Fuzzy sets and sheaves. Part I

Authors:
Ulrich Höhle
Affiliations:
Fachbereich C Mathematik und Naturwissenschaften Bergische Universität, D-42097 Wuppertal, Germany
Venue:
Fuzzy Sets and Systems
Year:
2007

Citing 15
Cited 19

Abstract and concrete categories

Abstract and concrete categories
Fuzzy congruence relations

Fuzzy Sets and Systems
Fuzzy relations on rings and groups

Fuzzy Sets and Systems
Fuzzy normal subgroups and fuzzy quotients

Fuzzy Sets and Systems
Free fuzzy groups and fuzzy group presentations

Fuzzy Sets and Systems
Product structure of the fuzzy factor groups

Fuzzy Sets and Systems
Generating fuzzy factor groups and the fundamental theorem of isomorphism

Fuzzy Sets and Systems
Fuzzy congruences in groups

Fuzzy Sets and Systems
Membership functions for a fuzzy group from similarity relations

Fuzzy Sets and Systems
Fuzzy Sets and Systems: Theory and Applications

Fuzzy Sets and Systems: Theory and Applications
A natural interpretation of fuzzy sets and fuzzy relations

Fuzzy Sets and Systems
A natural interpretation of fuzzy mappings

Fuzzy Sets and Systems
An Investigation of the Laws of Thought

An Investigation of the Laws of Thought
Fuzzy sets and sheaves. Part II

Fuzzy Sets and Systems
Similarity relations and fuzzy orderings

Information Sciences: an International Journal

Fuzzy sets and sheaves. Part II

Fuzzy Sets and Systems
Category theoretic aspects of chain-valued frames: Part I: Categorical and presheaf theoretic foundations

Fuzzy Sets and Systems
Category theoretic aspects of chain-valued frames: Part II: Applications to lattice-valued topology

Fuzzy Sets and Systems
A comprehensive theory of trichotomous evaluative linguistic expressions

Fuzzy Sets and Systems
Maximal fuzzy maps

Information Sciences: an International Journal
EQ-algebras

Fuzzy Sets and Systems
On ordered categories as a framework for fuzzification of algebraic and topological structures

Fuzzy Sets and Systems
Approximate fuzzy preorders and equivalences

FUZZ-IEEE'09 Proceedings of the 18th international conference on Fuzzy Systems
Fuzzy sets and geometric logic

Fuzzy Sets and Systems
Implication structures, fuzzy subsets, and enriched categories

Fuzzy Sets and Systems
Necessity of non-stratified and anti-stratified spaces in lattice-valued topology

Fuzzy Sets and Systems
From quantale algebroids to topological spaces: Fixed- and variable-basis approaches

Fuzzy Sets and Systems
A non-commutative and non-idempotent theory of quantale sets

Fuzzy Sets and Systems
Ambiguous representations as fuzzy relations between sets

Fuzzy Sets and Systems
Generalized fuzzy topology versus non-commutative topology

Fuzzy Sets and Systems
Preordered sets valued in a GL-monoid

Fuzzy Sets and Systems
The order-theoretic duality and relations between partial metrics and local equalities

Fuzzy Sets and Systems
Fuzzy presubsets as non-idempotent and non-commutative classifications of subalgebras

Fuzzy Sets and Systems
Isomorphisms of fuzzy sets and cut systems

IWANN'13 Proceedings of the 12th international conference on Artificial Neural Networks: advances in computational intelligence - Volume Part I

Quantified Score

Hi-index	0.21

Visualization

Abstract

This essay shows that large parts of fuzzy set theory are actually subfields of sheaf theory, respectively, of the theory of complete @W-valued sets. Hence fuzzy set theory is closer to the mainstream in mathematics than many people would expect. Part I of this essay divided into a series of two papers presents such basic concepts as @W-valued equalities, espaces etales, singleton monad, the change of base and the subobject classifier axiom. The application of these tools to the sheaf-theoretic foundations of fuzzy sets will appear in Part II.