Fuzzy relational inequations and equations in the framework of control problems

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:
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Year:
2011

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Abstract

The paper deals with fuzzy relational inequations and equations connected with closed fuzzy sets under a fixed fuzzy relation over the same domain. Such formulas arise in the framework of control problems. We show that fuzzy sets being solutions of these inequations and corresponding equations form a descending sequence with particular lower bounds which are also analyzed. Our approach is based on complete lattices as structures of membership values, which makes this investigation more general then the classical, real-interval valued approach.