International Journal of Innovative Research in Science, Engineering and Technology

International Journal of Innovative Research in Science, Engineering and Technology

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Fuzzy Soft La-Semigroups – A New Approach

S.Saranya1, Dr.A.Kalaichelvi2
  1. Research Scholar, Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore, Tamilnadu, India
  2. Associate Professor, Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore, Tamilnadu, India
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Abstract

Soft set theory is one of the recent topics gaining significance in finding rational and logical solutions to various real life problems which involve uncertainty, impreciseness and vagueness. In this paper the concept of fuzzy soft LA-semigroupsare introduced and some basic properties are studied.

Keywords
Fuzzy LA-semigroup, Fuzzy soft LA-semigroup, Fuzzy soft ideal

INTRODUCTION
Uncertainty is present in almost every sphere of our daily life. Traditional Mathematical tools are not sufficient to handle all practical problems in fields such as Medical Science, Social Science, Engineering, Economics etc. Zadeh[15], in 1965 was the first to come up with his remarkable theory of fuzzy sets for dealing these types of uncertainties. In 1999, Molodsov[9] initiated the theory of soft sets as a new mathematical tool for dealing uncertainty. Maji et al [8] initiated the concept of fuzzy soft sets. The algebraic structures of set theories dealing with uncertainties have been studied by many mathematicians. Rosenfeld [14] proposed the concept of fuzzy groups. Aktas and cagman [1] introduced the notion of soft groups. Aygunoglu and Aygun [4] introduced the concept of fuzzy soft groups. Studies of soft semigroups are carried out by several Researchers. In this paper the concept of fuzzy soft LA-semigroup is introduced and some basic properties are studied.

RELATED WORK
In 1972, Kazim and Naseerdin[6] introduced LA-semigroups and studied their properties. The notion of Soft semigroups are introduced by Ali and Shabir [3] in 2009. Fuzzy soft semigroups are introduced by Munazza Naz et al., [11] in 2013. In 2010, Muhammad Aslam, Muhammad shabir, Asif mehmood[10] introduced soft LA-semigroups and established some important theorems.

PRELIMINARIES
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CONCLUSION
The algebraic structure of set theories deal with uncertainties have been studied by many mathematicians. In this paper the concept of fuzzy soft LA-semigroup is introduced and some basic properties are studied.

References
  1. Aktas, H., Cagman, N., “Soft sets and soft groups”, Inform.Sci, doi:10.1016/j.ins.2006.12.008, Vol.177, pp.2726-2735, 2007.

  2. Ali, M. I.,Feng, F.,Liu, X. Y.,Min, W.K., and Shabir, M., “On some new operations in soft set theory”, Comput. Math. Appl., Vol.57, pp:1547-1553, 2009.

  3. Ali, M. I., and Shabir, M. “Soft ideals and generalized fuzzy ideals in semigroups”, New Math. Nat. Comp, Vol.5, pp. 599-615, 2009.

  4. Aygunoglu, A., and Aygun, H., “Introduction to Fuzzy Soft Groups”, Comput.Math.Appl, Vol.58, pp.1279-1286, 2009.

  5. Cheng-Fu Yang, “Fuzzy soft semigroups and fuzzy soft ideals”, Comput. Math.Appl. Vol.61, pp.255-561, 2011.

  6. Kazim, M. A.,Naseerudin, M., “On almost semigroup”, The Alig.Bull.Math, Vol.2, pp.1-7,1972.

  7. Kuroki, N., “On fuzzy semigroups”, Information Sciences, Vol.53, pp.203-236, 1991.

  8. Maji, P. K.,Biswas, R., and Roy, R., “Fuzzy soft sets”, The J. Fuzzy Math., Vol.9, pp.589-602, 2001,

  9. Molodtsov, D.,“Soft set theory first results”, Comput. Math.Appl, Vol.37, pp.19-31, 1999.

  10. Muhammad Aslam., Muhammad Shabir., AsifMehmood., “Some studies in soft LA-semigroups”, Journal of Advanced research in puremathematics, Vol.3, Issue.5, pp.128-150,2011.

  11. MunazzaNaz., Muhammad Shabir., and Muhammad Ifran Ali., “On Fuzzy soft semigroups”, World Applied Sciences Journal, Vol.22, pp.62- 83, 2013.

  12. Mushtaq, Q.,Kamran, M. S., “On LA-semigroup with weak associative law”.sci.khy., Vol.2, pp.69-71, 1989.

  13. Mushtaq, Q.,Yusuf, S. M., “On LA-semigroups”, The Alig.Bull.Math, Vol.8, pp.65-70, 1978.

  14. Rosenfeld, A., “Fuzzy Groups”, J.Math.Anal.Appl.,Vol.35, pp.512-517.

  15. Zadeh, L. A., “Fuzzy sets” Information and Control, Vol.8, pp.338-353,1965.