Fuzzy Relational Inequations and Equations in the Framework of Control Problems
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.
Keywordsfuzzy sets closed under fuzzy relations fuzzy control
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- 7.Ignjatović, J., Ćirić, M., Bogdanović, S.: On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations. Fuzzy Sets and Systems 161, 3081–3113Google Scholar