This paper gives analogies of Hutton’s quasi-uniformities for complete lattices and extensions of Shi’s pointwise quasi-uniformities to closed set lattices.CLGOH denotes the category of all complete lattices with generalized order homomorphisms asmorphisms and CSL the category of all closed set lattices.HQUnif and SPQUnif denote the categories of Hutton quasi-uniform spaces on complete lattices...

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library 1 We show how some c...

ARTMAP-DS extends fuzzy ARTMAP to discriminate between similar inputs by discounting similarities. When two or more candidate category representations are activated by a given input, features that the candidate representations have in common are ignored prior to determining the winning category. Simulations illustrate the network's ability to recognize similar inputs, such as STAR. and START, i...

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...

Category theory provides a compact method of encoding mathematical structures in a uniform way, thereby enabling the use of general theorems on, for example, equivalence and universal constructions. In this article we develop the method of additional structures on the objects of a monoidal Kleisli category. It is proposed to consider any uniform class of information transformers (ITs) as a fami...

In the recent past category regions have been introduced as new geometrical concepts and provide a visualization tool that facilitates significant insight into the nature of the competition among categories during both the training and performance phase of Fuzzy ART (FA) and Fuzzy ARTMAP (FAM). These regions are defined as the geometric interpretation of the Vigilance Test and the competition o...

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

The original definition of a topological space given by Hausdorff used neighborhood systems. Lattice-valued maps appear in this context when you identify a topology with a monoid in the Kleisli category of the filter monad on SET. H?hle’s notion of a lattice-valued topology [2] uses the same idea and it’s inspired in the classical lattice-valued topologies. Ltopological spaces are motivated by ...

The ohjective of this article is to suggest the application of fuzzy set theory to issues in scale development in marketing by conceptualizing response categories of a scale as fuzzy sets. Respondents' natural responses to scales are argued to have degrees of membership in more than one response category when a response scale does not match natural responses. In contrast to traditional scales, ...