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Fuzzy Quantifiers

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 193))

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References

  1. P.B. Andrews. An introduction to mathematical logic and type theory: to truth through proof. Academic Press, 1986.

    Google Scholar 

  2. T. Arnould and A. Ralescu. From “and” to “or”. In B. Bouchon-Meunier, L. Valverde, and R.R. Yager, editors, IPMU’ 92-Advanced Methods in Artificial Intelligence, volume 682 of Lecture Notes in Computer Science, pages 116–128. Springer, 1993.

    Google Scholar 

  3. S. Barro, A. Bugarín, P. Cariñena, and F. Díaz-Hermida. A framework for fuzzy quantification models. GSI-99-01, Departamento de Electrónica e Computación, Universidade de Santiago di Compostela, E15782 Santiago de Compostela, Spain, 1999.

    Google Scholar 

  4. S. Barro, A. Bugarín, P. Cariñena, and F. Díaz-Hermida. A framework for fuzzy quantification models analysis. IEEE Transactions on Fuzzy Systems, 11:89–99, 2003.

    Article  Google Scholar 

  5. J. Barwise. Monotone quantifiers and admissible sets. In Generalized Recursion Theory II, pages 1–38. North-Holland, Amsterdam, 1978.

    Google Scholar 

  6. J. Barwise. On branching quantifiers in English. Journal of Philosophical Logic, 8:47–80, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Barwise and R. Cooper. Generalized quantifiers and natural language. Linguistics and Philosophy, 4:159–219, 1981.

    Article  MATH  Google Scholar 

  8. J. Barwise and S. Feferman, editors. Model-Theoretic Logics. Springer, Berlin, 1985.

    Google Scholar 

  9. J. van Benthem. Determiners and logic. Linguistics and Philosophy, 6:447–478, 1983.

    Article  MATH  Google Scholar 

  10. J. van Benthem. Questions about quantifiers. Journal of Symbolic Logic, 49, 1984.

    Google Scholar 

  11. J.C. Bezdek. Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York, 1981.

    MATH  Google Scholar 

  12. J.C. Bezdek, D. Dubois, and H. Prade, editors. Fuzzy Sets in Approximate Reasoning and Information Systems. Kluwer Academic Publishers, Dordrecht, NL, 1999.

    MATH  Google Scholar 

  13. Z. Bien and K.C. Min, editors. Fuzzy Logic and its Applications to Engineering, Information Sciences, and Intelligent Systems. Information Science and Intelligent Systems. Kluwer Academic Publishers, Dordrecht, 1995.

    MATH  Google Scholar 

  14. M. Black. Vagueness: an exercise in logical analysis. Philosophy of Science, 4:427–455, 1937. Reprinted with omissions in [90, p. 69–81].

    Article  Google Scholar 

  15. N. Blanchard. Cardinal and ordinal theories about fuzzy sets. In M.M. Gupta and E. Sanchez, editors, Fuzzy Information and Decision Processes, pages 149–157. North-Holland, Amsterdam, 1982.

    Google Scholar 

  16. I. Bloch. Information combination operators for data fusion: a comparative review with classification. IEEE Transactions on Systems, Man, and Cybernetics, 26(1):52–67, 1996.

    Article  Google Scholar 

  17. I.M. Bocheński. A history of formal logic. Chelsea Publishing Company, New York, 2nd edition, 1970.

    MATH  Google Scholar 

  18. G. Bordogna, P. Carrara, and G. Pasi. Query term weights as constraints in fuzzy information retrieval. Information Processing & Management, 27(1):15–26, 1990.

    Article  Google Scholar 

  19. G. Bordogna and G. Pasi. A fuzzy information retrieval system handling users’ preferences on document sections. In H. Prade, and R.R. Yager, editors. Fuzzy Information Engineering. Wiley, New York, 1997 Dubois et al. [45].

    Google Scholar 

  20. P. Bosc, B.B. Buckles, F.E. Petry, and O. Pivert. Fuzzy databases. In D. Dubois, H. Prade, and J. Bezdek, editors, Fuzzy Sets in Approximate Reasoning and Expert Systems, pages 403–468. Kluwer, Dordrecht, NL, 1999.

    Google Scholar 

  21. P. Bosc and L. Lietard. Monotonic quantified statements and fuzzy integrals. In Proc. of the NAFIPS/IFI/NASA’ 94 Joint Conference, pages 8–12, San Antonio, Texas, 1994.

    Google Scholar 

  22. P. Bosc and L. Lietard. On the comparison of the Sugeno and Choquet fuzzy integrals for the evaluation of quantified statements. In Proceedings of EUFIT’ 95, pages 709–716, 1995.

    Google Scholar 

  23. P. Bosc and O. Pivert. Extending SQL retrieval features for the handling of flexible queries. In H. Prade, and R.R. Yager, editors. Fuzzy Information Engineering. Wiley, New York, 1997 Dubois et al. [45], pages 233–251.

    Google Scholar 

  24. N.R. Campbell. The sorites paradox. Philosophical Studies, 26:175–191, 1974.

    Article  Google Scholar 

  25. J. Cargile. The sorites paradox. British Journal for the Philosophy of Science, 1969.

    Google Scholar 

  26. S.J. Chen and C.L. Hwang. Fuzzy Multiple Attribute Decision Making: Methods and Applications. Springer, Heidelberg, 1992.

    MATH  Google Scholar 

  27. A. Church. A formulation of the simple theory of types. Journal of Symbolic Logic, 5:56–68, 1940.

    MATH  MathSciNet  Google Scholar 

  28. F. Díaz-Hermida, A. Bugarín, P. Cariñena, M. Mucientes, and D.E. Losoda. Fuzzy quantification in two real scenarios: Information retrieval and mobile robotics. International Journal of Intelligent Systems, 2005. to appear.

    Google Scholar 

  29. F. Díaz-Hermida, P. Cariñena, A. Bugarín, and S. Barro. Probabilistic evaluation of fuzzy quantified sentences: independence profile. Mathware and Soft Computing, VIII(3):255–274, 2001.

    Google Scholar 

  30. F. Díaz-Hermida, P. Cariñena, A. Bugarín, and S. Barro. Definition and classification of semi-fuzzy quantifiers for the evaluation of fuzzy quantified sentences. International Journal of Approximate Reasoning, 34(1):49–88, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  31. F. Díaz-Hermida, P. Cariñnena, A. Bugarín, and S. Barro. Random set-based approaches for modelling fuzzy operators. In Modelling with Words — Learning, Fusion, and Reasoning within a Formal Linguistic Representation Framework, volume 2873 of Lecture Notes in Computer Science, pages 1–25. Springer, 2003.

    Google Scholar 

  32. M. Delgado, F. Herrera, E. Herrera-Viedma, and L. Martinez. Combining numerical and linguistic information in group decision making. Information Sciences, 107:177–194, 1998.

    Article  MathSciNet  Google Scholar 

  33. M. Delgado, D. Sánchez, and M.A. Vila. Un enfoque lógico para calcular el grado de cumplimiento de sentencias con cuantificadores linguísticos. In Actas VII Congreso Español Sobre Tecnologías y Lógica Fuzzy (ESTYLF’ 97), pages 15–20, 1997.

    Google Scholar 

  34. M. Delgado, D. Sánchez, and M.A. Vila. A survey of methods for evaluating quantified sentences. In Proceedings of the First European Society for Fuzzy Logic and Technologies Conference (EUSFLAT’ 99), pages 279–282, 1999.

    Google Scholar 

  35. M. Delgado, D. Sánchez, and M.A. Vila. Fuzzy cardinality based evaluation of quantified statements. International Journal of Approximate Reasoning, 23(1):23–66, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  36. A. DeLuca and S. Termini. A definition of non-probabilistic entropy in the setting of fuzzy sets theory. Information and Control, 20(4):301–312, 1972.

    Article  MathSciNet  Google Scholar 

  37. P. Dienes. On an implication function in many-valued systems of logic. Journal of Symbolic Logic, 14:95–97, 1949.

    MATH  MathSciNet  Google Scholar 

  38. J. van der Does. The dynamics of sophisticated laziness. In J. Groenendijk, editor, Plurals and Anaphora, DYANA-2 (Dynamic Interpretation of Natural Language) ESPRIT Basic Research Project 6852, Deliverable R.2.2.A, Part I, pages 1–52, 1993.

    Google Scholar 

  39. D. Driankov, H. Hellendoorn, and M. Reinfrank. An Introduction to Fuzzy Control. Springer, 1996.

    Google Scholar 

  40. D. Dubois, L. Godo, R. Lopez de Mantaras, and H. Prade. Qualitative reasoning with imprecise probabilities. Journal of Intelligent Information Systems, 2:319–363, 1993.

    Article  Google Scholar 

  41. D. Dubois and H. Prade. Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, 1980.

    MATH  Google Scholar 

  42. D. Dubois and H. Prade. Fuzzy cardinality and the modelling of imprecise quantification. Fuzzy Sets and Systems, 16:199–230, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  43. D. Dubois and H. Prade. Fuzzy sets in approximate reasoning I, II. Fuzzy Sets and Systems, 40(1):143–202, 202–244, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  44. D. Dubois, H. Prade, and R. Yager. Merging fuzzy information. In D. Dubois, H. Prade, and J. Bezdek, editors, Fuzzy Sets in Approximate Reasoning and Expert Systems, pages 335–402. Kluwer, Dordrecht, NL, 1999.

    Google Scholar 

  45. D. Dubois, H. Prade, and R.R. Yager, editors. Fuzzy Information Engineering. Wiley, New York, 1997.

    Google Scholar 

  46. D. Edgington. Vagueness by degrees. In R. Keefe and P. Smith, editors, Vagueness: A Reader, pages 294–316. MIT Press/A Bradford Book, Cambridge, MA, 1997.

    Google Scholar 

  47. K. Fine. Vagueness, truth and logic. Synthese, 1975.

    Google Scholar 

  48. G. Frege. Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik, 100:25–50, 1892.

    Google Scholar 

  49. B.R. Gaines. Foundations of fuzzy reasoning. Int. Journal of Man-Machine Studies, 8:623–668, 1978.

    MathSciNet  Google Scholar 

  50. L.T.F. Gamut. Intensional Logic and Logical Grammar, volume II of Logic, Language, and Meaning. The University of Chicago Press, Chicago & London, 1984.

    Google Scholar 

  51. I. Glöckner. Evaluation of quantified propositions in generalized models of fuzzy quantification. International Journal of Approximate Reasoning, 37(2):93–126, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  52. I. Glöckner. Fuzzy Quantifiers in Natural Language: Semantics and Computational Models. Der Andere Verlag, Osnabrück, Germany, 2004.

    Google Scholar 

  53. I. Glöckner. DFS — an axiomatic approach to fuzzy quantification. TR97-06, Technical Faculty, University Bielefeld, 33501 Bielefeld, Germany, 1997.

    Google Scholar 

  54. I. Glöckner. A framework for evaluating approaches to fuzzy quantification. TR99-03, Technical Faculty, University Bielefeld, 33501 Bielefeld, Germany, 1999.

    Google Scholar 

  55. I. Glöckner. Advances in DFS theory. TR2000-01, Technical Faculty, University of Bielefeld, 33501 Bielefeld, Germany, 2000.

    Google Scholar 

  56. I. Glöckner. An axiomatic theory of quantifiers in natural languages. TR2000-03, Technical Faculty, University of Bielefeld, 33501 Bielefeld, Germany, 2000.

    Google Scholar 

  57. I. Glöckner. A broad class of standard DFSes. TR2000-02, Technical Faculty, University of Bielefeld, 33501 Bielefeld, Germany, 2000.

    Google Scholar 

  58. I. Glöckner. Standard models of fuzzy quantification. TR2001-01, Technical Faculty, University of Bielefeld, 33501 Bielefeld, Germany, 2001.

    Google Scholar 

  59. I. Glöckner. Fundamentals of fuzzy quantification: Plausible models, constructive principles, and efficient implementation. TR2002-07, Technical Faculty, University of Bielefeld, 33501 Bielefeld, Germany, 2003.

    Google Scholar 

  60. I. Glöckner and A. Knoll. Fuzzy quantifiers for processing natural language queries in content-based multimedia retrieval systems. TR97-05, Technical Faculty, University of Bielefeld, 33501 Bielefeld, Germany, 1997.

    Google Scholar 

  61. I. Glöckner and A. Knoll. Application of fuzzy quantifiers in image processing: A case study. In Proceedings of KES’99, Adelaide, Australia, 1999.

    Google Scholar 

  62. I. Glöckner and A. Knoll. Natural-language navigation in multimedia archives: An integrated approach. In Proceedings of the Seventh ACM Multimedia Conference (MM’ 99), pages 313–322, Orlando, Florida, 1999.

    Google Scholar 

  63. I. Glöckner and A. Knoll. Query evaluation and information fusion in a retrieval system for multimedia documents. In Proceedings of Fusion’99, pages 529–536, Sunnyvale, CA, 1999.

    Google Scholar 

  64. I. Glöckner and A. Knoll. Architecture and retrieval methods of a search assistant for scientific libraries. In W. Gaul and R. Decker, editors, Classification and Information Processing at the Turn of the Millennium. Springer, Heidelberg, 2000.

    Google Scholar 

  65. I. Glöckner and A. Knoll. Architecture and retrieval methods of a search assistant for scientific libraries. In W. Gaul and R. Decker, editors, Classification and Information Processing at the Turn of the Millennium, pages 460–468. Springer, Heidelberg, 2000.

    Google Scholar 

  66. I. Glöckner and A. Knoll. Fuzzy quantification in granular computing and its role for data summarisation. In W. Pedrycz, editor, Granular Computing: An Emerging Paradigm, Studies in Fuzziness and Soft Computing, pages 215–256. Physica-Verlag, Heidelberg, 2001.

    Google Scholar 

  67. I. Glöckner, A. Knoll, and A. Wolfram. Data fusion based on fuzzy quantifiers. In Proceedings of EuroFusion98, International Data Fusion Conference, pages 39–46, 1998.

    Google Scholar 

  68. J.A. Goguen. The logic of inexact concepts. Synthese, 19:325–373, 1969.

    Article  MATH  Google Scholar 

  69. F. Hamm. Natürlich-sprachliche Quantoren. Modelltheoretische Untersuchungen zu universellen semantischen Beschränkungen. Number 236 in Linguistische Arbeiten. Niemeyer, Tübingen, 1989.

    Google Scholar 

  70. C.J. Harris, C.G. Moore, and M. Brown. Intelligent Control: Aspects of Fuzzy Logic and Neural Nets. World Scientific, Singapore, 1993.

    MATH  Google Scholar 

  71. J. van Heijenoort. From Frege to Gödel — A Source Book in Mathematical Logic. Harvard University Press, Cambridge, MA, 1967.

    MATH  Google Scholar 

  72. I. Heim. The semantics of definite and indefinite noun phrases. PhD thesis, University of Massachusetts, Amherst, 1982.

    Google Scholar 

  73. H. Helbig. Die semantische Struktur natürlicher Sprache. Wissensrepräsentation mit MultiNet. Springer, Berlin, Heidelberg, 2000.

    Google Scholar 

  74. L. Henkin. Some remarks on infinitely long formulas. In Infinitistic methods, pages 167–183. Pergamon Press, New York, and Polish Scientific Publishers, Warsaw, 1961.

    Google Scholar 

  75. F. Herrera and J.L. Verdegay. On group decision making under linguistic preferences and fuzzy linguistic quantifiers. In B. Bouchon, R.R. Yager, and L.A. Zadeh, editors, Fuzzy Logic and Soft Computing, pages 173–180. World Scientific, 1995.

    Google Scholar 

  76. J. Hintikka. Quantifiers vs. quantification theory. Dialectica, 27:329–358, 1973.

    Google Scholar 

  77. P. Hájek and L. Kohout. Fuzzy implications and generalized quantifiers. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 4(3):225–233, 1996.

    Article  MathSciNet  Google Scholar 

  78. I. Homann. Fuzzy-Suchmethoden im Information-Retrieval. PhD thesis, University of Bielefeld, Bielefeld, Germany, 2004.

    Google Scholar 

  79. F. de Jongh and H. Verkuyl. Generalized quantifiers: The properness of their strength. In J. van Benthem and A. ter Meulen, editors, Generalized Quantifiers in Natural Language. Foris, Dordrecht, 1984.

    Google Scholar 

  80. J. Kacprzyk. Multistage Decision-Making under Fuzziness. Verlag TÜV Rheinland, Cologne, 1983.

    MATH  Google Scholar 

  81. J. Kacprzyk. Multistage Fuzzy Control: A Model-Based Approach to Control and Decision-Making. Wiley, Chichester, 1997.

    MATH  Google Scholar 

  82. J. Kacprzyk. Intelligent data analysis via linguistic data summaries: A fuzzy logic approach. In R. Decker and W. Gaul, editors, Classification and Information Processing at the Turn of the Millenium, pages 153–161. Springer, 2000.

    Google Scholar 

  83. J. Kacprzyk and P. Strykowski. Linguistic summaries of sales data at a computer retailer: A case study. In Proc. of 8th International Fuzzy Systems Association World Congress (IFSA’ 99), pages 29–33, 1999.

    Google Scholar 

  84. J. Kacprzyk and S. Zadrożny. Fuzzy queries in Microsoft Access V.2. InH. Prade, and R.R. Yager, editors. Fuzzy Information Engineering. Wiley, New York, 1997. Dubois et al. [45], pages 223–232.

    Google Scholar 

  85. J. Kacprzyk, S. Zadrożny, and M. Fedrizzi. An interactive GDSS for consensus reaching using fuzzy logic with linguistic quantifiers. InH. Prade, and R.R. Yager, editors. Fuzzy Information Engineering. Wiley, New York, 1997 Dubois et al. [45], pages 567–574.

    Google Scholar 

  86. J. Kacprzyk and A. Ziólkowsi. Database queries with fuzzy linguistic quantifiers. IEEE Transactions on Systems, Man, and Cybernetics, 16(3):474–479, 1986.

    Google Scholar 

  87. H. Kamp. A theory of truth and semantic representation. In J. Groenendijk, T. Janssen, and M. Stokhof, editors, Formal Methods in the Study of Language, Amsterdam: Mathematical Centre, 1981.

    Google Scholar 

  88. J. Kamp. Two theories about adjectives. In Edward Keenan, editor, Formal Semantics of Natural Language. Cambridge University Press, 1975.

    Google Scholar 

  89. A. Kaufmann. Introduction to the Theory of Fuzzy Subsets, volume 1: Fundamental theoretical elements. Academic Press, New York, 1975.

    MATH  Google Scholar 

  90. R. Keefe and P. Smith, editors. Vagueness: A Reader. A Bradford Book/MIT Press, Cambridge, MA, 1997.

    Google Scholar 

  91. E. Keenan and L. Moss. Generalized quantifiers and expressive power of natural language. In J. van Benthem and A. ter Meulen, editors, Generalized Quantifiers in Natural Language, pages 73–124. Foris, Dordrecht, 1984.

    Google Scholar 

  92. E. Keenan and J. Stavi. A semantic characterization of natural language determiners. Linguistics and Philosophy, 9:253–326, 1986.

    Article  MATH  Google Scholar 

  93. E. Keenan and D. Westerståhl. Generalized quantifiers in linguistics and logic. In J. van Benthem and A. Ter Meulen, editors, Handbook of Logic and Language, chapter 15, pages 837–893. Elsevier, Amsterdam, NL, 1997.

    Google Scholar 

  94. H.J. Keisler. Logic with the quantifier ‘There Exist Uncountably Many’. Annals of Mathematical Logic, 1:1–93, 1969.

    MathSciNet  Google Scholar 

  95. S.C. Kleene. Introduction to Metamathematics. North-Holland, Amsterdam, 1952.

    MATH  Google Scholar 

  96. E.P. Klement, R. Mesiar, and E. Pap. Quasi-and pseudo-inverses of monotone functions, and the construction of t-norms. Fuzzy Sets and Systems, 104:3–13, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  97. G.J. Klir and T.A. Folger. Fuzzy Sets, Uncertainty, and Information. Prentice Hall, Englewood Cliffs, NJ, 1988.

    MATH  Google Scholar 

  98. G.J. Klir, U.H. St. Clair, and B. Yuan. Fuzzy Set Theory: Foundations and Applications. Prentice Hall, Upper Saddle River, NJ, 1997.

    MATH  Google Scholar 

  99. G.J. Klir and B. Yuan. Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, Upper Saddle River, NJ, 1995.

    MATH  Google Scholar 

  100. G.J. Klir and B. Yuan, editors. Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers by Lotfi A. Zadeh. World Scientific, Singapore, 1996.

    Google Scholar 

  101. S. A. Kripke. Semantical analysis of modal logic II. In J.W. Addison and A. Tarski, editors, The theory of models, pages 206–220. North-Holland, Amsterdam, 1965.

    Google Scholar 

  102. S.A. Kripke. A completeness theorem in modal logic. Journal for Symbolic Logic, 24:1–14, 1959.

    MATH  MathSciNet  Google Scholar 

  103. R. Kruse, E. Schwecke, and J. Heinsohn. Uncertainty and Vagueness in Knowledge Based Systems: Numerical Methods. Springer, Heidelberg, 1991.

    MATH  Google Scholar 

  104. Y. Lai and C. Hwang. Fuzzy Mathematical Programming. Springer, Heidelberg, 1992.

    MATH  Google Scholar 

  105. G. Lakoff. Hedges: a study in meaning criteria and the logic of fuzzy concepts. Journal of Philosophical Logic, 2:458–508, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  106. P. Lindström. First order predicate logic with generalized quantifiers. Theoria, 32:186–195, 1966.

    MathSciNet  Google Scholar 

  107. P. Lindström. On extensions of elementary logic. Theoria, 35:1–11, 1969.

    Article  MATH  MathSciNet  Google Scholar 

  108. Y. Liu and E.E. Kerre. An overview of fuzzy quantifiers. (I). Interpretations. Fuzzy Sets and Systems, 95:1–21, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  109. Y. Liu and E.E. Kerre. An overview of fuzzy quantifiers. (II). Reasoning and applications. Fuzzy Sets and Systems, 96:135–146, 1998.

    MathSciNet  Google Scholar 

  110. D. Losada, S. Barro, A. Bugarín-Diz, and F. Díaz-Hermida. Experiments on using fuzzy quantified sentences in adhoc retrieval. In ACM Symposium on Applied Computing, pages 1059–1066, 2004.

    Google Scholar 

  111. K.F. Machina. Truth, belief and vagueness. Journal of Philosophical Logic, 5:47–78, 1976. Reprinted in [90, p. 174–203].

    Article  MATH  MathSciNet  Google Scholar 

  112. E.H. Mamdani and S. Assilian. An experiment in linguistic synthesis with a fuzzy logic controller. Int. Journal of Man-Machine Studies, 7:1–13, 1975.

    Article  MATH  Google Scholar 

  113. R. Mesiar and M. Navara. Diagonals of continuous triangular norms. Fuzzy Sets and Systems, 104:35–41, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  114. S. Miyamoto. Fuzzy Sets in Information Retrieval and Cluster Analysis. Kluwer Academic Publishers, Dordrecht, 1990.

    MATH  Google Scholar 

  115. R. Montague. The proper treatment of quantification in ordinary English. In J. Hintikka, J. Moravcsik, and P. Suppes, editors, Approaches to Natural Language, pages 221–242. Reidel, Dordrecht, 1973.

    Google Scholar 

  116. A. Mostowski. On a generalization of quantifiers. Fundamenta Mathematicae, 44:12–36, 1957.

    MATH  MathSciNet  Google Scholar 

  117. M. Mucientes, R. Iglesias, C. Regueiro, A. Bugarín, P. Cariñena, and S. Barro. Fuzzy temporal rules for mobile robot guidance in dynamic environments. IEEE Transactions on Systems, Man, and Cybernetics, Part C, 66(1), 2002.

    Google Scholar 

  118. M. Mukaidono. On some properties of fuzzy logic. Systems — Computers — Controls, 6(2):36–43, 1975.

    MathSciNet  Google Scholar 

  119. H. Nakanishi, I.B. Turksen, and M. Sugeno. A review and comparison of six reasoning methods. Fuzzy Sets and Systems, 57(3):257–294, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  120. C.V. Negoita. Expert Systems and Fuzzy Systems. Benjamin/Cummings, Menlo Park, CA, 1985.

    Google Scholar 

  121. S.E. Newstead and K. Coventry. The role of context and functionality in the interpretation of quantifiers. European Journal of Cognitive Psychology, 12:243–259, 2000.

    Article  Google Scholar 

  122. S.E. Newstead, P. Pollard, and D. Riezebos. The effect of set size on the interpretation of quantifiers used in rating scales. Applied Ergonomics, 18(3):178–182, 1987.

    Article  Google Scholar 

  123. H.T. Nguyen and E.A. Walker. A First Course in Fuzzy Logic. Chapman & Hall/CRC Press, Boca Raton, FL, 2nd edition, 2000.

    MATH  Google Scholar 

  124. S.K. Pal and D.K. Majumder. Fuzzy Mathematical Approach to Pattern Recognition. John Wiley, New York, 1986.

    MATH  Google Scholar 

  125. W. Pedrycz. Fuzzy Control and Fuzzy Systems. John Wiley, New York, 1989.

    MATH  Google Scholar 

  126. H. Prade. Lipski’s approach to incomplete information data bases restated and generalized in the setting of Zadeh’s possibility theory. Information Sciences, 9(1):27–42, 1984.

    MATH  Google Scholar 

  127. H. Prade. A two-layer fuzzy pattern matching procedure for the evaluation of conditions involving vague quantifiers. Journal of Intelligent and Robotic Systems, 3:93–103, 1990.

    Article  MathSciNet  Google Scholar 

  128. H. Prade and C. Testemale. Generalizing database relational algebra for the treatment of incomplete or uncertain information and vague queries. Information Sciences, 34(2):115–143, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  129. W.V. Quine. Word and Object. Cambridge University Press, Cambridge, Mass., 1960.

    MATH  Google Scholar 

  130. W.V. Quine. Ontological Relativity and other Essays. Columbia University Press, New York, 1969.

    Google Scholar 

  131. A. Ralescu, B. Bouchon, and D. Ralescu. Combining fuzzy quantifiers. In W. Chiang and J. Lee, editors, Fuzzy Logic for the Applications to Complex Systems, pages 246–252. World Scientific, Singapore, 1995.

    Google Scholar 

  132. A.L. Ralescu. A note on rule representation in expert systems. Information Sciences, 38:193–203, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  133. Anca Ralescu, Kaoru Hirota, and Dan Ralescu. Evaluation of fuzzy quantified expressions. In Fuzzy Logic in Artificial Intelligence (IJCAI Workshop), volume 1566 of Lecture Notes in Computer Science, pages 234–244. Springer, 1999.

    MathSciNet  Google Scholar 

  134. D. Ralescu. Cardinality, quantifiers, and the aggregation of fuzzy criteria. Fuzzy Sets and Systems, 69:355–365, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  135. D. Rasmussen and R.R. Yager. A fuzzy SQL summary language for data discovery. In H. Prade, and R.R. Yager, editors. Fuzzy Information Engineering. Wiley, New York, 1997 Dubois et al. [45], pages 253–264.

    Google Scholar 

  136. N. Rescher. Quantifiers in many-valued logic. Logique et Analyse, 7:181–184, 1964.

    MATH  MathSciNet  Google Scholar 

  137. N. Rescher. Many-valued logic. McGraw-Hill, 1969.

    Google Scholar 

  138. J.B. Rosser. The introduction of quantification into a Three-valued logic. reprinted for the members of the Fifth International Congress for the Unity of Science (Cambridge, 1939) from The Journal of Unified Science (Erkenntnis), vol. 9 (never published). Abstracted in: Journal of Symbolic Logic, vol. 4 (1939), 170–171, 1939.

    Google Scholar 

  139. J.B. Rosser and A.R. Turquette. Axiom schemes for m-valued functional calculi of first order. Part I. Definition of axiom schemes and proof of plausibility. Journal of Symbolic Logic, 13:177–192, 1948.

    MathSciNet  MATH  Google Scholar 

  140. J.B. Rosser and A.R. Turquette. Axiom schemes for m-valued functional calculi of first order. Part II. Deductive completeness. Journal of Symbolic Logic, 16:22–34, 1951.

    MathSciNet  MATH  Google Scholar 

  141. J.B. Rosser and A.R. Turquette. Many-valued logics. North-Holland, Amsterdam, 1952.

    MATH  Google Scholar 

  142. R. Rovatti and C. Fantuzzi. s-norm aggregation of infinite collections. Fuzzy Sets and Systems, 84:255–269, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  143. B. Russell. Mathematical logic as based on the theory of types. American Journal of Mathematics, 30:222–262, 1908.

    MATH  MathSciNet  Google Scholar 

  144. B. Russell. History of Western Philosophy. Unwin University Books, 1946.

    Google Scholar 

  145. I.A. Sag and E.F. Prince. Bibliography of works dealing with presupposition. In Oh and Dinneen, editors, Syntax and Semantics, volume 11: Presupposition, pages 389–403. Academic Press, New York, 1979.

    Google Scholar 

  146. R. van der Sandt. Context and Presupposition. Croom Helm, New York, 1988.

    Google Scholar 

  147. K. Schlechta. Defaults as generalized quantifiers. Journal of Logic and Computation, 5(4):473–494, 1995.

    MATH  MathSciNet  Google Scholar 

  148. B. Schweizer and A. Sklar. Probabilistic metric spaces. North-Holland, Amsterdam, 1983.

    MATH  Google Scholar 

  149. J. Sgro. Completeness theorems for topological models. Annals of Mathematical Logic, pages 173–193, 1977.

    Google Scholar 

  150. W. Silvert. Symmetric summation: A class of operations on fuzzy sets. IEEE Transactions on Systems, Man, and Cybernetics, 9:657–659, 1979.

    MATH  MathSciNet  Google Scholar 

  151. R.A. Sorensen. Blindspots. Clarendon Press, Oxford, 1988.

    Google Scholar 

  152. M. Spies. Syllogistic inference under uncertainty. Psychologie-Verlags-Union, München, 1989.

    Google Scholar 

  153. M. Stokhof and J. Groenendijk, editors. Studies in Discourse Representation Theory and the Theory of Generalized Quantifiers. De Gruyter, 1986.

    Google Scholar 

  154. M. Sugeno. Fuzzy measures and fuzzy integrals: A survey. In M.M. Gupta, G.N. Saridis, and B.R. Gaines, editors, Fuzzy Automata and Decision Processes, pages 89–102. North-Holland, Amsterdam, 1977.

    Google Scholar 

  155. P. Suppes. Introduction to logic. Van Nostrand, Princeton, New Jersey, 1957.

    MATH  Google Scholar 

  156. H. Thiele. Zum Aufbau einer systematischen Theorie von Fuzzy-Quantoren. In 13. Workshop “Interdisziplinäre Methoden in der Informatik” — Arbeitstagung des Lehrstuhls Informatik I, Forschungsbericht Nr. 506, pages 35–55. Fachbereich Informatik der Universität Dortmund, 1993.

    Google Scholar 

  157. H. Thiele. On T-quantifiers and S-quantifiers. In The Twenty-Fourth International Symposium on Multiple-Valued Logic, pages 264–269, Boston, MA, 1994.

    Google Scholar 

  158. H. Thiele. On fuzzy quantifiers. In K.C. Min, editors. Fuzzy Logic and its Applications to Engineering, Information Sciences, and Intelligent Systems. Information Science and Intelligent Systems. Kluwer Academic Publishers, Dordrecht, 1995 Bien and Min [13], pages 343–352.

    Google Scholar 

  159. H. Thiele. On median quantifiers. Technical report No. CI-27/98, University of Dortmund, Dept. of Computer Science/XI, 44221 Dortmund, Germany, 1998.

    Google Scholar 

  160. E. Thijsse. On some proposed universals of natural language. In A. ter Meulen, editor, Studies in Model-Theoretic Semantics, pages 19–36. Foris, Dordrecht, 1983.

    Google Scholar 

  161. H. Thöne. Precise conclusions under uncertainty and incompleteness in deductive databases. PhD thesis, University of Tübingen, Germany, 1994.

    Google Scholar 

  162. H. Thöne, U. Güntzer, and W. Kiessling. Toward precision of probability bound propagation. In Proc. of the 8th Conf. on Uncertainty in AI, pages 315–322, San Francisco, 1992. Morgan and Kaufmann.

    Google Scholar 

  163. R. Thomason, editor. Formal Philosophy: Selected Papers of Richard Montague. Yale University Press, New Haven, CT, 1974.

    Google Scholar 

  164. M. Tye. Sorites paradoxes and the semantics of vagueness. In J.E. Tomberlin, editor, Philosophical Perspectives 8: Logic and Language, pages 189–206. Ridgeview, Atascadero, CA, 1994. Reprinted with omissions in [90, p. 281–293].

    Google Scholar 

  165. M.A. Vila, J.C. Cubero, J.M. Medina, and O. Pons. Using OWA operator in flexible query processing. In R.R. Yager and J. Kacprzyk, editors, The Ordered Weighted Averaging Operators: Theory, Methodology and Applications, pages 258–274. Kluwer Academic Publishers, Boston, 1997.

    Google Scholar 

  166. W.J. Walkoe Jr. Finite partially-ordered quantification. Journal of Symbolic Logic, 35:535–555, 1970.

    MATH  MathSciNet  Google Scholar 

  167. D. Westerståhl. Branching generalized quantifiers and natural language. In P. Gärdenfors, editor, Generalized Quantifiers, pages 269–298. Reidel, 1987.

    Google Scholar 

  168. T. Williamson. Vagueness and ignorance. Proceedings of the Aristotelian Society, Supplementary Volume, 66:145–162, 1992. Reprinted in [90, p. 265–280].

    Google Scholar 

  169. C. Wright. Language-mastery and the sorites paradox. In G. Evans and J. McDowell, editors, Truth and Meaning: Essays in Semantics, pages 223–247. Clarendon Press, Oxford, 1976.

    Google Scholar 

  170. M. Wygralak. An axiomatic approach to scalar cardinalities of fuzzy sets. Fuzzy Sets and Systems 110, pages 175–179, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  171. R.R. Yager. A new approach to the summarization of data. Information Sciences, 28:69–86, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  172. R.R. Yager. A new approach to the summarization of data. Information Sciences, 28:69–86, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  173. R.R. Yager. Quantified propositions in a linguistic logic. Int. Journal of Man-Machine Studies, 19:195–227, 1983.

    Article  MATH  Google Scholar 

  174. R.R. Yager. Approximate reasoning as a basis for rule-based expert systems. IEEE Transactions on Systems, Man, and Cybernetics, 14(4):636–643, Jul./Aug. 1984.

    MATH  MathSciNet  Google Scholar 

  175. R.R. Yager. General multiple-objective decision functions and linguistically quantified statements. Int. Journal of Man-Machine Studies, 21:389–400, 1984.

    MATH  Google Scholar 

  176. R.R. Yager. Reasoning with fuzzy quantified statements. Part I. Kybernetes, 14:233–240, 1985.

    MATH  MathSciNet  Google Scholar 

  177. R.R. Yager. Reasoning with fuzzy quantified statements. Part II. Kybernetes, 15:111–120, 1985.

    MathSciNet  Google Scholar 

  178. R.R. Yager. A characterization of the extension principle. Fuzzy Sets and Systems, 18(3):205–217, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  179. R.R. Yager. On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Transactions on Systems, Man, and Cybernetics, 18(1):183–190, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  180. R.R. Yager. Connectives and quantifiers in fuzzy sets. Fuzzy Sets and Systems, 40:39–75, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  181. R.R. Yager. Fuzzy quotient operators for fuzzy relational databases. In Proceedings of IFES’ 91, pages 289–296, 1991.

    Google Scholar 

  182. R.R. Yager. On linguistic summaries of data. In W. Frawley and G. Piatetsky-Shapiro, editors, Knowledge Discovery in Databases, pages 347–363. AAAI/MIT Press, 1991.

    Google Scholar 

  183. R.R. Yager. A general approach to rule aggregation in fuzzy logic control. Journal of Applied Intelligence, 2:333–351, 1992.

    Article  Google Scholar 

  184. R.R. Yager. Counting the number of classes in a fuzzy set. IEEE Transactions on Systems, Man, and Cybernetics, 23(1):257–264, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  185. R.R. Yager. Families of OWA operators. Fuzzy Sets and Systems, 59:125–148, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  186. R.R. Yager and J. Kacprzyk. Linguistic data summaries: A perspective. In Proc. of 8th International Fuzzy Systems Association World Congress (IFSA’ 99), pages 44–48, 1999.

    Google Scholar 

  187. R.R. Yager, S. Ovchinnikov, R.M. Tong, and H.T. Nguyen, editors. Fuzzy Sets and Applications—Selected papers by L.A. Zadeh. John Wiley, New York, 1987.

    Google Scholar 

  188. L.A. Zadeh. Fuzzy sets. Information and Control, 8(3):338–353, 1965.

    Article  MATH  MathSciNet  Google Scholar 

  189. L.A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning. Information Sciences, 8,9:199–249, 301–357, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  190. L.A. Zadeh. Fuzzy logic and approximate reasoning. Synthese, 30:407–428, 1975.

    Article  MATH  Google Scholar 

  191. L.A. Zadeh. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1:3–28, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  192. L.A. Zadeh. PRUF—a meaning representation language for natural languages. Int. Journal of Man-Machine Studies, 10:395–460, 1978.

    MATH  MathSciNet  Google Scholar 

  193. L.A. Zadeh. A theory of approximate reasoning. In J. Hayes, D. Michie, and L. Mikulich, editors, Machine Intelligence, volume 9, pages 149–194. Halstead, New York, 1979.

    Google Scholar 

  194. L.A. Zadeh. Possibility theory and soft data analysis. In L. Cobb and R.M. Thrall, editors, Mathematical Frontiers of the Social and Policy Sciences, pages 69–129. Westview Press, Boulder, 1981.

    Google Scholar 

  195. L.A. Zadeh. Test-score semantics for natural languages and meaning representation via pruf. In B.B. Rieger, editor, Empirical Semantics, Vol. 1, pages 281–349. Brockmeyer, Bochum, 1981.

    Google Scholar 

  196. L.A. Zadeh. Fuzzy probabilities and their role in decision analysis. In Proc. of the IFAC Symp. on Theory and Application of Digital Control, pages 15–23, New Delhi, 1982.

    Google Scholar 

  197. L.A. Zadeh. A computational approach to fuzzy quantifiers in natural languages. Computers and Mathematics with Applications, 9:149–184, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  198. L.A. Zadeh. A theory of commonsense knowledge. In H.J. Skala et al., editor, Aspects of Vagueness, pages 257–295. Reidel, Dordrecht, 1984.

    Google Scholar 

  199. L.A. Zadeh. Syllogistic reasoning in fuzzy logic and its application to usuality and reasoning with dispositions. IEEE Transactions on Systems, Man, and Cybernetics, 15(6):754–763, 1985.

    MATH  MathSciNet  Google Scholar 

  200. L.A. Zadeh. A computational theory of dispositions. International Journal of Intelligent Systems, 2(1):39–63, 1987.

    MATH  MathSciNet  Google Scholar 

  201. L.A. Zadeh. The role of fuzzy logic in the management of uncertainty in expert systems. In R.R. Yager et al., editor, Fuzzy Sets and Applications: Selected Papers by L.A. Zadeh, pages 413–441. Wiley, New York, 1987.

    Google Scholar 

  202. S. Zadrożny and J. Kacprzyk. On database summarization using a fuzzy querying interface. In Proc. of 8th International Fuzzy Systems Association World Congress (IFSA’ 99), pages 39–43, 1999.

    Google Scholar 

  203. M. Zemankova and A. Kandel. Implementing imprecision in information systems. Information Sciences, 37(1–3):107–141, 1985.

    Article  MATH  Google Scholar 

  204. M. Zemankova-Leech and A. Kandel. Fuzzy Relational Data Bases: A Key to Expert Systems. Verlag TÜV Rheinland, Cologne, 1984.

    MATH  Google Scholar 

  205. H.J. Zimmermann. Fuzzy Sets, Decision Making, and Expert Systems. Kluwer, Boston, MA, 1987.

    Google Scholar 

  206. H.J. Zimmermann. Fuzzy Set Theory—and its Applications. Kluwer, Boston, MA, (2nd rev. ed.) edition, 1991.

    MATH  Google Scholar 

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(2006). Discussion. In: Fuzzy Quantifiers. Studies in Fuzziness and Soft Computing, vol 193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32503-4_13

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