| Title:
|
Validation sets in fuzzy logics (English) |
| Author:
|
Horčík, Rostislav |
| Author:
|
Navara, Mirko |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
[319]-326 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
validation set |
| Keyword:
|
$S$-fuzzy logic |
| Keyword:
|
$R$-fuzzy logic |
| MSC:
|
03B52 |
| idZBL:
|
Zbl 1265.03019 |
| idMR:
|
MR1944312 |
| . |
| Date available:
|
2009-09-24T19:46:14Z |
| Last updated:
|
2015-03-25 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135466 |
| . |
| Reference:
|
[1] Butnariu D., Klement E. P., Zafrany S.: On triangular norm-based propositional fuzzy logics.Fuzzy Sets and Systems 69 (1995), 241–255 Zbl 0844.03011, MR 1319229, 10.1016/0165-0114(94)00172-4 |
| Reference:
|
[2] Chang C. C.: Algebraic analysis of many valued logics.Trans. Amer. Math. Soc. 88 (1958), 467–490 Zbl 0084.00704, MR 0094302, 10.1090/S0002-9947-1958-0094302-9 |
| Reference:
|
[3] Cignoli R., D’Ottaviano I. M. L., Mundici D.: Algebraic Foundations of Many-valued Reasoning.(Trends in Logic 7.) Kluwer, Dordrecht 1999 Zbl 0937.06009, MR 1786097 |
| Reference:
|
[4] Dubois D., Prade H.: A review of fuzzy set aggregation connectives.Inform. Sci. 36 (1985), 85–121 Zbl 0582.03040, MR 0813766, 10.1016/0020-0255(85)90027-1 |
| Reference:
|
[5] Esteva F., Godo L., Hájek, P., Navara M.: Residuated fuzzy logics with an involutive negation.Arch. Math. Logic 39 (2000), 103–124 MR 1742377, 10.1007/s001530050006 |
| Reference:
|
[6] Gehrke M., Walker, C., Walker E. A.: DeMorgan systems on the unit interval.Internat. J. Intelligent Syst. 11 (1996), 733–750 Zbl 0865.04005, 10.1002/(SICI)1098-111X(199610)11:10<733::AID-INT2>3.0.CO;2-# |
| Reference:
|
[7] Gödel K.: Zum intuitionistischen Aussagenkalkül.Anz. Österreich. Akad. Wiss. Math.–Natur. Kl. 69 (1932), 65–66 |
| Reference:
|
[8] Gottwald S.: Mehrwertige Logik.Akademie–Verlag, Berlin 1989 Zbl 0714.03022, MR 1117450 |
| Reference:
|
[9] Gottwald S.: Fuzzy Sets and Fuzzy Logic.Foundations of Application – from a Mathematical Point of View. Vieweg, Braunschweig – Wiesbaden 1993 Zbl 1088.03024, MR 1218623 |
| Reference:
|
[10] Hájek P.: Metamathematics of Fuzzy Logic.(Trends in Logic 4.) Kluwer, Dordrecht 1998 Zbl 1007.03022, MR 1900263 |
| Reference:
|
[11] Hájek P., Godo, L., Esteva F.: A complete many-valued logic with product-conjunction.Arch. Math. Logic 35 (1996), 191–208 Zbl 0848.03005, MR 1385789, 10.1007/BF01268618 |
| Reference:
|
[12] Hekrdla J., Klement, E.š P., Navara M.: Two approaches to fuzzy propositional logics.Multiple–valued Logic, accepted Zbl 1043.03017 |
| Reference:
|
[13] Klement E. P., Mesiar, R., Pap E.: Triangular Norms.(Trends in Logic 8.) Kluwer, Dordrecht 2000 Zbl 1087.20041, MR 1790096 |
| Reference:
|
[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 Zbl 0947.03035, MR 1796598 |
| Reference:
|
[15] Klement E. P., Navara M.: A survey on different triangular norm-based fuzzy logics.Fuzzy Sets and Systems 101 (1999), 241–251 Zbl 0945.03032, MR 1676917 |
| Reference:
|
[16] Ling C. M.: Representation of associative functions.Publ. Math. Debrecen 12 (1965), 189–212 MR 0190575 |
| Reference:
|
[17] Łukasiewicz J.: Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls.Comptes Rendus Séances Société des Sciences et Lettres Varsovie cl. III 23 (1930), 51–77 |
| Reference:
|
[18] Navara M.: Satisfiability in fuzzy logics.Neural Network World 10 (2000), 845–858 |
| Reference:
|
[19] Navara M.: Product Logic is Not Compact.Research Report No. CTU–CMP–2001–09, Center for Machine Perception, Czech Technical University, Prague 2001 |
| Reference:
|
[20] Nguyen H. T., Walker E.: A First Course in Fuzzy Logic.CRC Press, Boca Raton 1997 Zbl 1083.03031, MR 1404930 |
| Reference:
|
[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 |
| Reference:
|
[22] Pedrycz W.: Fuzzy relational equations with generalized connectives and their applications.Fuzzy Sets and Systems 10 (1983), 185–201 Zbl 0525.04004, MR 0705207 |
| Reference:
|
[23] Schweizer B., Sklar A.: Probabilistic Metric Spaces.North–Holland, Amsterdam 1983 Zbl 0546.60010, MR 0790314 |
| Reference:
|
[24] Zadeh L. A.: Fuzzy sets.Inform. and Control 8 (1965), 338–353 Zbl 0139.24606, MR 0219427, 10.1016/S0019-9958(65)90241-X |
| . |
