Interpretations of various uncertainty theories using models of modal logic: A summary

Fuzzy Sets and Systems

Volumn 80, Issue 1, 1996, Pages 7-14

  Resconi, Germane ^a   Klir, George J ^b   Harmanec, David ^b   St Claïr, Ute ^b  

^a UNIVERSITÀ CATTOLICA DEL SACRO CUORE   (Italy)

^b State University of New York at Binghamton   (United States)

Author keywords

Dempster shafer theory; Fuzzy set theory; Modal logic; Possibility theory; Probability theory; Uncertainty

Indexed keywords

EID: 0005268970     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/0165-0114(95)00262-6     Document Type: Article

References (28)

1. M. Black, Vagueness: an exercise in logical analysis, Philos. Sci. 4 (1937) 427-455;
2. reprinted in Internat. J. General Systems 17 (1990) 107-128.
3. B.F. Chellas, Modal Logic: An Introduction (Cambridge Univ. Press, Cambridge, 1980).
4. F.L. Del Cerro and A. Herzig, A modal analysis of possibility theory, in: R. Kruse and P. Siegel, Eds., Symbolic and Quantitative Approaches to Uncertainty (Springer, New York, 1991) 58-62.
5. D. Dubois and H. Prade, Possibility Theory (Plenum Press, New York, 1988).
6. G. Forbes, The Metaphysics of Modality (Oxford Univ. Press, Oxford, 1985).
7. J.W. Guan and D.A. Bell, Evidence Theory and its Applications, Vols. 1 and 2 (North-Holland, New York, 1991, 1992).
8. S. Haack, Philosophy of Logics (Cambridge Univ. Press, Cambridge, 1978).
9. D. Harmanec, G.J. Klir and G. Resconi, Completing interpretation of Dempster-Shafer theory within the semantics of modal logic, in: Proc. 2nd European Congr. on System Science (1993) 1031-1038.
10. D. Harmanec, G.J. Klir and G. Resconi, On a modal logic interpretation of Dempster-Shafer theory of evidence, Internat. J. Intelligent Systems 9 (1994) 941-951.
11. D. Harmanec, G.J. Klir and Z. Wang, Modal logic interpretation of Dempster-Shafer theory: an infinite case, Internat. J. Approx. Reason., submitted.
12. G.E. Hughes and M.J. Cresswell, An Introduction to Modal Logic (Methuen, London, 1968).
13. G.E. Hughes and M.J. Cresswell, A Companion to Modal Logic (Methuen, London, 1984).
14. G.J. Klir and D. Harmanec, On modal logic interpretation of possibility theory, Internat. J. Uncertainty Fuzziness Knowledge-Based Systems 2 (1994) 237-245.
15. G.J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications (Prentice-Hall, Englewood Cliffs, NJ, 1995).
16. V. Novak, Fuzzy Sets and their Applications (Adam Hilger, Philadelphia, 1989).
17. G. Resconi, Vectorial and tensorial representation of uncertainty by modal logic, in: Proc. 5th IFSA World Congr. (1993) 92-95.
18. G. Resconi, G.J. Klir and U. St. Clair, Hierarchical uncertainty metatheory based upon modal logic, Internat. J. Gen. Systems 21 (1992) 23-50.
19. G. Resconi, G.J. Klir, U. St. Clair and D. Harmanec, On the integration of uncertainty theories, Internat. J. Uncertainty Fuzziness Knowledge-Based Systems 1 (1993) 1-18.
20. G. Shafer, A Mathematical Theory of Evidence (Princeton Univ. Press, Princeton, NJ, 1976).
21. P. Smets, Belief functions, in: P. Smets et al., Eds., Non-Standard Logics for Automated Reasoning (Academic Press, San Diego, 1988) 253-286.
22. H. Suzuki and S. Arimoto, Embedment of fuzzy logic system into a Boolean lattice for satisfying a complementary law, Inform. Sci. 78 (1994) 257-268.
23. Z. Wang and G.J. Klir, Fuzzy Measure Theory (Plenum Press, New York, 1992).
24. Z. Wang, G.J. Klir and G. Resconi, Fuzzy measure and modal logic, in: Proc. 5th IFSA World Congr. (1993) 89-91.
25. Z. Wang, G.J. Klir and G. Resconi, Expressing fuzzy measure by a model of modal logic: a discrete case, in: Selected papers from the IFSA '93 World Congr. (1995).
26. R.R. Yager, S. Ovchinnikov, R.M. Tong and H.T. Nguyen, Eds., Fuzzy Sets and Applications: Selected Papers by L.A. Zadeh (Wiley, New York, 1987).
27. L.A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965) 338-353.
28. L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1 (1978) 3-28.