A voting mechanism for fuzzy logic. (English) Zbl 0937.03032
Summary: An extended notion of binary valuation, referred to as fuzzy valuation, is introduced for vague or fuzzy concepts. It is shown that the behaviour of agents voting on the truth of sentences from a language of the propositional calculus according to such valuations can be described in terms of fuzzy logic. The concept of fuzzy valuation is extended to the predicate calculus and is shown to generate a notion of fuzzy interpretation of a predicate. The relationship between fuzzy valuations, fuzzy sets, random sets and mass assignments is explored. Finally a semantics for possibility measures based on fuzzy valuations is described.
MSC:
| 03B52 | Fuzzy logic; logic of vagueness |
| 68T37 | Reasoning under uncertainty in the context of artificial intelligence |
Keywords:
voting model; fuzzy valuation; fuzzy logic; fuzzy interpretation; random sets; mass assignments; semantics for possibility measuresSoftware:
FRILReferences:
| [1] | Gaines, B. R., Fuzzy and probability uncertainty logics, Journal of Information and Control, 38, 154-169 (1978) · Zbl 0391.03015 |
| [2] | Gaines, B. R., Foundations of fuzzy reasoning international, Journal of Man-Machine Studies, 8, 623-668 (1976) · Zbl 0342.68056 |
| [3] | Hajek, P., Fuzzy Logic from the Logical Point of View SOFSEM 95: Theory and Practice of Informatics, (Bartosek, M.; Staudek, J.; Wiedermann, J., Lecture Notes in Computer Science, vol. 1012 (1995)), 31-49 · Zbl 07882450 |
| [4] | Trillas, E., Sobre functiones de negacion en la teoria de conjunctos difusos, Stochastica, 3, 1, 47-59 (1979) · Zbl 0419.03035 |
| [5] | Paris, J. B., The Uncertain Reasoners Companion &— A Mathematical Perspective (1995), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0838.68104 |
| [6] | Goodman, I. R.; Nguyen, H. T., Uncertainty Models for Knowledge Based Systems (1985), North Holland: North Holland Amsterdam · Zbl 0576.94001 |
| [7] | Cohen, D. L., Measure Theory (1942), Birkhauser: Birkhauser Boston |
| [8] | Baldwin, J. F.; Martin, T. P.; Pilsworth, B. W., Fril &— Fuzzy and Evidential Reasoning (1995), Wiley: Wiley New York |
| [9] | Baldwin, J. F., Evidential support logic programming, Fuzzy Sets and Systems, 24, 1-26 (1987) · Zbl 0639.68105 |
| [10] | Shafer, G., A Mathematical Theory of Evidence (1976), Princeton University Press: Princeton University Press Princeton, NJ · Zbl 0359.62002 |
| [11] | Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 3-28 (1978) · Zbl 0377.04002 |
| [12] | Drakopoulos, J., Probabilities, Possibilities, and Fuzzy Sets, Department of Computer Science, Stanford University Technical Report (1994) |
| [13] | Dubois, D.; Prade, H., Fuzzy numbers: An overview, (Bezdek, J. C., Analysis of Fuzzy Information (1987), CRC Press), 3-39 · Zbl 0663.94028 |
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