Validation sets in fuzzy logics

Rostislav Horčík; Mirko Navara

Kybernetika (2002)

  • Volume: 38, Issue: 3, page [319]-326
  • ISSN: 0023-5954

Abstract

top
The validation set of a formula in a fuzzy logic is the set of all truth values which this formula may achieve. We summarize characterizations of validation sets of S -fuzzy logics and extend them to the case of R -fuzzy logics.

How to cite

top

Horčík, Rostislav, and Navara, Mirko. "Validation sets in fuzzy logics." Kybernetika 38.3 (2002): [319]-326. <http://eudml.org/doc/33585>.

@article{Horčík2002,
abstract = {The validation set of a formula in a fuzzy logic is the set of all truth values which this formula may achieve. We summarize characterizations of validation sets of $S$-fuzzy logics and extend them to the case of $R$-fuzzy logics.},
author = {Horčík, Rostislav, Navara, Mirko},
journal = {Kybernetika},
keywords = {validation set; $S$-fuzzy logic; $R$-fuzzy logic; validation set; -fuzzy logic; -fuzzy logic},
language = {eng},
number = {3},
pages = {[319]-326},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Validation sets in fuzzy logics},
url = {http://eudml.org/doc/33585},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Horčík, Rostislav
AU - Navara, Mirko
TI - Validation sets in fuzzy logics
JO - Kybernetika
PY - 2002
PB - Institute of Information Theory and Automation AS CR
VL - 38
IS - 3
SP - [319]
EP - 326
AB - The validation set of a formula in a fuzzy logic is the set of all truth values which this formula may achieve. We summarize characterizations of validation sets of $S$-fuzzy logics and extend them to the case of $R$-fuzzy logics.
LA - eng
KW - validation set; $S$-fuzzy logic; $R$-fuzzy logic; validation set; -fuzzy logic; -fuzzy logic
UR - http://eudml.org/doc/33585
ER -

References

top
  1. Butnariu D., Klement E. P., Zafrany S., 10.1016/0165-0114(94)00172-4, Fuzzy Sets and Systems 69 (1995), 241–255 (1995) Zbl0844.03011MR1319229DOI10.1016/0165-0114(94)00172-4
  2. Chang C. C., 10.1090/S0002-9947-1958-0094302-9, Trans. Amer. Math. Soc. 88 (1958), 467–490 (1958) Zbl0084.00704MR0094302DOI10.1090/S0002-9947-1958-0094302-9
  3. Cignoli R., D’Ottaviano I. M. L., Mundici D., Algebraic Foundations of Many-valued Reasoning, (Trends in Logic 7.) Kluwer, Dordrecht 1999 Zbl0937.06009MR1786097
  4. Dubois D., Prade H., 10.1016/0020-0255(85)90027-1, Inform. Sci. 36 (1985), 85–121 (1985) Zbl0582.03040MR0813766DOI10.1016/0020-0255(85)90027-1
  5. Esteva F., Godo L., Hájek, P., Navara M., 10.1007/s001530050006, Arch. Math. Logic 39 (2000), 103–124 MR1742377DOI10.1007/s001530050006
  6. Gehrke M., Walker, C., Walker E. A., 10.1002/(SICI)1098-111X(199610)11:10<733::AID-INT2>3.0.CO;2-#, Internat. J. Intelligent Syst. 11 (1996), 733–750 (1996) Zbl0865.04005DOI10.1002/(SICI)1098-111X(199610)11:10<733::AID-INT2>3.0.CO;2-#
  7. Gödel K., Zum intuitionistischen Aussagenkalkül, Anz. Österreich. Akad. Wiss. Math.–Natur. Kl. 69 (1932), 65–66 (1932) 
  8. Gottwald S., Mehrwertige Logik, Akademie–Verlag, Berlin 1989 Zbl0714.03022MR1117450
  9. Gottwald S., Fuzzy Sets and Fuzzy Logic, Foundations of Application – from a Mathematical Point of View. Vieweg, Braunschweig – Wiesbaden 1993 Zbl1088.03024MR1218623
  10. Hájek P., Metamathematics of Fuzzy Logic, (Trends in Logic 4.) Kluwer, Dordrecht 1998 Zbl1007.03022MR1900263
  11. Hájek P., Godo, L., Esteva F., 10.1007/BF01268618, Arch. Math. Logic 35 (1996), 191–208 (1996) Zbl0848.03005MR1385789DOI10.1007/BF01268618
  12. Hekrdla J., Klement, E.š P., Navara M., Two approaches to fuzzy propositional logics, Multiple–valued Logic, accepted Zbl1043.03017
  13. Klement E. P., Mesiar, R., Pap E., Triangular Norms, (Trends in Logic 8.) Kluwer, Dordrecht 2000 Zbl1087.20041MR1790096
  14. Klement E. P., Navara M., Propositional fuzzy logics based on Frank t-norms: A comparison, In: Fuzzy Sets, Logics and Reasoning about Logics (D. Dubois, E. P. Klement and H. Prade, eds., Applied Logic Series 15), Kluwer, Dordrecht 1999, pp. 17–38 (1999) Zbl0947.03035MR1796598
  15. Klement E. P., Navara M., A survey on different triangular norm-based fuzzy logics, Fuzzy Sets and Systems 101 (1999), 241–251 (1999) Zbl0945.03032MR1676917
  16. Ling C. M., Representation of associative functions, Publ. Math. Debrecen 12 (1965), 189–212 (1965) MR0190575
  17. Łukasiewicz J., Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls, Comptes Rendus Séances Société des Sciences et Lettres Varsovie cl. III 23 (1930), 51–77 (1930) 
  18. Navara M., Satisfiability in fuzzy logics, Neural Network World 10 (2000), 845–858 
  19. Navara M., Product Logic is Not Compact, Research Report No. CTU–CMP–2001–09, Center for Machine Perception, Czech Technical University, Prague 2001 
  20. Nguyen H. T., Walker E., A First Course in Fuzzy Logic, CRC Press, Boca Raton 1997 Zbl1083.03031MR1404930
  21. Novák V., On the syntactico-semantical completeness of first-order fuzzy logic, Part I – Syntactical aspects; Part II – Main results. Kybernetika 26 (1990), 47–66, 134–154 (1990) 
  22. Pedrycz W., Fuzzy relational equations with generalized connectives and their applications, Fuzzy Sets and Systems 10 (1983), 185–201 (1983) Zbl0525.04004MR0705207
  23. Schweizer B., Sklar A., Probabilistic Metric Spaces, North–Holland, Amsterdam 1983 Zbl0546.60010MR0790314
  24. Zadeh L. A., 10.1016/S0019-9958(65)90241-X, Inform. and Control 8 (1965), 338–353 (1965) Zbl0139.24606MR0219427DOI10.1016/S0019-9958(65)90241-X

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.