Column stacking approach to resolution of systems of fuzzy relational inequalities

This paper investigates several kinds of fuzzy relational inequalities (FRIs) and systems of fuzzy relational inequalities (SFRIs) with the max–min composition, and proposes a column stacking approach. Firstly, the equivalent column stacking forms of the considered FRIs and SFRIs are obtained based...

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Bibliographic Details
Published inJournal of the Franklin Institute Vol. 356; no. 6; pp. 3314 - 3332
Main Authors Wang, Shuling, Li, Haitao
Format Journal Article
LanguageEnglish
Published Elmsford Elsevier Ltd 01.04.2019
Elsevier Science Ltd
Subjects
Algorithms
Boolean algebra
Fuzzy logic
Fuzzy systems
Inequalities
Matrix
Nonlinear equations
Stacking
Tensors
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ISSN0016-0032
1879-2693
0016-0032
DOI10.1016/j.jfranklin.2019.02.007

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Summary:This paper investigates several kinds of fuzzy relational inequalities (FRIs) and systems of fuzzy relational inequalities (SFRIs) with the max–min composition, and proposes a column stacking approach. Firstly, the equivalent column stacking forms of the considered FRIs and SFRIs are obtained based on the Boolean Kronecker product of matrices, which converts the resolution of the considered FRIs and SFRIs to the resolution of an FRI with the same form. Secondly, using the semi-tensor product (STP) of matrices, the resolution of FRIs is converted to finding all the parameter set solutions, based on which, the solution set of the considered FRIs and SFRIs is characterized. Finally, a general algorithm is established for the resolution of the considered FRIs and SFRIs.
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ISSN:0016-0032
1879-2693
0016-0032
DOI:10.1016/j.jfranklin.2019.02.007