Logics
دوره 11 شماره
صفحات -
تاریخ انتشار 2000