Yao, Y. Y.; Lingras, P. J. Interpretations of belief functions in the theory of rough sets. (English) Zbl 0923.04007 Inf. Sci. 104, No. 1-2, 81-106 (1998). Summary: This paper reviews and examines interpretations of belief functions in the theory of rough sets with finite universe. The concept of standard rough set algebras is generalized in two directions. One is based on the use of nonequivalence relations. The other is based on relations over two universes, which leads to the notion of interval algebras. Pawlak rough set algebras may be used to interpret belief functions whose focal elements form a partition of the universe. Generalized rough set algebras using nonequivalence relations may be used to interpret belief functions which have less than \(| U|\) focal elements, where \(| U|\) is the cardinality of the universe \(U\) on which belief functions are defined. Interval algebras may be used to interpret any belief functions. Cited in 58 Documents MSC: 03E72 Theory of fuzzy sets, etc. 68T30 Knowledge representation Keywords:belief functions; theory of rough sets with finite universe; rough set algebras; interval algebras; nonequivalence relations PDFBibTeX XMLCite \textit{Y. Y. Yao} and \textit{P. J. Lingras}, Inf. Sci. 104, No. 1--2, 81--106 (1998; Zbl 0923.04007) Full Text: DOI References: [1] Corrêa da Silva, F.; Bundy, A., On some equivalence relations between incidence calculus and Dempster-Shafer theory of evidence, (Proceedings of Uncertainty in Artificial Intelligence ’90 (1990), GE Corporation: GE Corporation Cambridge, MA), 378-383 [2] Chellas, B. F., Modal Logic: An Introduction (1980), Cambridge University Press: Cambridge University Press Cambridge, U.K · Zbl 0431.03009 [3] Dempster, A. P., Upper and lower probabilities induced by a multivalued mapping, Ann. Math. Statist., 38, 325-339 (1967) · Zbl 0168.17501 [4] Dubois, D.; Prade, H., Rough fuzzy sets and fuzzy rough sets, Int. J. Gen. 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