CHARACTERIZATIONS OF h -HEMIREGULAR AND h -SEMISIMPLE HEMIRINGS BY INTERVAL VALUED ( , ) q -FUZZY h -IDEALS
Abstract
In this paper we define interval valued ( , ) q -fuzzy h-subhemirings, interval valued ( , ) q -fuzzy interior h-ideals, interval valued ( , ) q -fuzzy prime h-ideals, interval valued ( , ) q -fuzzy semiprime h-ideals. We characterize hhemiregular and h-semisimple hemirings by the properties of these interval valued ( , ) q -fuzzy h-ideals. Keywords: Interval valued ( , ) q -fuzzy h-ideals, interval valued ( , ) q -fuzzy interior h-ideals, interval valued ( , ) q -fuzzy prime h-ideals, interval valued ( , ) q -fuzzy semiprime h-ideals, h-hemiregular, h-semisimple hemirings.References
A. W. Aho and J. D. Ullman, Introduction to
Automata Theory, Languages and Computation,
Addison Wesley, Reading, MA (1979).
J. Ahsan, K. Saifullah and M. F. Khan, Fuzzy Sets
Syst. 60 (1993) 309.
W. A. Dudek, M. Shabir and R. Anjum, Comput.
Math. Appl. 59 (2010) 3167.
W. A. Dudek, M. Shabir and M. Irfan Ali, Comput.
Math. Appl. 58 (2009) 310.
S. Ghosh, Inform. Sci. 90 (1996) 221.
K. Glazek, A Guide to Litrature On Semirings and
Their Applications in Mathematics and Information
Sciences: With Complete Bibliography, Kluwer
Acad. Publ. Nederland (2002).
J. S. Golan, Semirings and Their Applications,
Kluwer Acad. Publ. (1999).
U. Hebisch and H. J. Weinert, Semirings: Algebraic
Theory and Applications in the Computer Science,
World Scientific (1998).
M. Henriksen, Amer. Math. Soc. Notices 6 (1958)
K. Iizuka, Tohoku Math. J. 11 (1959) 409.
Y. B. Jun, M. A. Özürk and S. Z. Song, Inform. Sci.
(2004) 211.
V.N. Kolokoltsov and V.P. Maslov. em,
Idempotent Analysis and its applications,
Mathematics and its applications. Kluwer, 401
(1997).
D. R. La Torre, Publ. Math. Debrecen 12 (1965)
X. Ma and J. Zhan, J. Syst. Sci. Complexity 20
(2007) 470.
J. N. Mordeson and D. S. Malik, Fuzzy Automata
and Languages, Theory and Applications,
Computational Mathematics Series, Chapman and
Hall/CRC, Boca Raton (2002).
V. Murali, Inform. Sci. 158 (2004) 277.
H. T. Nguyen and E. A. Walker, A First Course in
Fuzzy Logic, Chapman and Hall/CRC, Boca Raton
(2005).
P. M Pu and Y. M. Liu, J. Math. Anal. Appl. 76
(1980) 571.
A. Rosenfeld, J. Math. Anal. Appl. 35 (1971) 512.
M. Shabir, Y. Nawaz and T. Mahmood,
Characterizations of Hemirings by
, q -
Fuzzy Ideals, Neural Computing and Applications
(2012) 21 (Suppl 1):S93–S103.
M. Shabir and T. Mahmood, Quasigroups and
Related Systems 19 (2011) 101.
M. Shabir and T. Mahmood, Characterizations of
h -hemiregular and h -semisimple Hemirings by Characterizations of h-hemiregular and h-semisimple Hemirings 27
Interval Valued Fuzzy
h -ideals, submitted &
accepted in World Applied Science Journal.
G. Sun, Y. Yin and Y. Li, Int. Math. Forum 5
(2010) 545.
H.S. Vandiver, Bull. Amer. Math. Soc. 40 (1934)
W. Wechler, The Concept of Fuzziness in
Automata and Language Theory, Akademic Verlog,
Berlin, (1978).
Y.Q. Yin, X. Huang, D. Xu and H. Li, Int. J. of
Fuzzy Systems 11 (2009) 116.
Y.Q. Yin and H. Li, Inform. Sci. 178 (2008) 3451.
L.A. Zadeh, Fuzzy Sets, Information and Control 8
(1965) 338.
L.A. Zadeh, Information and Control 18 (1975)
J. Zhan and W. A. Dudek, Inform. Sci. 177 (2007)
