in this article, we have shown, for the add-point monad t, thepartial morphism category set*is isomorphic to the kleisli category sett. alsowe have proved that the category, sett, of t-algebras is isomorphic to thecategory set of pointed sets. finally we have established commutative squaresinvolving these categories.

This paper presents an investigation of many valued lattices from the point of view of enriched category theory. For a bounded partially ordered set P , the conditions for P to become a lattice can be postulated as existence of certain adjunctions. Reformulating these adjunctions, by aid of enriched category theory, in many valued setting, two kinds of many valued lattices, weak -lattices and -...

We introduce the category IVRel(H) consisting of interval-valued H-fuzzy relational spaces and relation preserving mappings between them and we study structures of the category IVRel(H) in the viewpoint of the topological universe introduced by Nel. Thus we show that IVRel(H) satisfies all the conditions of a topological universe over Set except the terminal separator property and IVRel(H) is C...

If the standard concepts of partial-order relation and subset are fuzzified, taking valuation in a unital commutative quantale Q, corresponding concepts of joins and join-preserving mappings can be introduced. We present constructions of limits, colimits and Hom-objects in categories Q-Sup of Q-valued fuzzy joinsemilattices, showing the analogy to the ordinary category Sup of join-semilattices.

In this writing, first, we disclose the first and second category of a ΓτF-fuzzy proximal contraction for mapping O:U→V which is nonself also declare fuzzy q-property to confirm existence best proximity point function O. Then, discover few results using continuous discontinuous O in non-Archimedean metric space. Later, discuss another result as well. between theorems, many examples are presente...

We provide an extension of the notion of chain-valued frame introduced by Pultr and Rodabaugh in [Category theoretic aspects of chain-valued frames: parts I and II, Fuzzy Sets and Systems 159 (2008) 501–528 and 529–558] by relaxing the assumption that L be a complete chain. As a result of this investigation we formulate the category L-Frm of L-frames under the weaker assumption that L is a comp...

A description of relational databases in categorical terminology given here has as intended application the study of database dynamics in par ticular we view i updates as database objects in a suitable category indexed by a topos ii L fuzzy databases as database objects in sheaves Indexed cate gories are constructed to model the databases on a xed family of domains and also all databases for a ...

This is a description of a simple system that is able of performing abductive reasoning over fuzzy data using a back-propagation neural net for the hypothesis generation process. I will rst outline and exemplify the notion of abduction as a process of building hypotheses on the basis of a given set of data, evaluating them to nd the best hypothesis and give explanation for the made selection. I...

For classical sets one has their cumulative hierarchy, and also the category SET of all sets and mappings as standard approaches toward the universe of all sets. We discuss the corresponding situation for fuzzy set theory and give is a (concise) survey of a lot of such approaches which have been offered in the past approximately 35 years.