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Some Properties of Interval-Valued Intuitionistic Anti Fuzzy Lie Primary Ideal


Affiliations
1 Department of Mathematics, Government Arts College, Paramakudi – 623 707, Tamil Nadu, India
2 Ramanujan Research Centre, PG and Research Department of Mathematics, Government Arts College (Autonomous), Kumbakonam - 612 001, Tamil Nadu, India
 

In this paper, the theory of fuzzy semiprimary ideal [16] is extended by introducing intuitionistic anti fuzzy primary ideals as well as intuitionistic anti fuzzy semiprimary ideals in rings. Similarly, Interval-Valued Intuitionistic Anti Fuzzy Lie Primary Ideals (IVIAFLPI) is defined. Various properties of IVIAFLPI are discussed. Finally, Interval-Valued Intuitionistic Fuzzy Lie Semiprimary Ideals (IVIAFLSPI) is established.

Keywords

Intuitionistic Fuzzy Set, Intuitionistic Anti Fuzzy Ideal, Intuitionistic Anti Fuzzy Primary Ideal, Intuitionistic Anti Fuzzy Semi-Primary Ideal, Interval-Valued Intuitionistic Anti Fuzzy Lie Primary Ideals.
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  • Atanassov K. T., “Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, Vol. 20(1), p. 87–96, 1986.

  • Atanassov K., “Operators over interval-valued intuitionistic fuzzy sets”, Fuzzy Sets and Systems, Vol. 64(2), p. 159–174, 1994.

  • Chakrabarty K., Biswas R., Nanda S., “A note on union and intersection of intuitionistic fuzzy sets”, Notes on Intuitionistic Fuzzy Sets, Vol. 3(4), 1997.

  • Deschrijver G., “Arithmetic operators in interval-valued fuzzy theory”, Information Sciences, Vol. 177, p. 2906–2924, 2007.

  • Humphreys J. E., Introduction to lie algebras and representation theory, springer, New York.

  • Qin K., Qiao Q., Chen C., “Some properties of fuzzy Lie algebras”. The Journal of Fuzzy Mathematics, Vol. 9(4), p. 985–989, 2001.

  • Akram M., Dudek W. A., “Interval-valued intuitionistic fuzzy Lie ideals of Lie algebras”, World Applied Sciences Journal, Vol. 7, p. 812–819, 2009.

  • Bhowmik M., Pal M., “Generalized interval-valued intuitionistic fuzzy sets”, International Journal Fuzzy Mathematics, Vol. 18(2), p. 357–371, 2010.

  • Palanivelrajan M., Nandakumar S., “Some properties of intuitionistic fuzzy primary and semiprimary ideals”, Notes on Intuitionistic Fuzzy Sets, Vol. 18(3), p. 68–74, 2012.

  • Sharma P. K., “On intuitionistic Anti-fuzzy ideal and Quotient ring, Global Research publications”, Vol. 4(2), p. 109–119, 2012.

  • Rajesh K., “Fuzzy semiprimary ideals of rings”, Fuzzy Sets and Systems, Vol. 42, p. 263–272, 1991.

  • Zadeh L. A., “Fuzzy sets”, Information and Control, Vol. 8, p. 338–353, 1965.

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  • Some Properties of Interval-Valued Intuitionistic Anti Fuzzy Lie Primary Ideal

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Authors

M. Palanivelrajan
Department of Mathematics, Government Arts College, Paramakudi – 623 707, Tamil Nadu, India
K. Gunasekaran
Ramanujan Research Centre, PG and Research Department of Mathematics, Government Arts College (Autonomous), Kumbakonam - 612 001, Tamil Nadu, India
E. Adilakshmi
Ramanujan Research Centre, PG and Research Department of Mathematics, Government Arts College (Autonomous), Kumbakonam - 612 001, Tamil Nadu, India

Abstract


In this paper, the theory of fuzzy semiprimary ideal [16] is extended by introducing intuitionistic anti fuzzy primary ideals as well as intuitionistic anti fuzzy semiprimary ideals in rings. Similarly, Interval-Valued Intuitionistic Anti Fuzzy Lie Primary Ideals (IVIAFLPI) is defined. Various properties of IVIAFLPI are discussed. Finally, Interval-Valued Intuitionistic Fuzzy Lie Semiprimary Ideals (IVIAFLSPI) is established.

Keywords


Intuitionistic Fuzzy Set, Intuitionistic Anti Fuzzy Ideal, Intuitionistic Anti Fuzzy Primary Ideal, Intuitionistic Anti Fuzzy Semi-Primary Ideal, Interval-Valued Intuitionistic Anti Fuzzy Lie Primary Ideals.

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DOI: https://doi.org/10.15613/sijrs%2F2015%2Fv2i2%2F114280