CHARACTERIZATIONS OF h -HEMIREGULAR AND h -SEMISIMPLE HEMIRINGS BY INTERVAL VALUED ( , ) q -FUZZY h -IDEALS

T. Mahmood

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.

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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)


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