期刊
IEEE TRANSACTIONS ON FUZZY SYSTEMS
卷 17, 期 2, 页码 385-397出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2009.2013634
关键词
Belief functions; fuzzy implication operators; fuzzy rough sets; monotone capacity; rough sets
资金
- Hong Kong Research Grants Council [CUHK 4126/04H]
Determined by a fuzzy implication operator, a general type of fuzzy belief structure and its induced dual pair of fuzzy belief and plausibility functions in infinite universes of discourse are first defined. Relationship between the belief-structure-based and the belief-space-based fuzzy Dempster-Shafer models is then established. It is shown that the lower and upper fuzzy probabilities induced by the fuzzy belief space yield a dual pair of fuzzy belief and plausibility functions. For any fuzzy belief structure, there must exist a fuzzy belief space such that the fuzzy belief and plausibility functions defined by the given fuzzy belief structure are just the lower and upper fuzzy probabilities induced by the fuzzy belief space, respectively. Essential properties of the fuzzy belief and plausibility functions are also examined. The fuzzy belief and plausibility functions are, respectively, a fuzzy monotone Choquet capacity and a fuzzy alternating Choquet capacity of infinite order.
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