Connecting Fuzzy submonoids, fuzzy preorders and quasi-metrics
نویسنده
چکیده
This paper is an extended abstract of my paper [12] published in Fuzzy Set and Systems. We start from a residuated lattice L and a monoid M , and we define a Galois connection from the lattice of the compatible L-preorders in M and the lattice of L-submonoids of M . Given a set S we define a Galois connection between the lattice of the L-preorders in S and the lattice of L-submonoids of the monoid (SS , ◦, i). A link with the notion of quasi-metric is also established.
منابع مشابه
Connecting Fuzzifying Topologies and Generalized Ideals by Means of Fuzzy Preorders
The present paper investigates the relations between fuzzifying topologies and generalized ideals of fuzzy subsets, as well as constructing generalized ideals and fuzzifying topologies by means of fuzzy preorders. Furthermore, a construction of generalized ideals from preideals, and vice versa, is obtained. As a particular consequence of the results in this paper, a construction of fuzzifying t...
متن کاملFuzzy quasi-metrics for the Sorgenfrey line
We endow the set of real numbers with a family of fuzzy quasi-metrics, in the sense of George and Veeramani, which are compatible with the Sorgenfrey topology. Although these fuzzy quasi-metrics are not deduced explicitly from a quasi-metric, they possess interesting properties related to completeness. For instance, we prove that they are balanced and complete in the sense of Doitchinov and tha...
متن کاملGenerating Hasse trees of fuzzy preorder closures: an algorithmic approach
Mathematical theories are pervaded with the use of partial orders and more general preorders also called quasi orders i e re exive and transitive binary rela tions Preorders also play an important role in appli cations for instance as preference relations in multi criteria decision aid techniques The observation that classical relations do not allow to express partial or graded relationships ha...
متن کاملQuantale-valued preorders: Globalization and cocompleteness
Each divisible and unital quantale is associated with two quantaloids. Categories enriched over these two quantaloids can be regarded respectively as crisp sets endowed with fuzzy preorders and fuzzy sets endowed with fuzzy preorders. This paper deals with the relationship between these two kinds of enriched categories. This is a special case of the change-base issue in enriched category theory...
متن کاملA non-commutative and non-idempotent theory of quantale sets
In fuzzy set theory non-idempotency arises when the conjunction is interpreted by arbitrary t-norms. There are many instances in mathematics where set theory ought to be non-commutative and/or non-idempotent. The purpose of this paper is to combine both ideas and to present a theory of non-commutative and non-idempotent quantale sets (among other things, standard concepts like fuzzy preorders a...
متن کامل