Skip to main content
SpringerLink
Log in

Towards Fuzzy Logic

  • Chapter
Computing with Words in Information/Intelligent Systems 1

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 33))

Abstract

The mental activity of people (concerning mainly information handling) for a long time has been divided into two groups: calculating and reasoning. The former deals with numbers and occasionally is called computing with numbers and the latter deals with words and is called computing with words.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Andreoli, G. (1956). La logica del finito e del concreto, Giornale di matematiche, volume LXXXIV, 19–48.

    Google Scholar 

  2. Barwise J. and Cooper R. (1981). Generalized quantifiers and natural language, Linguistics and Philosophy,vol.4, 159–219.

    Google Scholar 

  3. Becker, O. (1930). Zur Logik der Modalitaeten, Jahrbuch f Phil. and phaenomenologische Forschung, 11, 497–548.

    Google Scholar 

  4. BeightlerC., Philips D., Wilde D. (1982), Foundations of Optimisation, Prentice-Hall

    Google Scholar 

  5. Bell, D. (1979). Frege’s theory of judgement, Clarendon Press, Oxford.

    Google Scholar 

  6. Birkhoff, G. (1967). Lattice theory, Providence, Rhode Island.

    MATH  Google Scholar 

  7. BIRKHOFF, G. (1969). Mathematics and psychology, SIAM Review, vol. 11, 429–469.

    Article  MathSciNet  MATH  Google Scholar 

  8. Black, M. (1937). Vagueness, Phil. of Science, 4, 427–455.

    Article  Google Scholar 

  9. Bolzano, B. (1837). Wissenschaftslehre vol. II., Sulzbach.

    Google Scholar 

  10. Borel, E. (1956).Probabilite’ et certitude, Presses Universitaives de France, Paris, ( Russin translation by Nauka 1964 ).

    Google Scholar 

  11. Bradley, R. Schwartz, N. (1979), Possible worlds, Basil Blackwell,Oxford.

    Google Scholar 

  12. Bronowski, J. Neyman J. (1944), The variance of the measure of a two-dimensional random set, Ann. Math. Stat. 16 nr. 4, 330–341.

    Article  MathSciNet  Google Scholar 

  13. Bunge, M. (1967). Scientific research I, The search for systems,Springer Verlag.

    Google Scholar 

  14. Bunge, M. (1967). Scientific research II, The search for truth,Springer Verlag.

    Google Scholar 

  15. Calabrese P. (1987). An algebraic synthesis of the foundations of logic and probability, Information Sci., 42, 187–237.

    Article  MathSciNet  MATH  Google Scholar 

  16. Checkland P. (1980), Systems Thinking, Systems Practice, John Wiley.

    Google Scholar 

  17. Chwistek, L. (1948). The limits of science, Routledge and Kegan Paul, London

    Google Scholar 

  18. Cohen, M. R. and Nagel, E. (1962). An introduction to logic,Harcourt Brace and World.

    Google Scholar 

  19. Copi, I. M. (1986). Introduction to logic. Macmillan Publishing Company, NY, Collier Macmillan Publishers, London.

    Google Scholar 

  20. Copilowish, I. M. (1939). Border-line cases, vagueness, and ambiguity, Phil. of Science, 6, 181–195.

    Article  Google Scholar 

  21. Cox E. (1992). The great myth of fuzzy logic, AI Expert, January, 40–43.

    Google Scholar 

  22. Curry, M. B. (1963). Foundations of mathematical logic, McGraw-Hill, N.Y.

    MATH  Google Scholar 

  23. Czezowski, T. (1949). Logika, PZWS, Warszawa.

    Google Scholar 

  24. Davis M. (1983), The prehistory and early history of automated deduction, in: Siekman J., Whrigston G. (eds.), Automation of Reasoning, Springer Verlag, 1–11.

    Google Scholar 

  25. Davis P. J. ( (1986). Descartes’ dream, Harcourt Brace Jovanovich.

    Google Scholar 

  26. Dubois, D., Prade, H., Yager, R. R.(1982). Readings in Fuzzy Sets for Intelligent Systems. (eds), Academic Press

    Google Scholar 

  27. Dubois, D., Prade, H. (1980). Fuzzy Sets and Systems. Theory and Applications,Academic Press.

    Google Scholar 

  28. Eisler, R. (1899). Wörterbuch der Philosophischen Begriffe und Ausdrücke,Berlin.

    Google Scholar 

  29. Fine, T. (1973). Theories of probability, Academic Press, New York.

    MATH  Google Scholar 

  30. von Furstenberg G. M. (1990). Acting under uncertainty,Kluwer.

    Google Scholar 

  31. Fraenkel, A. A., Bar-Hillel, Y., A. Levy, A. (1973). Foundations of set theory,North-Holland.

    Google Scholar 

  32. Garret, B. (1991). Vague identity and vague objects,Nous

    Google Scholar 

  33. Gentilhomme, Y. (1968). Les ensables flous et linguistquee, Cahiers de linguistique theoriqueet appliquee, v.47, Bucarest.

    Google Scholar 

  34. Goguen, J.A.. (1968). The logic of inexact concepts, Synthese, 19, 325–373.

    Article  Google Scholar 

  35. Gottwald, S. (1984). Fuzzy sets theory: some aspects of the early development in: H. J. Skala, S. Termini, E. Trillas (eds.), Aspects of vaguness,D. Reidel, 13–29.

    Google Scholar 

  36. Gupta, M. M. (1977). Fuzzy-ism, the first decade, in: M.M.Gupta, G.N.Saridis, B.R.Gaines (eds.), Fuzzy automata and decision processes, North-Holland, Amsterdam.

    Google Scholar 

  37. Hacking, I. (1975). The emergence of probability,Cambridge University Press.

    Google Scholar 

  38. Hasenjaeger C. (1972). Introduction to the basic concepts and problems of modern logic,D. Reidel.

    Google Scholar 

  39. Halmos, P. R. (1960). Naive set theory. Princeton.

    Google Scholar 

  40. Höhle, U. (1991). Foundation of fuzzy sets, Fuzzy sets and systems, 40, 257–296.

    Article  MathSciNet  MATH  Google Scholar 

  41. Hempel, C. G. (1939). Vagueness and logic, Phil. of Science, 6, 163–180

    Article  Google Scholar 

  42. Hilbert D, Bernays P. (1968), Grundlagen der Mathematik, Springer. 43.Iwanus, B.(1973). On Lesniewsli’s elementary ontology, Studia logica, 31, 73119.

    Google Scholar 

  43. Jevons, W.S. (1870). Elementary lessons in logic,London; Polish translation: Logika,1886,Warszawa.

    Google Scholar 

  44. Kaplan, A.(1946). Definition and specification of meanings, J. Phil., 43, 28 1288.

    Google Scholar 

  45. Kaplan A., Schott H.F. (1951). A calculus for empirical classes, Methodos, vol. III, n. 11, 165–188.

    Google Scholar 

  46. Katsoff, (1937). Modality and probability, Phil. Rev., 46, 78–85.

    Article  Google Scholar 

  47. Kemeny, J. G. (1963). Analyticity versus fuzziness, Synthese, 15, 57–80.

    Article  Google Scholar 

  48. Kotarbinski, T. (1985). Wyklady z dziejów logiki, PWN, Warszawa.

    Google Scholar 

  49. Kruze- Blachowicz, K. (1982). Leibniz’s Demonstratio Existentiae Dei ad mathematicam certitudinem exacta. A logical analysis, Studies in Logic, Grammar and Rethoric, Bialystok, 43–55.

    Google Scholar 

  50. Kruze- Blachowicz, K. (1991/92). Ontological import of the logical analysis of Leibniz’s Demonstratio Existentiae Dei, Studia in logic,Grammar and Rethoric, X/XI, 5–19.

    Google Scholar 

  51. Kruze- Blachowicz, K. (1992). Leibniz, wczesne pojgcie substancji, Zaklad Teorii Poznania, Bialystok.

    Google Scholar 

  52. Kubinski, T. (1958). Nazwy nieostre, Studia logica, 7, 115–179.

    Article  MathSciNet  MATH  Google Scholar 

  53. Kubinski, T (1960). An attempt to bring logic nearer to colloquial language, Studia logica, 10, 61–75.

    Article  Google Scholar 

  54. Kyburg, R. E., Smockler, H.E. (eds.).(1964). Studies in subjective probability, J. Wiley.

    Google Scholar 

  55. Lejewski, C. (1990). S. Lesniewski, Wiadomosci Mat., 28, 153–182.

    MathSciNet  MATH  Google Scholar 

  56. Lesniewski, S. (1916). Podstawy ogólnej teorii mnogosci,Prace Polskiego Kola Naukowego w Moskwie, Nr. 2, Moscow.

    Google Scholar 

  57. Lesniewski, S. (1992). Collected works, Polish Scientific Publishers, Warszawa

    MATH  Google Scholar 

  58. Lukasiewicz, J. (1910). 0 zasadzie sprzecznosci u Arystotelesa. Studium Krytyczne (On the principle of contradiction in Aristotle. A critical study) (new edition by PWN 1987 ).

    Google Scholar 

  59. Lukasiewicz, J. (1910). 0 zasadzie wyl4czonego srodka, Przeglqd Filozoficzny, 13, 372–373.

    Google Scholar 

  60. Lukasiewicz, J. (1920). 0logice trójwartosciowej, Ruch Filozoficzny,5, 170171.

    Google Scholar 

  61. Lukasiewicz, J. (1970). Selected works,North-Holland and PWN.

    Google Scholar 

  62. MacColl, H. (1897). Symbolic reasoning II, Mind, 6, 494–510.

    Google Scholar 

  63. MacColl, H. (1900). Symbolic reasoning III, Mind, 9

    Google Scholar 

  64. Marciszewski, W. (1981). On Leibniz’s anticipation of comprehension axiom in the light of a formalization of “Demonstratio existentiae Dei”, Studies in Logic, Grammar and Rhetoric II, Warsaw University, Bialystok Branch, 2941.

    Google Scholar 

  65. Matheron G. (1975). Random sets and integral geometry,J.Wiley.

    Google Scholar 

  66. Mellor, D. H. (1965). Experimental error and deducibility, Phil. of Science. vol. 32, Nr. 2, 102–122.

    Google Scholar 

  67. Mellor, D. H. (1966). Inexactness and explanation, Phil. of Science. vol. 33, Nr. 4, 345–359.

    Article  Google Scholar 

  68. Mellor, D. H. (1967). Imprecision and explanation, Phil. of Science. vol. 34, Nr. 1, 1–10.

    Article  Google Scholar 

  69. Menger, K. (1951). Ensembles flous et fonctions aleatories, Comptes Rendus de l’Academie de Sciences Paris 232, 2001–2003.

    MathSciNet  MATH  Google Scholar 

  70. Menger, K. (1951). Probabilistic geometry, Proc. N.A.S. vol. 37, 226–229

    Article  Google Scholar 

  71. Menger, K. (1951). Probabilistic theories of relations, Proc. Natl. Acad. Sci., vol. 37, 178–180

    Article  MathSciNet  Google Scholar 

  72. Menger, K. (1979). Selected papers in logic and foundations, didactics, economics,D. Reidel.

    Google Scholar 

  73. Moisil, Gr.C. (1935). Récherches sur l’algébre de la logique, Annales Scientifiques de L’université de Jassy, XXII, 1–118.

    Google Scholar 

  74. Mostowski, A. (1957). On a generalization of quantifiers, Fund. Math. vol. 44, 12–36.

    MathSciNet  Google Scholar 

  75. Murawski, R. (1994), Filozofia matematyki, antologia tekstow klasycznych, Wyd. naukowe UAM, Poznan.

    Google Scholar 

  76. Narens, L. (1981). A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness, Theory and Decision, 13, 1–70.

    Article  MathSciNet  MATH  Google Scholar 

  77. Nguen, H. T. (1982). On the possibilistic approach to the analysis of evidence in. R. Yager (ed.), Fuzzy sets and possibility theory, Pergamon Press, 395401.

    Google Scholar 

  78. Orlov, A. I. (1975). Foundations of fuzzy sets (generalisation of Zadehian concept) in: Algorithms of multidimensional statistical analysis and their applications, CEMI AN SSSR, Moscow 1980 pp. 287–308 (in Russian).

    Google Scholar 

  79. Orlov, A. I. (1980). Random sets with independent elements (Lucyeans) and their applications in: Ayvasian S. A., Enyukov I. C. (eds.), Algorithms and programms for applied statistical analysis, Nauka, Moscow 1980 pp. 287–308 (in Russian).

    Google Scholar 

  80. Ostasiewicz, W. (1988). Formalisation of quantifier phrases, in Gupta M. M. and Yamawa T. (eds.) Fuzzy logic in knowledge-based systems, 271–286, North-Holland.

    Google Scholar 

  81. Ostasiewicz, W. (1991). Pioneers of fuzziness, Busefal, 46, 4–15

    Google Scholar 

  82. Ostasiewicz, W. (1992). Uncertainty and vagueness, in: Tofan I., Gill Aluja J., Costinescu O. and Teodorescu H. N. (eds.). Advances in fuzzy sets and applications, Iasi.

    Google Scholar 

  83. Ostasiewicz, W. (1992). Half a century of fuzzy sets, Kybernetika, 28, 17–20.

    MathSciNet  MATH  Google Scholar 

  84. Ostasiewicz, W. (1994). Remarks on various kinds of sets, Proc. of EUFIT’94

    Google Scholar 

  85. Ostasiewicz, W. (1996). Some phylosophical aspects of fuzzy sets, Fuzzy Economic Review, 2, 3–33.

    Google Scholar 

  86. Pawlak, Z. (1985). Rough sets, and fuzzy sets, Fuzzy Sets and Systems, 17, 99–102.

    Article  MathSciNet  MATH  Google Scholar 

  87. Penrose R., (1989). Emperor’s New Mind, Oxford University Press.

    Google Scholar 

  88. Perzanowski (1973). The development of Cantor’s definition of the set, in: Surma S. (ed.) Studies in the history of mathematical logic, Ossolineum, 269274.

    Google Scholar 

  89. Post, E. L. (1921). Introduction to a general theory of elementary propositions, American J. of Mathematics 43, 165–185.

    MathSciNet  Google Scholar 

  90. Przelecki, (1958). W sprawie terminów nieostrych, Studia Logica, 8, 313–317.

    Google Scholar 

  91. Quine, W. V. (1981). Theories and things, The Belknap Press of Harvard University Press, Cambridge.

    Google Scholar 

  92. Quine, W. V. (1960). Word and object, The MIT Press, Cambridge.

    MATH  Google Scholar 

  93. Ramirez D. (1990). G.W. Leibniz, J. Bernuolli i les interpretacions de la probabilitat. De L’ars cogitandi a L’ars conjectandi,Barcelona, 85–105.

    Google Scholar 

  94. Rasiowa, H. (1962). On non -classical calculi of classes, Tihany, 11–15 Sept.

    Google Scholar 

  95. Rasiowa, H. (1964). A generalisation of a formalised theory of fields of sets on non-classical logics, Rozprawy Matematyczne, 42, 3–29.

    MathSciNet  Google Scholar 

  96. Rasiowa, H. (1974). An algebraic approach to non-classical logics, PWN, Warszawa.

    MATH  Google Scholar 

  97. Reichenbach, H. (1949). The theory of probability,University of California Press.

    Google Scholar 

  98. Reichenbach, H. (1966). Elements of symbolic logic, The Free Press, New York

    Google Scholar 

  99. Rescher, N. (1964). Introduction to logic, St. Martins Press, New York. 101.Robinson, R. (1941). III.- Ambiguity, Mind, 50, 140–155

    Google Scholar 

  100. Robbins, H. E. (1944). On the measure of random set, Ann. of Math. Stat. vol. 15, 70–74.

    Google Scholar 

  101. Rogers, R. (1971). Mathematical logic and formalised theories,North-Holland.

    Google Scholar 

  102. Rolf, B. (1980). A theory of vagueness, Jour. of philosophical logic, 9, 315325.

    Google Scholar 

  103. Rolf, B. (1981). Topics on vagueness, Ph. D. Thesis, University of Lund.

    Google Scholar 

  104. Russell, B. (1923). Vagueness, Austr. J. of Philosophy, 1, 84–92.

    Google Scholar 

  105. Russell, B. (1924). The problem of philosophy, Williams and Norgate, London.

    Google Scholar 

  106. Schutz, W.C. (1959). Some applications of the logical calculus for empirical classes for social methodology, Psychometrica, 24, 69–87.

    Google Scholar 

  107. Strzednicki, J.T.J., Rickey, V.F., Czelakowski, J. (eds.) (1984). Lesniewski’s System Ontology and Mereology,Martinus Nijhoff and Ossolineum.

    Google Scholar 

  108. Szpilrajn, E. (1936). Sur l equvalence des suites d’ensembles of l’equivalence des fonctions, Fundamenta Mathematicae, 26, 302–326.

    Google Scholar 

  109. Tarski, A. (1933), Pojgcie prawdy w jezykach nauk dedukcyjnych, Nakladem Towarzystwa Naukowego Warszawskiego, Warszawa.

    Google Scholar 

  110. Tarski, A. (1940). Introduction to logic,Oxford University Press.

    Google Scholar 

  111. Tatarkiewicz, W. (1982). Dzieje szesciu pojgc, PWN, Warszawa.

    Google Scholar 

  112. Toth, H. (1987). From fuzzy-set theory to fuzzy set-theory: some critical remarks on existing concepts, Fuzzy Sets and Systems, 23, 219–237

    Google Scholar 

  113. Vopenka, P., Hajek, P. (1972). The theory of semisets, Academia, Prague.

    Google Scholar 

  114. Wajsberg, M. (1931). Aksjomatyzacja trówarto§ciowego rachunku zdan, Comp. Rend. Seanc. Soc. Sci. Lett. Varsovie, Classe III, 24, 126–148

    Google Scholar 

  115. Weyl, H. (1940). The ghost of modality in: Philosophical essays in memory of Edmund Husserl, Cambridge (Mass.), 278–303.

    Google Scholar 

  116. Weyl, H. (1946). Mathematic and logic, Amer. Math. Month. 53, 2–13.

    Google Scholar 

  117. Wolenski, J. (1985). Filozoficzna szkola lwowsko-warszawska, PWN, Warszawa.

    Google Scholar 

  118. Young, C. (1931). The algebra of many-valued quantities, Mathematische Annalen, vol. 104, 260–290.

    Google Scholar 

  119. Zadeh, L. H. (1965), Fuzzy sets, Information Control, 8, 338–353.

    Google Scholar 

  120. Zawirski, Z. (1932). Les logiques nouvelles at le champ de leur application, Revue de métaphysique et de morale.

    Google Scholar 

  121. Zawirski, Z. (1934). Stosunek logiki wielowartoseiowej do rachunku prawdopodobienstwa, Polskie Towarzystwo Przyjaciól Nauk, Poznan 124.Zemach, E. M. (1991). Vague objects, Nous, 3, 323–340.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Wrocław University of Economics, Komandorska 118/120, 53-345, Wroclaw, Poland

    Walenty Ostasiewicz

Authors
  1. Walenty Ostasiewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Berkeley Initiative in Soft Computing (BISC) Computer Science Division and Electronics Research Laboratory Department of Electrical and Electronics Engineering and Computer Science, University of California, 94720-1776, Berkeley, CA, USA

    Lotfi A. Zadeh

  2. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ostasiewicz, W. (1999). Towards Fuzzy Logic. In: Zadeh, L.A., Kacprzyk, J. (eds) Computing with Words in Information/Intelligent Systems 1. Studies in Fuzziness and Soft Computing, vol 33. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1873-4_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-7908-1873-4_12

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-11362-2

  • Online ISBN: 978-3-7908-1873-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation