Fuzzy correspondence inequations and equations

Authors:
Jorge Jiménez;Susana Montes;Branimir Šešelja;Andreja Tepavčević
Affiliations:
University of Oviedo, Gijón, Spain;University of Oviedo, Gijón, Spain;University of Novi Sad, Novi Sad, Serbia;University of Novi Sad, Novi Sad, Serbia
Venue:
Fuzzy Sets and Systems
Year:
2014

Citing 10
Cited 0

On direct and inverse problems for fuzzy equation systems with tolerances

Fuzzy Sets and Systems
On the existence of minimal solutions for fuzzy equations with tolerances

Fuzzy Sets and Systems
Equality relations as a basis for fuzzy control

Fuzzy Sets and Systems
Completion of ordered structures by cuts of fuzzy sets: an overview

Fuzzy Sets and Systems - Logic and algebra
Fuzzy equivalence relations and their equivalence classes

Fuzzy Sets and Systems
On the construction of fuzzy eigen solutions in given regions

Fuzzy Sets and Systems
On lattice valued up-sets and down-sets

Fuzzy Sets and Systems
On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations

Fuzzy Sets and Systems
Fuzzy relational inequations and equations in the framework of control problems

ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Lattice-valued approach to closed sets under fuzzy relations: Theory and applications

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.20

Visualization

Abstract

The paper deals with fuzzy correspondences, i.e., with mappings from a direct product of sets into a complete lattice. Fuzzy control problems connected with fuzzy correspondence inequations and equations are considered. A fuzzy correspondence is fixed, while the solutions are investigated for the input and output fuzzy sets which are unknown. First we prove that these solutions can be analyzed and formulated in crisp framework, solving the corresponding cut problems. Further, the space of solutions of an inequation is proved to be a complete lattice; the same holds for the space of solutions of the corresponding equation. In case the membership values belong to an infinitely distributive lattice (frame), the solutions can be found in specified intervals; moreover, we were able to locate in such intervals minimal and maximal solutions of these problems.