Authors: Jiménez, Jorge
Montes, Susana
Šešelja, Branimir
Tepavčević, Andreja 
Title: Fuzzy correspondence inequations and equations
Journal: Fuzzy Sets and Systems
Volume: 239
First page: 81
Last page: 90
Issue Date: 16-Mar-2014
Rank: M21a
ISSN: 0165-0114
DOI: 10.1016/j.fss.2012.06.003
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.
Keywords: Fuzzy control | Fuzzy correspondences | Fuzzy equations and inequations
Publisher: Elsevier
Project: Development of methods of computation and information processing: theory and applications 
Provincial Secretariat for Science and Technological Development, Autonomous Province of Vojvodina, grant “Ordered structures and applications”

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