How to construct left-continuous triangular norms--state of the art
نویسنده
چکیده
Left-continuity of triangular norms is the characteristic property to make it a residuated lattice. Nowadays residuated lattices are subjects of intense investigation in the ÿelds of universal algebra and nonclassical logic. The recently known construction methods resulting in left-continuous triangular norms are surveyed in this paper.
منابع مشابه
How to costruct left-continuous triangular norms
Triangular norms (t-norms for short) play a crucial role in several fields of mathematics and AI. For an exhaustive overview on t-norms we refer to [20]. Recently an increasing interest of left-continuous t-norm based theories can be observed (see e.g. [3, 5, 6, 7, 18]). In this paper we discuss in detail the presently existing construction methods which result in left-continuous triangular nor...
متن کاملStructure of left-continuous triangular norms with strong induced negations
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 ...
متن کاملArchimedean components of triangular norms
The Archimedean components of triangular norms (which turn the closed unit interval into an abelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordina...
متن کاملContinuous triangular subnorms
Triangular subnorms are associative commutative non-decreasing operations on the unit interval, upper bounded by the minimum. Continuous triangular subnorms are shown to be ordinal sum of Archimedean continuous t-subnorms with at most one proper t-subnorm summand. Special attention is paid to generate continuous t-subnorms. An application of continuous t-subnorms to the construction of left-con...
متن کاملAlternative approaches to obtain t-norms and t-conorms on bounded lattices
Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Fuzzy Sets and Systems
دوره 143 شماره
صفحات -
تاریخ انتشار 2004