International Journal of Intelligent Systems and Applications(IJISA)
ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)
Published By: MECS Press
IJISA Vol.4, No.11, Oct. 2012
An Introduction to the Theory of Imprecise Soft Sets
Full Text (PDF, 470KB), PP.75-83
This paper aims to introduce the theory of imprecise soft sets which is a hybrid model of soft sets and imprecise sets. It has been established that two independent laws of randomness are necessary and sufficient to define a law of fuzziness. Further, in case of fuzzy sets, the set theoretic axioms of exclusion and contradiction are not satisfied. Accordingly, the theory of imprecise sets has been developed where these mistakes arising in the literature of fuzzy sets are absent. Our work is an endeavor to combine imprecise sets with soft sets resulting in imprecise soft sets. We have put forward a matrix representation of imprecise soft sets. Finally we have studied the notion of similarity of two imprecise soft sets and put forward an application of similarity in a decision problem.
Cite This Paper
Tridiv Jyoti Neog, Dusmanta Kumar Sut,"An Introduction to the Theory of Imprecise Soft Sets", International Journal of Intelligent Systems and Applications(IJISA), vol.4, no.11, pp.75-83, 2012. DOI: 10.5815/ijisa.2012.11.09
H. K. Baruah, “The Theory of Fuzzy Sets: Beliefs and Realities”, International Journal of Energy, Information and Communications, Vol. 2, Issue 2, pp. 1-22, May 2011.
H. K. Baruah, “An Introduction to The Theory of Imprecise Sets: The Mathematics of Partial Presence”, Journal of Mathematical and Computational Sciences, Vol. 2, No. 2, pp. 110-124, 2012.
D.A. Molodtsov, “Soft Set theory –First Result”, Computer and Mathematics with Applications 37 (1999) 19-31.
P. K. Maji and A.R. Roy, “Soft Set Theory”, Computers and Mathematics with Applications 45 (2003) 555 – 562.
T.J. Neog and D. K. Sut, “ A New Approach To The Theory of Soft Sets” , International Journal of Computer Applications, Vol 32, No 2,October 2011, pp 1-6.
P.K.Maji, R.Biswas and A.R.Roy , “Fuzzy soft Sets”, Journal of Fuzzy Mathematics, Vol 9 , no.3, pp.-589-602, 2001.
B. Ahmad and A. Kharal, “On Fuzzy Soft Sets”, Advances in Fuzzy Systems, Volume 2009.
T.J. Neog, D. K. Sut, “ On Fuzzy Soft Complement And Related Properties” International Journal of Energy, Information and Communications, Volume 3, Issue 1, February-2012, pp. 23-34 .
T.J. Neog, D. K. Sut, “Theoty of Fuzzy Soft Sets from a new perspective”, International Journal of Latest Trends in computing, Vol2, No 3, September 2011, pp. 439-450.
H. K. Baruah, “Towards Forming A Field of Fuzzy Sets”, International Journal of Energy, Information and Communications, Vol. 2, Issue 1, pp. 16-20, February 2011.
H. K. Baruah, “Theory of Fuzzy Sets: The Case of Subnormality”, International Journal of Energy, Information and Communications, Vol. 2, Issue 3, pp. 1-8, August 2011.
H. K. Baruah, “In search of the root of fuzziness: The measure theoretic meaning of partial presence”, Annals of Fuzzy Mathematics and Informatics, 2011.