Abstract
This Ch. is entirely dedicated to the study of the Boolean (i.e. non-fuzzy) solutions of a max-min fuzzy equation defined on a complete Brouwerian lattice L with universal bounds 0 and 1. In Sec.1, we give a simple necessary and sufficient condition for the existence of the greatest Boolean solution of S and in Sec.2, using some results of Ch.3, we determine the minimal Boolean elements of S if L is a linear lattice. In Sec.3, if Boolean solutions do not exist, an algorithm is presented to find the elements of S with maximum Boolean degree, i.e. with the maximum number of 0 and 1. The referential sets are assumed to be necessarily finite in Secs.2 and 3.
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References
A. Di Nola and A. Ventre, On Booleanity of relational equation in Brouwerian lattices, Boll. Un. Mat. Ital. (6) 3 - B (1984), 871 - 882.
S. Sessa, Characterizing the Boolean solutions of relational equations in Brouwerian lattices, Boll. Un. Mat. Ital. (6) 5 - B (1986), 39 - 49.
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© 1989 Springer Science+Business Media Dordrecht
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di Nola, A., Sessa, S., Pedrycz, W., Sanchez, E. (1989). Boolean Solutions of Max-Min Fuzzy Equations. In: Fuzzy Relation Equations and Their Applications to Knowledge Engineering. Theory and Decision Library, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1650-5_5
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DOI: https://doi.org/10.1007/978-94-017-1650-5_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4050-3
Online ISBN: 978-94-017-1650-5
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