Abstract
In this article, we introduced the notions fuzzy soft subalgebras and fuzzy soft ideal of subtraction algebras. We showed that fuzzy soft image and fuzzy soft inverse image of fuzzy soft ideal are both fuzzy soft ideal under certain conditions. We have studied their related properties in details.
Similar content being viewed by others
References
Abbott JC (1969) Sets, lattices and Boolean algebra. Allyn and Bacon, Boston
Ahmad B, Athar K (2009) Mappings on fuzzy soft classes. In: Advances in fuzzy systems, pp 1–6
Aygünoğlu A, Aygün H (2009) Introduction to fuzzy soft groups. Comput Math Appl 58:1279–1286
Çeven Y, Öztürk MA (2009) Some results on subtraction algebras. Hacettepe J Math Stat 38:299–304
Jun YB, Lee KJ, Park CH (2010) Fuzzy soft set theory applied to BCK/BCI-algebras. Comput Math Appl 59:3180–3192
Jun YB, Kim HS, Roh EH (2005) Ideal theory of subtraction algebras. Sci Math Jpn 61:459–464
Jun YB, Kim HS (2007) On ideals in subtraction algebras. Sci Math Jpn 65:129–134
Molodtsov D (1999) Soft set theory-first results. Comput Math Appl 37:19–31
Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44:1077–1083
Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45:555–562
Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9:589–602
Lee KJ, Park CH (2007) Some questions on fuzzifications of ideals in subtraction algebras. Commun Korean Math Soc 22:359–363
Schein BM (1992) Difference semigroups. Commun Algebra 20:2153–2169
Yang C (2011) Fuzzy soft semigroups and fuzzy soft ideals. Comput Math Appl 61:255–261
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Zelinka B (1995) Subtraction semigroup. Math Bohemica 120:445–447
Acknowledgments
The authors would like to express their thanks to the Editor in Chief Prof. John MacIntyre and referees for their comments and suggestions, which improved the paper. The first author was supported by Ministry of Higher Education, Sultanate of Oman.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Prince Williams, D.R., Borumand Saeid, A. Fuzzy soft ideals in subtraction algebras. Neural Comput & Applic 21 (Suppl 1), 159–169 (2012). https://doi.org/10.1007/s00521-011-0753-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-011-0753-9