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Year 2020, Volume: 12 Issue: 1, 8 - 17, 29.06.2020

Venkateswarlu Bollineni , Talasila Srılakshmı Yalamanchili Adı Narayana

Abstract

References

  • Acar, U., Koyuncu F., Tanay, B., {\em Soft sets and soft rings}, Comput. and Math. with Appl., \textbf{59}(2010), 3458--3463.
  • Aktas H., Cagman, N., {\em Soft sets and soft groups}, Infor. Sci., \textbf{177}(2007), 2726--2735.
  • Ghosh,J., Dinda, B., Samanta, T. K., {\em Fuzzy soft rings and fuzzy soft ideals}, Int. J. Proc. App. Sci. Tech., \textbf{2(2)}(2011), 66--74.
  • Good, R. A., Hughes, D. R., {\em Associated groups for a semigroup}, Bull. Amer. Math. Soc., \textbf{58}(1952), 624--625.
  • Feng, F., Jun, Y. B., Zhao, X., {\em Soft semirings}, Comput. and Math. with Appli., \textbf{56}(2008), 2621--2628.
  • Henriksen, M., {\em Ideals in semirings with commutative addition}, Amer. Math. Soc. Not., \textbf{5}(1958), 321.
  • Iseki, K., {\em Quasi-ideals in semirings without zero}, Proc. Japan Acad., \textbf{34}(1958), 79--84.
  • Iseki, K., {\em Ideal theory of semiring}, Proc. Japan Acad., \textbf{32}(1956), 554--559.
  • Iseki, K., {\em Ideal in semirings}, Proc. Japan Acad., \textbf{34}(1958), 29--31.
  • Jagatap, R. D., Pawar, Y.S., {\em Quasi-ideals and minimal quasi-ideals in $\Gamma-$ semirings}, Novi Sad J. Math., \textbf{39(2)}(2009), 79--87.
  • Kuroki, N., {\em On fuzzy semigroups}, Infor. Sci., \textbf{53(3)}(1991), 203--236.
  • Lajos, S., {\em On the bi-ideals in semigroups}, Proc. Japan Acad., \textbf{45}(1969), 710--712.
  • Lajos, S., Szasz, F. A., {\em On the bi-ideals in associative ring}, Proc. Japan Acad., \textbf{46}(1970), 505--507.
  • Liu, W. J., {\em Fuzzy invariant subgroups and fuzzy ideals}, Fuzzy sets and Systems, \textbf{8(2)}(1982), 133--139.
  • Maji, P. K., Biswas, R., Roy, A. R., {\em Fuzzy soft sets}, The J. of Fuzzy Math., \textbf{9(3)}(2001), 589--602.
  • Majumdar, P., Samanta, S.K., {\em Generalised fuzzy soft sets}, Comput. and Math. with Appl., \textbf{59}(2010), 1425--1432.
  • Mandal, D., {\em Fuzzy ideals and fuzzy interior ideals in ordered semirings}, Fuzzy info. and Engg., \textbf{6}(2014), 101--114.
  • Molodtsov, D., {Soft set theory-first results}, Comput. and Math. with Appl., \textbf{37}(1999), 19--31.
  • Murali Krishna Rao, M., {\em $T-$fuzzy ideals in ordered $\Gamma-$ semirings}, Anl. of Fuzzy Math. and Info., \textbf{13(2)}( 2017), 253--276.
  • Murali Krishna Rao, M., {\em Left bi-quasi ideals of semirings}, Bull. Int. Math. Virtual Inst., \textbf{8}(2018), 45--53 .
  • Murali Krishna Rao, M., {\em Bi-quasi-ideals and fuzzy bi-quasi-ideals of $\Gamma-$ semigroups}, Bull. Int. Math. Virtual Inst., \textbf{7(2)}(2017), 231--242.
  • Murali Krishna Rao, M., {\em Fuzzy left and right bi-quasi ideals of semirings}, Bull. Int. Math. Virtual Inst., \textbf{8(3)}(2018), 449--460.
  • Murali Krishna Rao, M., Venkateswarlu, B., Adi Naryana, Y., Bi-interior ideals of semiring, (communicated).
  • Murali Krishna Rao, M., {\em Fuzzy soft $\Gamma-$ semiring and fuzzy soft $k-$ideal over $\Gamma -$ semiring}, Anl. of Fuzzy Math. and Info., \textbf{9(2)}(2015), 12--25.
  • Rosenfeld, A., {\em Fuzzy groups}, J. Math. Anal. Appl., \textbf{35}(1971), 512--517.
  • Steinfeld, O., {\em Uher die quasi ideals}, Von halbgruppend Publ. Math., Debrecen, \textbf{4}(1956), 262--275.
  • Swamy, U. M., Swamy, K. L. N., {\em Fuzzy prime ideals of rings}, J. Math. Anal. Appl., \textbf{134}(1988), 94--103.
  • Vandiver, H. S., {\em Note on a simple type of algebra in which cancellation law of addition does not hold}, Bull. Amer. Math. Soc.(N.S.), \textbf{40}(1934), 914--920.
  • Venkateswarlu, B., T. Sri Lakshmi and Y. Adi Naryana, Fuzzy bi-interior ideals of semirings, (comminicated).
  • Zadeh, L. A., {\em Fuzzy sets}, Information and control, \textbf{8}(1965), 338--353.

Fuzzy Soft Bi-Interior Ideals Over Semirings

Year 2020, Volume: 12 Issue: 1, 8 - 17, 29.06.2020

Venkateswarlu Bollineni , Talasila Srılakshmı Yalamanchili Adı Narayana

Abstract

 In this paper, we introduce the notion of fuzzy soft bi-interior ideals over semirings and study some of their algebraical properties.                                                                                                                                                                                                                                                                                                                       

Keywords

Bi-interior ideal Fuzzy soft bi-interior ideal Semiring

References

  • Acar, U., Koyuncu F., Tanay, B., {\em Soft sets and soft rings}, Comput. and Math. with Appl., \textbf{59}(2010), 3458--3463.
  • Aktas H., Cagman, N., {\em Soft sets and soft groups}, Infor. Sci., \textbf{177}(2007), 2726--2735.
  • Ghosh,J., Dinda, B., Samanta, T. K., {\em Fuzzy soft rings and fuzzy soft ideals}, Int. J. Proc. App. Sci. Tech., \textbf{2(2)}(2011), 66--74.
  • Good, R. A., Hughes, D. R., {\em Associated groups for a semigroup}, Bull. Amer. Math. Soc., \textbf{58}(1952), 624--625.
  • Feng, F., Jun, Y. B., Zhao, X., {\em Soft semirings}, Comput. and Math. with Appli., \textbf{56}(2008), 2621--2628.
  • Henriksen, M., {\em Ideals in semirings with commutative addition}, Amer. Math. Soc. Not., \textbf{5}(1958), 321.
  • Iseki, K., {\em Quasi-ideals in semirings without zero}, Proc. Japan Acad., \textbf{34}(1958), 79--84.
  • Iseki, K., {\em Ideal theory of semiring}, Proc. Japan Acad., \textbf{32}(1956), 554--559.
  • Iseki, K., {\em Ideal in semirings}, Proc. Japan Acad., \textbf{34}(1958), 29--31.
  • Jagatap, R. D., Pawar, Y.S., {\em Quasi-ideals and minimal quasi-ideals in $\Gamma-$ semirings}, Novi Sad J. Math., \textbf{39(2)}(2009), 79--87.
  • Kuroki, N., {\em On fuzzy semigroups}, Infor. Sci., \textbf{53(3)}(1991), 203--236.
  • Lajos, S., {\em On the bi-ideals in semigroups}, Proc. Japan Acad., \textbf{45}(1969), 710--712.
  • Lajos, S., Szasz, F. A., {\em On the bi-ideals in associative ring}, Proc. Japan Acad., \textbf{46}(1970), 505--507.
  • Liu, W. J., {\em Fuzzy invariant subgroups and fuzzy ideals}, Fuzzy sets and Systems, \textbf{8(2)}(1982), 133--139.
  • Maji, P. K., Biswas, R., Roy, A. R., {\em Fuzzy soft sets}, The J. of Fuzzy Math., \textbf{9(3)}(2001), 589--602.
  • Majumdar, P., Samanta, S.K., {\em Generalised fuzzy soft sets}, Comput. and Math. with Appl., \textbf{59}(2010), 1425--1432.
  • Mandal, D., {\em Fuzzy ideals and fuzzy interior ideals in ordered semirings}, Fuzzy info. and Engg., \textbf{6}(2014), 101--114.
  • Molodtsov, D., {Soft set theory-first results}, Comput. and Math. with Appl., \textbf{37}(1999), 19--31.
  • Murali Krishna Rao, M., {\em $T-$fuzzy ideals in ordered $\Gamma-$ semirings}, Anl. of Fuzzy Math. and Info., \textbf{13(2)}( 2017), 253--276.
  • Murali Krishna Rao, M., {\em Left bi-quasi ideals of semirings}, Bull. Int. Math. Virtual Inst., \textbf{8}(2018), 45--53 .
  • Murali Krishna Rao, M., {\em Bi-quasi-ideals and fuzzy bi-quasi-ideals of $\Gamma-$ semigroups}, Bull. Int. Math. Virtual Inst., \textbf{7(2)}(2017), 231--242.
  • Murali Krishna Rao, M., {\em Fuzzy left and right bi-quasi ideals of semirings}, Bull. Int. Math. Virtual Inst., \textbf{8(3)}(2018), 449--460.
  • Murali Krishna Rao, M., Venkateswarlu, B., Adi Naryana, Y., Bi-interior ideals of semiring, (communicated).
  • Murali Krishna Rao, M., {\em Fuzzy soft $\Gamma-$ semiring and fuzzy soft $k-$ideal over $\Gamma -$ semiring}, Anl. of Fuzzy Math. and Info., \textbf{9(2)}(2015), 12--25.
  • Rosenfeld, A., {\em Fuzzy groups}, J. Math. Anal. Appl., \textbf{35}(1971), 512--517.
  • Steinfeld, O., {\em Uher die quasi ideals}, Von halbgruppend Publ. Math., Debrecen, \textbf{4}(1956), 262--275.
  • Swamy, U. M., Swamy, K. L. N., {\em Fuzzy prime ideals of rings}, J. Math. Anal. Appl., \textbf{134}(1988), 94--103.
  • Vandiver, H. S., {\em Note on a simple type of algebra in which cancellation law of addition does not hold}, Bull. Amer. Math. Soc.(N.S.), \textbf{40}(1934), 914--920.
  • Venkateswarlu, B., T. Sri Lakshmi and Y. Adi Naryana, Fuzzy bi-interior ideals of semirings, (comminicated).
  • Zadeh, L. A., {\em Fuzzy sets}, Information and control, \textbf{8}(1965), 338--353.
There are 30 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Venkateswarlu Bollineni 0000-0003-3669-350X

Talasila Srılakshmı This is me 0000-0002-1273-3709

Yalamanchili Adı Narayana This is me 0000-0002-8836-3732

Publication Date June 29, 2020
Published in Issue Year 2020 Volume: 12 Issue: 1

Cite

APA Bollineni, V., Srılakshmı, T., & Adı Narayana, Y. (2020). Fuzzy Soft Bi-Interior Ideals Over Semirings. Turkish Journal of Mathematics and Computer Science, 12(1), 8-17.
AMA Bollineni V, Srılakshmı T, Adı Narayana Y. Fuzzy Soft Bi-Interior Ideals Over Semirings. TJMCS. June 2020;12(1):8-17.
Chicago Bollineni, Venkateswarlu, Talasila Srılakshmı, and Yalamanchili Adı Narayana. “Fuzzy Soft Bi-Interior Ideals Over Semirings”. Turkish Journal of Mathematics and Computer Science 12, no. 1 (June 2020): 8-17.
EndNote Bollineni V, Srılakshmı T, Adı Narayana Y (June 1, 2020) Fuzzy Soft Bi-Interior Ideals Over Semirings. Turkish Journal of Mathematics and Computer Science 12 1 8–17.
IEEE V. Bollineni, T. Srılakshmı, and Y. Adı Narayana, “Fuzzy Soft Bi-Interior Ideals Over Semirings”, TJMCS, vol. 12, no. 1, pp. 8–17, 2020.
ISNAD Bollineni, Venkateswarlu et al. “Fuzzy Soft Bi-Interior Ideals Over Semirings”. Turkish Journal of Mathematics and Computer Science 12/1 (June 2020), 8-17.
JAMA Bollineni V, Srılakshmı T, Adı Narayana Y. Fuzzy Soft Bi-Interior Ideals Over Semirings. TJMCS. 2020;12:8–17.
MLA Bollineni, Venkateswarlu et al. “Fuzzy Soft Bi-Interior Ideals Over Semirings”. Turkish Journal of Mathematics and Computer Science, vol. 12, no. 1, 2020, pp. 8-17.
Vancouver Bollineni V, Srılakshmı T, Adı Narayana Y. Fuzzy Soft Bi-Interior Ideals Over Semirings. TJMCS. 2020;12(1):8-17.