Generalized fuzzy quantifiers and the modeling of fuzzy branching quantification

International Journal of Intelligent Systems

Volumn 24, Issue 6, 2009, Pages 624-648

  Glockner, Ingo ^a  

^a UNIVERSITY OF HAGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; SOFTWARE ENGINEERING;

FUZZY QUANTIFICATION; FUZZY QUANTIFIERS; GENERALIZED QUANTIFIERS; LINGUISTIC DATA; NEW YORK; SEVERAL VARIABLES; SIMULTANEOUS BINDINGS; VAGUE QUANTIFIERS;

LINGUISTICS;

EID: 67049132499     PISSN: 08848173     EISSN: 1098111X     Source Type: Journal    
DOI: 10.1002/int.20351     Document Type: Article

References (36)

1. Zadeh LA. A computational approach to fuzzy quantifiers in natural languages. Computers Math Appl 1983;9:149-184.
2. Yager RR. Approximate reasoning as a basis for rule-based expert systems. IEEE Trans Syst, Man, and Cybern 1984;14(4):636-643.
3. Ralescu AL. A note on rule representation in expert systems. Inform Sci 1986;38:193-203.
4. Yager RR. On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans Syst, Man, and Cyber 1988;18(1):183-190.
5. Delgado M, Sánchez D, Vila MA. Fuzzy cardinality based evaluation of quantified statements. Int J Approx Reason 2000;23(1):23-66.
6. Barwise J, Cooper R. Generalized quantifiers and natural language. Linguistics Philos 1981;4:159-219.
7. Keenan E, Stavi J. A semantic characterization of natural language determiners. Linguistics Philos 1986;9:253-326.
8. Barwise J. On branching quantifiers in English. J Philo Logic 1979;8:47-80.
9. Barwise J, Feferman S. editors. Model-theoretic logics. Berlin: Springer; 1985.
10. Lindström P. First order predicate logic with generalized quantifiers. Theoria 1966;32:186- 195.
11. Westerståhl D. Branching generalized quantifiers and natural language. In: Gårdenfors P, editor, Generalized quantifiers, Reidel;1987. New York: pp 269-298.
12. Kacprzyk J. Intelligent data analysis via linguistic data summaries: A fuzzy logic approach. In: Decker R, Gaul W, editors, Classification and information processing at the turn of the millenium, Barlin: Springer; 2000. pp 153-161.
13. Yager RR. A new approach to the summarization of data. Inform Sci 1982;28:69-86.
14. Bordogna G, Pasi G. A fuzzy information retrieval system handling users' preferences on document sections. In: DuboisH, Prade H,Yager RR, editors. Fuzzy information engineering New York: Wiley, 1997.
15. Dîaz-Hermida F, Losada DE, Bugarîn A, Barro S. A probabilistic quantifier fuzzification mechanism: the model and its evaluation for information retrieval. IEEE Trans Fuzzy Syst 2005;13(5):688-700.
16. Bosc P, Pivert O. Extending SQL retrieval features for the handling of flexible queries. In Dubois D, Prade H, Yager RR, editors. Fuzzy information engineering. New York: Wiley, 1997. pp 233-251.
17. Kacprzyk J, Ziólkowsi A. Database queries with fuzzy linguistic quantifiers. IEEE Trans Syst Man, and Cybern 1986;16(3):474-479.
18. Delgado M, Herrera F, Herrera-Viedma E, Martinez L. Combining numerical and linguistic information in group decision making. Inform Sci, 1998;107:177-194.
19. Herrera F, Verdegay JL. On group decision making under linguistic preferences and fuzzy linguistic quantifiers. In: Bouchon B, Yager RR, Zadeh LA, editors, Fuzzy logic and soft computing, Singapore: World Scientific; 1995. pp 173-180.
20. Barro S, Bugarîn A, Cariñena P, Dîaz-Hermida F. A framework for fuzzy quantification models analysis. IEEE Trans on Fuzzy Systems 2003;11:89-99.
21. Glöckner I. A framework for evaluating approaches to fuzzy quantification. TR99-03, Technische Facultät, Universität Bielefeld, Bielefeld, Germany; 1999.
22. Glöckner I, Fuzzy quantifiers in natural language: Semantics and computational models. Tönning, Germany, 2004. Der Andere Verlag.
23. Yager RR. Counting the number of classes in a fuzzy set. IEEE Trans Syst, Man, Cybern 1993;23(1):257-264.
24. Arnould T, Ralescu A. From "and" to "or." In. Bouchon-Meunier B, Valverde L, Yager RR, editors, IPMU '92 Advanced Methods in Artificial Intelligence, Volume 682 of Lecture Notes in Computer Science, Berlin: Springer, 1993. pp 116-128.
25. Yager RR. Connectives and quantifiers in fuzzy sets. Fuzzy Sets Syst 1991;40:39-75.
26. Yager RR. A general approach to rule aggregation in fuzzy logic control. J Appl Intell 1992;2:333-351.
27. Yager RR. Fuzzy quotient operators for fuzzy relational databases. In: Proc IFES 91, 1991. pp 289-296.
28. Glöckner I. DFS an axiomatic approach to fuzzy quantification. TR97-06, Technische Fakultät, Universität Bielefeld, Bielefeld, Germany; 1997.
29. Liu Y, Kerre EE. An overview of fuzzy quantifiers. (I). Interpretations. Fuzzy Sets Syst 1998;95:1-21.
30. Dîaz-Hermida F, Cariñena P, Bugarîn A, Barro S. Definition and classification of semifuzzy quantifiers for the evaluation of fuzzy quantified sentences. Int J Approx Reason 2003;34(1):49-88.
31. Thiele H. On T-quantifiers and S-quantifiers. In: The twenty-fourth International Symposium on Multiple-Valued Logic, Boston, MA, 1994. pp 264-269.
32. Mostowski A. On a generalization of quantifiers. Fundam Mathe 1957;44:12-36.
33. Mukaidono M. On some properties of fuzzy logic. Syst Comput Controls. 1975;6(2):36- 43.
34. Glöckner I. Fundamentals of fuzzy quantification: plausible models, constructive principles, and efficient implementation. TR2002-07, Technische Fakultät, Universität Bielefeld, Bielefeld, Germany; 2003.
35. Yager RR. Quantified propositions in a linguistic logic. Int. J Man-Machine Stud 1983;19:195-227.
36. Dubois D, Prade H. Fuzzy cardinality and the modelling of imprecise quantification. Fuzzy Sets Syst 1985;16:199-230.