Related papers: Fuzzy Categories
Fuzzy set theory opens new vistas in computability theory and here I show this by defining a new computational metaphor--the fuzzy chemical metaphor. This metaphor is an extension of the chemical metaphor. In particular, I introduce the…
In this article, we first define the concept of ordered intervals, then introduce ordered fuzzy inner product and describe some of its properties.
Dilatations modify categories by imposing that some morphisms factorize through some others. This is formalized by a universal property. This text is devoted to introduce and study this construction. Examples of dilatations of categories…
For a category with subobjects and factorization, here we describe a new category which we call category of chain bundles and it is shown that this new category is also a category with subobjects and admits factorization under certain…
Categorical bundles provide a natural framework for gauge theories involving multiple gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality, and hence also of local triviality, for categorical…
Restriction categories were introduced to provide an axiomatic setting for the study of partially defined mappings; they are categories equipped with an operation called restriction which assigns to every morphism an endomorphism of its…
This paper proposes two kinds of fuzzy abductive inference in the framework of fuzzy rule base. The abductive inference processes described here depend on the semantic of the rule. We distinguish two classes of interpretation of a fuzzy…
We define a concept which we call multiplicity. First, multiplicity of a morphism is defined. Then the multiplicity of an object over another object is defined to be the minimum of the multiplicities of all morphisms from one to another.…
In the subjective Bayesian approach uncertainty is described by a prior distribution chosen by the statistician. Fuzzy set theory is another way of representing uncertainty. Here we give a decision theoretic approach which allows a Bayesian…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. After…
This paper introduces the notion of fuzzy process as a formalism for the idea of fuzzy contact between a device and its environment. The notions of absolute correctness and relative correctness are defined. In order to work with concurrency…
This article generalizes object-oriented dynamic networks to the fuzzy case, which allows one to represent knowledge on objects and classes of objects that are fuzzy by nature and also to model their changes in time. Within the framework of…
We introduce a notion of globular multicategory with homomorphism types. These structures arise when organizing collections of "higher category-like" objects such as type theories with identity types. We show how these globular…
Especially in research areas of computer science such as data mining, image segmentation, clustering image capturing and networking. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that…
In this paper, we introduce a new type fuzzy boundary and study some related set theoretic identities. Further, this new type of fuzzy boundary is compared with different existing fuzzy boundaries.
In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category…
Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…
Crisp and $L$-fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced. It is shown that, for each pair of compact Hausdorff spaces, the set of (crisp or $L$-fuzzy) ambiguous…
Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple Lie groups. Fuzzy spheres emerge from quantizing S^2 and are associated with the group SU(2) in this manner. They are useful for regularizing quantum field…
We study, in an abstract axiomatic setting, the notion of sectional category of a morphism. From this, we unify and generalize known results about this invariant in different settings as well as we deduce new applications.