Weakly linear systems of fuzzy relation inequalities: The heterogeneous case

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• 作者：Jelena Ignjatovi膰^a ; ^{jelena.ignjatovic@pmf.edu.rs} ; Miroslav 膯iri膰^a ; ^{miroslav.ciric@pmf.edu.rs} ; ^{mciric@pmf.ni.ac.rs} ; Nada Damljanovi膰^b ; ^{nada@tfc.kg.ac.rs} ; Ivana Jan膷i膰^a ; ^{ivanajancic84@gmail.com}
• 关键词：Fuzzy relations ; Fuzzy relational systems ; Fuzzy relation inequalities ; Residuals of fuzzy relations ; Complete residuated lattices ; Post-fixed points
• 刊名：Fuzzy Sets and Systems
• 出版年：2012
• 期刊代码：55_01650114
• 类别：cp
• 出版时间：16 July, 2012
• 卷：199
• 期：Complete
• 页码：64-91
• 文件大小：404 K

摘要

New types of systems of fuzzy relation inequalities and equations, called weakly linear, have been recently introduced in [J. Ignjatovi膰 et al., On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations, Fuzzy Sets Syst. 161 (2010) 3081-3113]. The mentioned paper dealt with homogeneous weakly linear systems, composed of fuzzy relations on a single set, and a method for computing their greatest solutions has been provided. This method is based on the computing of the greatest post-fixed point, contained in a given fuzzy relation, of an isotone function on the lattice of fuzzy relations. Here we adapt this method for computing the greatest solutions of heterogeneous weakly linear systems, where the unknown fuzzy relation relates two possibly different sets. We also introduce and study quotient fuzzy relational systems and establish relationships between solutions to heterogeneous and homogeneous weakly linear systems. Besides, we point out to applications of the obtained results in the state reduction of fuzzy automata and computing the greatest simulations and bisimulations between fuzzy automata, as well as in the positional analysis of fuzzy social networks.