Title :
Solving a class of fuzzy relation inequalities via semi-tensor product
Author :
Fan, Hongbiao ; Feng, Jun-e ; Zhang, Lequn
Author_Institution :
Sch. of Math., Shandong Univ., Jinan, China
Abstract :
The problem of solving a class of fuzzy relation inequalities (FRIs) is investigated. First, it is shown that if the FRI is solvable, there is a corresponding parameter solution set (briefly, PSS). Then the semi-tensor product of matrices is used to convert the logical inequality into its algebraic form via the vector expression of logical variables. Under this form all the PSS can be obtained. It is proved that all the solutions can be derived from their corresponding PSS. An example is presented to demonstrate the effectiveness of the algorithm provided in this paper.
Keywords :
fuzzy set theory; matrix algebra; tensors; FRI; PSS; algebraic form; fuzzy relation inequalities; logical inequality; logical variables; semitensor matrix product; vector expression; Educational institutions; Equations; Fuzzy systems; Indexes; Linear matrix inequalities; Matrix converters; Vectors; Fuzzy relation inequality; PSS; multi-valued logic; semi-tensor product;
Conference_Titel :
Intelligent Control and Automation (WCICA), 2012 10th World Congress on
Conference_Location :
Beijing
Print_ISBN :
978-1-4673-1397-1
DOI :
10.1109/WCICA.2012.6358110