Koguep Njionou, Blaise B.; Kwuida, Léonard; Lele, Celestin (2022). Formal Concepts and Residuation on Multilattices Fundamenta Informaticae, 188(4), pp. 217-237. IOS Press 10.3233/FI-222147
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Multilattices are generalisations of lattices introduced by Mihail Benado in [4]. He replaced the existence of unique lower (resp. upper) bound by the existence of maximal lower (resp. minimal upper) bound(s). A multilattice will be called pure if it is not a lattice. Multilattices could be endowed with a residuation, and therefore used as set of truth-values to evaluate elements in fuzzy setting. In this paper we exhibit the smallest pure multilattice and show that it is a sub-multilattice of any pure multilattice. We also prove that any bounded residuated multilattice that is not a residuated lattice has at least seven elements. We apply the ordinal sum construction to get more examples of residuated multilattices that are not residuated lattices. We then use these residuated multilattices to evaluate objects and attributes in formal concept analysis setting, and describe the structure of the set of corresponding formal concepts. More precisely, if
Item Type: |
Journal Article (Original Article) |
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Division/Institute: |
Business School > Institute for Applied Data Science & Finance Business School > Institute for Applied Data Science & Finance > Applied Data Science Business School |
Name: |
Koguep Njionou, Blaise B.; Kwuida, Léonard  0000-0002-9811-0747 and Lele, Celestin |
ISSN: |
01692968 |
Publisher: |
IOS Press |
Language: |
English |
Submitter: |
Léonard Kwuida |
Date Deposited: |
30 Jun 2023 09:43 |
Last Modified: |
30 Jun 2023 09:43 |
Publisher DOI: |
10.3233/FI-222147 |
Related URLs: |
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Uncontrolled Keywords: |
multilattices, sub-multilattices, residuated multilattices, Formal Concept Analysis, ordinal sum of residuated multilattices |
ARBOR DOI: |
10.24451/arbor.19467 |
URI: |
https://arbor.bfh.ch/id/eprint/19467 |
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