Integrated semantics and logic metric spaces

Fuzzy Sets and Systems

Volumn 136, Issue 1, 2003, Pages 71-91

  Wang, Guo Jun ^a   Leung, Yee ^b  

^a SHAANXI NORMAL UNIVERSITY   (China)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Approximate reasoning; Integrated HS; Integrated MP; R logic metric space; Tautology degree

Indexed keywords

FORMAL LOGIC; FUZZY SETS; PROBABILITY;

TAUTOLOGY DEGREE;

SEMANTICS;

EID: 0037449120     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0114(02)00328-7     Document Type: Article

References (31)

1. Bandler W., Kohout L.J. Fuzzy power sets and fuzzy implication operators. Fuzzy Sets and Systems. 4:1980;13-30.
2. Bellman R.E., Zadeh L.A. Local and fuzzy logics. Epstein G. Modern Uses of Multiple-Valued Logic. 1977;103-165 Reidel, Dordrecht.
3. Chang C.C., Keisler H.J. Model Theory. 1973;North-Holland, Amsterdam.
4. Cohn D.L. Measure Theory. 1980;Birkhäuser, Boston.
5. Dubois D., Prade H. Fuzzy Sets and Systems. 1980;Academic Press, New York.
6. Dubois D., Prade H., Lang J. Fuzzy sets in approximate reasoning, part 1, part 2. Fuzzy Sets and Systems. 40:1991;143-244.
7. Engelking R. General Topology. 1989;Heldermann Verlag, Berlin.
8. Gaines B.R. Foundations of fuzzy reasoning. Internat. J. Man-Machine Stud. 6:1976;623-668.
9. Gerla G., Tortora R. Fuzzy natural deduction. Zeitschr. Math. Logik Grund. d. Math. 36:1990;67-77.
10. Goguen J.A. The logic of inexact concepts. Syntheses. 19:1968/69;325-373.
11. Graham I., Jones L.P. Expert Systems-Knowledge, Uncertainty and Decision. 1998;Chapman and Hall Computing, London.
12. Hájek P. Metamathematics of Fuzzy Logic. 1998;Kluwer Academic Publishers, London.
13. Hamilton A.G. Logic For Mathematicians. 1978;Cambridge University Press, London.
14. Leung Y. Intelligent Spatial Decision Support Systems. 1997;Springer, Berlin.
15. McNaughton R. A theorem about infinite-valued sentential logic. J. Symbolic Logic. 16:1951;1-13.
16. Mundici D. Averaging the truth value in Lukasiewicz sentential logic. Studia Logica. 55:1995;113-127.
17. Novak V. First-order fuzzy logic. Studia Logica. 46:1987;87-109.
18. J. Pavelka, On fuzzy logic I,II,III, Zeitschr. Math. Logik Grund. d. Math. 25 (1979) 45-72, 119-134, 447-464.
19. Shortliffe E.H., Buchanan B.G. A model of inexact reasoning in medicine. Math. Biosci. 23:1975;351-379.
20. E. Trillas, L. Valverde, On some functionally expressable implications for fuzzy set theory, Proc. 3rd Internat. Seminar on Fuzzy Set Theory, Linz, Austria, 1981, pp. 173-190.
21. Wang G.J. A formal deductive system for fuzzy propositional calculus. Chinese Sci. Bull. 42:1997;18:1521-1526.
22. Wang G.J. On the logic fundation of fuzzy reasoning. Inform. Sci. 117:1999;47-88.
23. Wang G.J. Theory of Non-classical Logic and Approximate Reasoning. 2000;Science in China Press, Beijing. (in Chinese).
24. Wang G.J. A universal theory of measure and integral on valuation spaces with respect to diverse implication operators. Sci. China Ser. E. 43:2000;6:586-594.
25. Wang G.J. Separable Boolean functions and generalized Fibonacci sequences. Comput. Math. Appl. 39:2000;205-216.
26. Ying M.S. A logic for approximate reasoning. J. Symbolic Logic. 59:1994;3:830-837.
27. Zadeh L.A. Outline of a new approach to the analysis of complex system and decision processes. IEEE Trans. Systems Man Cybernet. 3:1973;28-44.
28. L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, parts 1-3, Inform. Sci. 8 (1975) 199-249, 301-357; 9 (1975) 43-80.
29. L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, parts 1-3, Inform. Sci. 8 (1975) 199-249, 301-357; 9 (1975) 43-80.
30. Zadeh L.A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems. 1:1978;3-28.
31. Zhang W.X., Leung Y. The Uncertainty Reasoning Principles. 1996;Xi'an Jiaotong University Press, Xi'an. (in Chinese).