메뉴 건너뛰기




Volumn 201, Issue 3, 1996, Pages 786-826

On the fundamentals of fuzzy set theory

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0030215021     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.0285     Document Type: Article
Times cited : (102)

References (54)
  • 4
    • 0001443226 scopus 로고
    • Triangular norm-based measures and their Markov kernel representation
    • 4. D. Butnariu and E. P. Klement, Triangular norm-based measures and their Markov kernel representation, J. Math. Anal. Appl. 162 (1991), 111-143.
    • (1991) J. Math. Anal. Appl. , vol.162 , pp. 111-143
    • Butnariu, D.1    Klement, E.P.2
  • 5
    • 84968495744 scopus 로고
    • Algebraic analysis of many valued logics
    • 5. C. C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490.
    • (1958) Trans. Amer. Math. Soc. , vol.88 , pp. 467-490
    • Chang, C.C.1
  • 6
    • 84968503880 scopus 로고
    • A new proof of the completeness of the Łukasiewicz axioms
    • 6. C. C. Chang, A new proof of the completeness of the Łukasiewicz axioms, Trans. Amer. Math. Soc. 93 (1959), 74-80.
    • (1959) Trans. Amer. Math. Soc. , vol.93 , pp. 74-80
    • Chang, C.C.1
  • 8
    • 0011653279 scopus 로고
    • New algebras of logic
    • 8. O. Frink, New algebras of logic, Amer. Math. Monthly 45 (1938), 210-219.
    • (1938) Amer. Math. Monthly , vol.45 , pp. 210-219
    • Frink, O.1
  • 10
    • 0011586017 scopus 로고
    • Axiomatization of infinite-valued predicate calculus
    • 10. L. S. Hay, Axiomatization of infinite-valued predicate calculus, J. Symbolic Logic 28 (1963), 77-86.
    • (1963) J. Symbolic Logic , vol.28 , pp. 77-86
    • Hay, L.S.1
  • 12
    • 0011586018 scopus 로고
    • A remark on entropies with respect to plausibility measures
    • R. Trappl, Ed., North-Holland, Amsterdam
    • 12. U. Höhle, A remark on entropies with respect to plausibility measures, in "Cybernetics and System Research" (R. Trappl, Ed.), pp. 735-738, North-Holland, Amsterdam, 1982.
    • (1982) Cybernetics and System Research , pp. 735-738
    • Höhle, U.1
  • 13
    • 0011656201 scopus 로고
    • Editorial of the special issue: Mathematical aspects of fuzzy set theory
    • 13. U. Höhle, Editorial of the Special Issue: Mathematical aspects of fuzzy set theory, Fuzzy Sets and Systems 40 (1991), 253-256.
    • (1991) Fuzzy Sets and Systems , vol.40 , pp. 253-256
    • Höhle, U.1
  • 14
    • 0001781835 scopus 로고
    • M-valued sets and sheaves over integral cl-monoids
    • S. E. Rodabaugh et al., Eds., Kluwer, Boston
    • 14. U. Höhle, M-valued sets and sheaves over integral cl-monoids, in "Applications of Category Theory to Fuzzy Subsets" (S. E. Rodabaugh et al., Eds.), pp. 33-72 Kluwer, Boston, 1992.
    • (1992) Applications of Category Theory to Fuzzy Subsets , pp. 33-72
    • Höhle, U.1
  • 15
    • 0002753240 scopus 로고
    • Commutative, residuated 1-monoids
    • U. Köhle and E. P. Klement, Eds., Kluwer, Boston
    • 15. U. Höhle, Commutative, residuated 1-monoids, in "Non-classical Logics and Their Applications to Fuzzy Subsets" (U. Köhle and E. P. Klement, Eds.), pp. 53-106, Kluwer, Boston, 1995.
    • (1995) Non-classical Logics and Their Applications to Fuzzy Subsets , pp. 53-106
    • Höhle, U.1
  • 16
    • 0002908674 scopus 로고
    • Presheaves over GL-monoids
    • U. Höhle and E. P. Klement, Eds., Kluwer, Boston
    • 16. U. Höhle, Presheaves over GL-monoids, in "Non-classical Logics and Their Applications to Fuzzy Subsets" (U. Höhle and E. P. Klement, Eds.), pp. 127-157, Kluwer, Boston, 1995.
    • (1995) Non-classical Logics and Their Applications to Fuzzy Subsets , pp. 127-157
    • Höhle, U.1
  • 17
    • 0011583750 scopus 로고
    • Plausibility measures - A general framework for possibility and fuzzy probability measures
    • H. J. Skala et al., Eds., Reidel, Dordrecht
    • 17. U. Höhle and E. P. Klement, Plausibility measures - A general framework for possibility and fuzzy probability measures, in "Aspects of Vagueness (H. J. Skala et al., Eds.), pp. 31-50, Reidel, Dordrecht, 1984.
    • (1984) Aspects of Vagueness , pp. 31-50
    • Höhle, U.1    Klement, E.P.2
  • 19
    • 0004072372 scopus 로고
    • Cambridge Univ. Press, Cambridge
    • 19. P. T. Johnstone, "Stone Spaces," Cambridge Univ. Press, Cambridge, 1982.
    • (1982) Stone Spaces
    • Johnstone, P.T.1
  • 20
    • 0000507321 scopus 로고
    • Characterization of finite fuzzy measures using Markoff-kernels
    • 20. E. P. Klement, Characterization of finite fuzzy measures using Markoff-kernels, J. Math. Anal. Appl. 75 (1980), 330-339.
    • (1980) J. Math. Anal. Appl. , vol.75 , pp. 330-339
    • Klement, E.P.1
  • 21
    • 0000099202 scopus 로고
    • Construction of fuzzy σ-algebras using triangular norms
    • 21. E. P. Klement, Construction of fuzzy σ-algebras using triangular norms, J. Math. Anal. Appl. 85 (1982), 543-565.
    • (1982) J. Math. Anal. Appl. , vol.85 , pp. 543-565
    • Klement, E.P.1
  • 23
    • 0000596363 scopus 로고
    • An elementary theory of the category of sets
    • 23. F. W. Lawvere, An elementary theory of the category of sets, Proc. Nat. Acad. Sci. USA 51 (1964), 1506-1510.
    • (1964) Proc. Nat. Acad. Sci. USA , vol.51 , pp. 1506-1510
    • Lawvere, F.W.1
  • 25
    • 0025404409 scopus 로고
    • Fuzzy logic in control systems: Fuzzy logic controller part I
    • 25. C. C. Lee, Fuzzy logic in control systems: Fuzzy logic controller part I, IEEE Trans. Systems Man Cybernet. 20 (1990), 404-418.
    • (1990) IEEE Trans. Systems Man Cybernet , vol.20 , pp. 404-418
    • Lee, C.C.1
  • 26
    • 0025405010 scopus 로고
    • Fuzzy logic in control systems: Fuzzy logic controller part II
    • 26. C. C. Lee, Fuzzy logic in control systems: Fuzzy logic controller part II, IEEE Trans. Systems Man Cybernet. 20 (1990), 419-443.
    • (1990) IEEE Trans. Systems Man Cybernet , vol.20 , pp. 419-443
    • Lee, C.C.1
  • 27
    • 4244018481 scopus 로고
    • On the axiomatic treatment of probability
    • 27. J. Łos, On the axiomatic treatment of probability, Colloq. Math. 3 (1955), 125-137.
    • (1955) Colloq. Math. , vol.3 , pp. 125-137
    • Łos, J.1
  • 28
    • 51249180799 scopus 로고
    • O ciatach zdarzeń i ich definicji w aksjomatycznej teorii prawdopodobieństwa
    • 28. J. Łos, O ciatach zdarzeń i ich definicji w aksjomatycznej teorii prawdopodobieństwa, Studio Logica 9 (1960), 95-132; Eng. trans., Fields of events and their definitions in the axiomatic treatment of probability theory, in "Selected Translations of Mathematical Statistics and Probability," Vol. 7, pp. 17-39, Inst. of Math. Stat., Amer. Math. Soc., Providence, RI, 1968.
    • (1960) Studio Logica , vol.9 , pp. 95-132
    • Łos, J.1
  • 29
    • 85029972541 scopus 로고    scopus 로고
    • Fields of events and their definitions in the axiomatic treatment of probability theory
    • 28. J. Łos, O ciatach zdarzeń i ich definicji w aksjomatycznej teorii prawdopodobieństwa, Studio Logica 9 (1960), 95-132; Eng. trans., Fields of events and their definitions in the axiomatic treatment of probability theory, in "Selected Translations of Mathematical Statistics and Probability," Vol. 7, pp. 17-39, Inst. of Math. Stat., Amer. Math. Soc., Providence, RI, 1968.
    • Selected Translations of Mathematical Statistics and Probability , vol.7 , pp. 17-39
  • 30
    • 0011648537 scopus 로고
    • Providence, RI
    • 28. J. Łos, O ciatach zdarzeń i ich definicji w aksjomatycznej teorii prawdopodobieństwa, Studio Logica 9 (1960), 95-132; Eng. trans., Fields of events and their definitions in the axiomatic treatment of probability theory, in "Selected Translations of Mathematical Statistics and Probability," Vol. 7, pp. 17-39, Inst. of Math. Stat., Amer. Math. Soc., Providence, RI, 1968.
    • (1968) Inst. of Math. Stat., Amer. Math. Soc.
  • 31
    • 0001529063 scopus 로고
    • O logice trójwartościowej
    • 29. J. Łukasiewicz, O logice trójwartościowej, Ruch Filozof. 5 (1920), 170-171; Engl. trans., On three-valued logic, in "Jan Łukasiewicz Selected Works," pp. 87-88, North-Holland, Amsterdam, 1970.
    • (1920) Ruch Filozof. , vol.5 , pp. 170-171
    • Łukasiewicz, J.1
  • 32
    • 0041993583 scopus 로고
    • On three-valued logic
    • North-Holland, Amsterdam
    • 29. J. Łukasiewicz, O logice trójwartościowej, Ruch Filozof. 5 (1920), 170-171; Engl. trans., On three-valued logic, in "Jan Łukasiewicz Selected Works," pp. 87-88, North-Holland, Amsterdam, 1970.
    • (1970) Jan Łukasiewicz Selected Works , pp. 87-88
  • 33
    • 0002086082 scopus 로고
    • Untersuchungen über den aussagenkalkül
    • CL. III
    • 30. J. Łukasiewicz and A. Tarski, Untersuchungen über den Aussagenkalkül, C.R. Sci. Lett. Varsovie 23 (1930), CL. III, 30-50.
    • (1930) C.R. Sci. Lett. Varsovie , vol.23 , pp. 30-50
    • Łukasiewicz, J.1    Tarski, A.2
  • 34
    • 0017703889 scopus 로고
    • Applications of fuzzy logic to approximate reasoning using linguistic systems
    • 31. E. H. Mamdani, Applications of fuzzy logic to approximate reasoning using linguistic systems, IEEE Trans. Comput. 26 (1977), 1182-1191.
    • (1977) IEEE Trans. Comput. , vol.26 , pp. 1182-1191
    • Mamdani, E.H.1
  • 36
    • 0000451025 scopus 로고
    • A proof of the completeness of the infinite-valued calculus of Łukasiewicz with one variable
    • U. Höhle and E. P. Klement, Eds., Kluwer, Boston
    • 33. D. Mundici and M. Pasquetto, A proof of the completeness of the infinite-valued calculus of Łukasiewicz with one variable, in "Non-classical Logics and Their Applications to Fuzzy Subsets" (U. Höhle and E. P. Klement, Eds.), pp. 107-123, Kluwer, Boston, 1995.
    • (1995) Non-classical Logics and Their Applications to Fuzzy Subsets , pp. 107-123
    • Mundici, D.1    Pasquetto, M.2
  • 37
    • 85025771512 scopus 로고
    • Fuzzy topology I: Neighborhood systems of a fuzzy point and Moore-Smith convergence
    • 34. P.-M. Pu and Y.-M. Liu, Fuzzy topology I: Neighborhood systems of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76 (1980), 571-599.
    • (1980) J. Math. Anal. Appl. , vol.76 , pp. 571-599
    • Pu, P.-M.1    Liu, Y.-M.2
  • 39
    • 0037570312 scopus 로고
    • Fuzziness and equality
    • H. J. Skala et al., Eds., Reidel, Dordrecht
    • 36. A. Pultr, Fuzziness and equality, in "Aspects of Vagueness" (H. J. Skala et al., Eds.), pp. 119-135, Reidel, Dordrecht, 1984.
    • (1984) Aspects of Vagueness , pp. 119-135
    • Pultr, A.1
  • 40
    • 0001520633 scopus 로고
    • A proof of the completeness theorem of Gödel
    • 37. H. Rasiowa and R. Sikorski, A proof of the completeness theorem of Gödel, Fund. Math. 37 (1950), 193-200.
    • (1950) Fund. Math. , vol.37 , pp. 193-200
    • Rasiowa, H.1    Sikorski, R.2
  • 42
    • 0003319882 scopus 로고
    • Quantales and their applications
    • Longman, Harlow
    • 39. K. I. Rosenthal, "Quantales and Their Applications," Pitman Research Notes in Math., Vol. 234, Longman, Harlow, 1990.
    • (1990) Pitman Research Notes in Math. , vol.234
    • Rosenthal, K.I.1
  • 43
    • 84968466832 scopus 로고
    • Fragments of many-valued statement calculi
    • 40. A. Rose and J. B. Rosser, Fragments of many-valued statement calculi, Trans. Amer. Math. Soc. 87 (1958), 1-53.
    • (1958) Trans. Amer. Math. Soc. , vol.87 , pp. 1-53
    • Rose, A.1    Rosser, J.B.2
  • 44
    • 0011648540 scopus 로고
    • Recent developments in mathematical classification using fuzzy sets
    • G. E. Lasker, Ed., Pergamon, Elmsford, NY
    • 41. E. H. Ruspini, Recent developments in mathematical classification using fuzzy sets, in "Applied Systems and Cybernetics" (G. E. Lasker, Ed.), pp. 2785-2790, Pergamon, Elmsford, NY, 1981.
    • (1981) Applied Systems and Cybernetics , pp. 2785-2790
    • Ruspini, E.H.1
  • 45
    • 0001072945 scopus 로고
    • Die nichtaxiomatisierbarkeit des unendlichwertigen prädikatenkalküls von Łukasiewicz
    • 42. B. Scarpellini, Die Nichtaxiomatisierbarkeit des unendlichwertigen Prädikatenkalküls von Łukasiewicz, J. Symbolic Logic 27 (1962), 159-170.
    • (1962) J. Symbolic Logic , vol.27 , pp. 159-170
    • Scarpellini, B.1
  • 46
    • 0001661753 scopus 로고
    • Identity and existence in intuitionistic logic
    • Springer-Verlag, New York/Berlin
    • 43. D. S. Scott, Identity and existence in intuitionistic logic, in "Applications of Sheaves," Lecture Notes in Math., Vol. 753, pp. 660-696, Springer-Verlag, New York/Berlin, 1979.
    • (1979) "Applications of Sheaves," Lecture Notes in Math. , vol.753 , pp. 660-696
    • Scott, D.S.1
  • 48
    • 0001380459 scopus 로고
    • Allocations of probability
    • 45. G. Shafer, Allocations of probability, Ann. Probab. 7 (1979), 827-839.
    • (1979) Ann. Probab. , vol.7 , pp. 827-839
    • Shafer, G.1
  • 49
    • 0011647863 scopus 로고
    • The integral in a boolean algebra
    • 46. R. Sikorski, The integral in a Boolean algebra, Colloq. Math. 2 (1949), 20-26.
    • (1949) Colloq. Math. , vol.2 , pp. 20-26
    • Sikorski, R.1
  • 51
    • 0002340507 scopus 로고
    • An inquiry into indistinguishability operators
    • H. J. Skala et al., Eds., Reidel, Dordrecht
    • 48. E. Trillas and L. Valverde, An inquiry into indistinguishability operators, in "Aspects of Vagueness" (H. J. Skala et al., Eds.), pp. 231-256, Reidel, Dordrecht, 1984.
    • (1984) Aspects of Vagueness , pp. 231-256
    • Trillas, E.1    Valverde, L.2
  • 52
    • 0000515054 scopus 로고
    • From circuit theory to system theory
    • 49. L. A. Zadeh, From circuit theory to system theory, Proc. Inst. Radio Eng. 50 (1962), 856-865.
    • (1962) Proc. Inst. Radio Eng. , vol.50 , pp. 856-865
    • Zadeh, L.A.1
  • 54
    • 49349133217 scopus 로고
    • Fuzzy sets as a basis for a theory of possibility
    • 51. L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1 (1978), 3-28.
    • (1978) Fuzzy Sets and Systems , vol.1 , pp. 3-28
    • Zadeh, L.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.