Generalized Fuzzy Relations

John N. Mordeson, Sunil Mathew () and Davender S. Malik ()
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John N. Mordeson: Department of Mathematics, Creighton University, Omaha, Nebraska 68178, USA
Sunil Mathew: Department of Mathematics, National Institute of Technology, Calicut, Kerala 673601, India
Davender S. Malik: Department of Mathematics, Creighton University, Omaha, Nebraska 68178, USA

New Mathematics and Natural Computation (NMNC), 2018, vol. 14, issue 02, 187-202

Abstract: Fuzzy relations are fundamental in applications of fuzzy set theory and fuzzy logic. The entire literature on fuzzy relations as applied to fuzzy graph theory are based on Rosenfeld’s relations. Rosenfeld used minimum and maximum as the norm and conorm in his study of compositions of fuzzy relations. In this paper, we generalize fuzzy relations using arbitrary t-norms and t-conorms. Many of the results do not hold when minimum and maximum are replaced by an arbitrary norm and an arbitrary conorm. Reflexive, symmetric and transitive generalized fuzzy relations are also discussed and an application to human trafficking and illegal immigration is presented.

Keywords: Fuzzy relation; composition; t-norm; t-conorm; fuzzy equivalence relation; illegal immigration routes to U.S (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S1793005718500126

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