Folding theory applied to BL-algebras

Young Jun; Jung Ko

Open Mathematics (2004)

  • Volume: 2, Issue: 4, page 584-592
  • ISSN: 2391-5455

Abstract

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The notion of n-fold grisly deductive systems is introduced. Some conditions for a deductive system to be an n-fold grisly deductive system are provided. Extension property for n-fold grisly deductive system is established.

How to cite

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Young Jun, and Jung Ko. "Folding theory applied to BL-algebras." Open Mathematics 2.4 (2004): 584-592. <http://eudml.org/doc/268777>.

@article{YoungJun2004,
abstract = {The notion of n-fold grisly deductive systems is introduced. Some conditions for a deductive system to be an n-fold grisly deductive system are provided. Extension property for n-fold grisly deductive system is established.},
author = {Young Jun, Jung Ko},
journal = {Open Mathematics},
keywords = {03G10; 03B52; 06B05},
language = {eng},
number = {4},
pages = {584-592},
title = {Folding theory applied to BL-algebras},
url = {http://eudml.org/doc/268777},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Young Jun
AU - Jung Ko
TI - Folding theory applied to BL-algebras
JO - Open Mathematics
PY - 2004
VL - 2
IS - 4
SP - 584
EP - 592
AB - The notion of n-fold grisly deductive systems is introduced. Some conditions for a deductive system to be an n-fold grisly deductive system are provided. Extension property for n-fold grisly deductive system is established.
LA - eng
KW - 03G10; 03B52; 06B05
UR - http://eudml.org/doc/268777
ER -

References

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  1. [1] L. Biacino and G. Gerla: “An extension principle for closure operators”, J. Math. Anal. Appl., Vol. 198, (1996), pp. 1–24. http://dx.doi.org/10.1006/jmaa.1996.0064 Zbl0855.54007
  2. [2] A. DiNola, G. Georgescu and L. Leustean. “Boolean products of BL-algebras”, J. Math. Appl., Vol. 251, (2000), pp. 106–131. http://dx.doi.org/10.1006/jmaa.2000.7024 
  3. [3] J.A. Goguen: “L-fuzzy sets”, J. Math. Appl., Vol. 18, (1967), pp. 145–174. http://dx.doi.org/10.1016/0022-247X(67)90189-8 
  4. [4] P. Hájek: Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998. 
  5. [5] Y.B. Jun and J.M. Ko: “Deductive systems of BL-algebras”, Bull. Korean Math. Soc., [submitted]. Zbl1333.03249
  6. [6] Y.B. Jun and J.M. Ko: “Grisly deductive systems of BL-algebras”, Bull. Korean Math. Soc., [submitted]. Zbl1076.03041
  7. [7] J.M. Ko and Y.C. Kim: “Some properties of BL-algebras”, J. Korea Fuzzy Logic and Intelligent Systems, Vol. 11(3), (2001), pp. 286–291. 
  8. [8] J.M. Ko and Y.C. Kim: “Closure operators on BL-algebras”, Comm. Korean Math. Soc., Vol. 19(2), (2004), pp. 219–232. Zbl1101.03316
  9. [9] E. Turunen: “Boolean deductive systems of BL-algebras”, Arch. Math. Logic, Vol. 40, (2001), pp. 467–473. http://dx.doi.org/10.1007/s001530100088 Zbl1030.03048
  10. [10] E. Turunen: Mathematics behind fuzzy logic, Springer-Verlag Co., Heidelberg, 1999. Zbl0940.03029
  11. [11] L.A. Zadeh: “From circuit theory to system theory”, Proc. Inst. Radio Eng., Vol. 50, (1962), pp.856–865. 
  12. [12] L.A. Zadeh: “Fuzzy sets”, Inform. and Control, Vol. 8, (1965) pp. 338–353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X Zbl0139.24606

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