Abstract
In this paper, credibilistic logic is introduced as a new branch of uncertain logic system by explaining the truth value of fuzzy formula as credibility value. First, credibilistic truth value is introduced on the basis of fuzzy proposition and fuzzy formula, and the consistency between credibilistic logic and classical logic is proved on the basis of some important properties about truth values. Furthermore, a credibilistic modus ponens and a credibilistic modus tollens are presented. Finally, a comparison between credibilistic logic and possibilistic logic is given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bolc L., Borowik P. (1992) Many-valued logics. Springer, Berlin
Bonissone P. (1987) Summarizing and propagating uncertain information with triangular norms. International Journal of Approximate Reasoning 1: 71–101
Buckley, J., Siler, W., & Tucker, D. (1986). A fuzzy expert system. Fuzzy Sets and Systems, 20, 1–16.
Chang C., Lee R. (1973) Symbolic logic and mechanical theorem proving. Academic Press, New York
Dubois D., Prade H. (1987) Necessity measure and resolution principle. IEEE Transactions on Man Cybenet 17: 474–478
Dubois, D., & Prade, H. (1991). Possibilistic logic, preference models, non-monotonicity and related issues. Proceedings of 12th International Joint Conference on Artificial Intelligence (pp. 419–424), Sydney, Australia, August 24–30.
Dubois D., Lang J., Prade H. (1991) Fuzzy sets in approximate reasoning, Part 2: Logical approaches. Fuzzy Sets and Systems 40: 203–244
Goguen J. (1969) The logic of inexact concepts. Synthese 19: 325–373
Lee, R. (1972). Fuzzy logic and the resolution principle. Journal of the Association for Computing Machinery, 19(1), 109–119.
Li, P., & Liu, B. (2008). Entropy of credibility distributions for fuzzy variables. IEEE Transactions on Fuzzy Systems, 16(1), 123–129.
Li, X., & Liu, B. (2006). A sufficient and necessary condition for credibility measures. International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, 14(5), 527–535.
Li, X., & Liu, B. (2007). Maximum entropy principle for fuzzy variables. International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, 15(Suppl 2), 40–48.
Liu B. (2004) Uncertainty Theory. Springer, Berlin
Liu B. (2006) A survey of credibility theory. Fuzzy Optimization and Decision Making 5(4): 387–408
Liu, B. (2007a). Uncertainty Theory, 2nd ed., Berlin: Springer.
Liu, B. (2007b). A survey of entropy of fuzzy variables. Journal of Uncertain Systems, 1(1), 4–13.
Liu, B. (2008). Uncertainty Theory, 3rd ed. http://orsc.edu.cn/liu/ut.pdf.
Liu, B., & Liu, Y. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10(4), 445–450.
Liu, Y., & Gao, J. (2007). The independence of fuzzy variables with applications to fuzzy random optimization. International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, 15(Suppl 2), 1–20.
Nilsson N. (1986) Probabilistic logic. Artificial Intelligence 28: 71–87
Prade, H. (1985). A computational approach to approximate and plausible reasoning with applications to expert systems. IEEE Transactions on Pattern Anal. Machine Intelligence, 7(3), 260–283.
Skala, H. (1978). On multi-valued logics, fuzzy sets, fuzzy logics and their applications. Fuzzy Sets and Systems, 1, 129–149.
Yager, R. (1985). Inference in a multivalued logic system. International Journal of Man-Machine Studies, 23, 27–44.
Zadeh, L. (1965). Fuzzy sets. Information and Control, 8, 338–353.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, X., Liu, B. Foundation of credibilistic logic. Fuzzy Optim Decis Making 8, 91–102 (2009). https://doi.org/10.1007/s10700-009-9053-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10700-009-9053-6