Bipolar equations on complete distributive symmetric residuated lattices : the case of a join-irreducible right-hand side
- Author
- M. Eugenia Cornejo, David Lobo, Jesús Medina and Bernard De Baets (UGent)
- Organization
- Project
- Abstract
- Bipolar max-* equations, with * a triangular norm, have recently become a popular research topic embedded in the broad field of fuzzy relational equations. In this paper, we lift the work from the restrictive setting of the real unit interval - obfuscating the underlying lattice-theoretical essence - to the general setting of complete distributive symmetric residuated lattices, allowing to build upon the vast body of knowledge on unipolar sup-* equations on complete distributive residuated lattices. We determine the full solution set, with particular emphasis on the extremal solutions, of a bipolar sup-* equation in case the right-hand side is a join-irreducible element. The results are illustrated by means of ample examples.
- Keywords
- Artificial Intelligence, Logic, Bipolar equation, Distributive symmetric residuated lattice, Negation operator, Irreducible element, FUZZY RELATION EQUATIONS, RESOLUTION
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8755564
- MLA
- Cornejo, M. Eugenia, et al. “Bipolar Equations on Complete Distributive Symmetric Residuated Lattices : The Case of a Join-Irreducible Right-Hand Side.” FUZZY SETS AND SYSTEMS, vol. 442, 2022, pp. 92–108, doi:10.1016/j.fss.2022.02.003.
- APA
- Cornejo, M. E., Lobo, D., Medina, J., & De Baets, B. (2022). Bipolar equations on complete distributive symmetric residuated lattices : the case of a join-irreducible right-hand side. FUZZY SETS AND SYSTEMS, 442, 92–108. https://doi.org/10.1016/j.fss.2022.02.003
- Chicago author-date
- Cornejo, M. Eugenia, David Lobo, Jesús Medina, and Bernard De Baets. 2022. “Bipolar Equations on Complete Distributive Symmetric Residuated Lattices : The Case of a Join-Irreducible Right-Hand Side.” FUZZY SETS AND SYSTEMS 442: 92–108. https://doi.org/10.1016/j.fss.2022.02.003.
- Chicago author-date (all authors)
- Cornejo, M. Eugenia, David Lobo, Jesús Medina, and Bernard De Baets. 2022. “Bipolar Equations on Complete Distributive Symmetric Residuated Lattices : The Case of a Join-Irreducible Right-Hand Side.” FUZZY SETS AND SYSTEMS 442: 92–108. doi:10.1016/j.fss.2022.02.003.
- Vancouver
- 1.Cornejo ME, Lobo D, Medina J, De Baets B. Bipolar equations on complete distributive symmetric residuated lattices : the case of a join-irreducible right-hand side. FUZZY SETS AND SYSTEMS. 2022;442:92–108.
- IEEE
- [1]M. E. Cornejo, D. Lobo, J. Medina, and B. De Baets, “Bipolar equations on complete distributive symmetric residuated lattices : the case of a join-irreducible right-hand side,” FUZZY SETS AND SYSTEMS, vol. 442, pp. 92–108, 2022.
@article{8755564,
abstract = {{Bipolar max-* equations, with * a triangular norm, have recently become a popular research topic embedded in the broad field of fuzzy relational equations. In this paper, we lift the work from the restrictive setting of the real unit interval - obfuscating the underlying lattice-theoretical essence - to the general setting of complete distributive symmetric residuated lattices, allowing to build upon the vast body of knowledge on unipolar sup-* equations on complete distributive residuated lattices. We determine the full solution set, with particular emphasis on the extremal solutions, of a bipolar sup-* equation in case the right-hand side is a join-irreducible element. The results are illustrated by means of ample examples.}},
author = {{Cornejo, M. Eugenia and Lobo, David and Medina, Jesús and De Baets, Bernard}},
issn = {{0165-0114}},
journal = {{FUZZY SETS AND SYSTEMS}},
keywords = {{Artificial Intelligence,Logic,Bipolar equation,Distributive symmetric residuated lattice,Negation operator,Irreducible element,FUZZY RELATION EQUATIONS,RESOLUTION}},
language = {{eng}},
pages = {{92--108}},
title = {{Bipolar equations on complete distributive symmetric residuated lattices : the case of a join-irreducible right-hand side}},
url = {{http://doi.org/10.1016/j.fss.2022.02.003}},
volume = {{442}},
year = {{2022}},
}
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