Solving Generalized Equations with Bounded Variables and Multiple Residuated Operators

M. Eugenia Cornejo, David Lobo and Jesús Medina
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M. Eugenia Cornejo: Department of Mathematics, University of Cádiz, 11510 Puerto Real, Spain
David Lobo: Department of Mathematics, University of Cádiz, 11510 Puerto Real, Spain
Jesús Medina: Department of Mathematics, University of Cádiz, 11510 Puerto Real, Spain

Mathematics, 2020, vol. 8, issue 11, 1-21

Abstract: This paper studies the resolution of sup-inequalities and sup-equations with bounded variables such that the sup-composition is defined by using different residuated operators of a given distributive biresiduated multi-adjoint lattice. Specifically, this study has analytically determined the whole set of solutions of such sup-inequalities and sup-equations. Since the solvability of these equations depends on the character of the independent term, the resolution problem has been split into three parts distinguishing among the bottom element, join-irreducible elements and join-decomposable elements.

Keywords: join-irreducible element; join-decomposable element; adjoint triples; multi-adjoint sup-inequalities; multi-adjoint sup-equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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