Generalized Union and Intersection of Fuzzy Soft Sets

  IJMTT-book-cover
 
International Journal of Mathematical Trends and Technology (IJMTT)          
 
© 2011 by IJMTT Journal
Volume-2 Issue-2                           
Year of Publication : 2011
Authors : Chandana Goswami, Tridiv Jyoti Neog, Dusmanta Kumar Sut

MLA

Chandana Goswami, Tridiv Jyoti Neog, Dusmanta Kumar Sut"Generalized Union and Intersection of Fuzzy Soft Sets"International Journal of Mathematical Trends and Technology (IJMTT),V2(2):11-14.June 2011. Published by Seventh Sense Research Group.

Abstract
The generalization of the notion of union and intersection laid down by Zadeh in his pioneer work in 1965 was initiated by Chakrabarty. The necessity of such an attempt was also stated with practical examples. Maji initiated the notion of fuzzy soft set and introduced some properties regarding fuzzy soft union, intersection, complement of a fuzzy soft set, DeMorgan Laws etc. These results were further revised and improved by Ahmad and Kharal. They defined arbitrary fuzzy soft union and intersection and proved DeMorgan Inclusions and DeMorgan Laws in Fuzzy Soft Set Theory. In 2011, Neog and Sut studied further and put forward some more propositions on fuzzy soft set theory. In this paper, we have studied the notion of union and intersection of two fuzzy soft sets in two fuzzy soft classes and propose some related results. Our work is an attempt to generalize the notion of union and intersection of fuzzy soft sets.

References

[1] B. Ahmad and Athar Kharal, “On Fuzzy Soft Sets”, Advances in Fuzzy Systems, Volume 2009.
[2] P. K. Maji, R. Biswas and A.R. Roy, “Fuzzy Soft Sets”, Journal of Fuzzy Mathematics, Vol 9 , no.3,pp.-589-602,2001
[3] D.A. Molodstov, “Soft Set Theory - First Result”, Computers and Mathematics with Applications 37 (1999) 19-31
[4] Kankana Chakrabarty, Ranjit Biswas, Sudarshan Nanda, “ A note on fuzzy union and fuzzy intersection” , Fuzzy sets and Systems 105 (1999) 499 - 502
[5] R. Biswas, “On rough sets and fuzzy rough sets,” Bull. Polish. Acad. Sci. Math 42(4) (1994) 345 - 349.
[6] Kankana Chakrabarty, Ranjit Biswas, Sudarshan Nanda, “ Nearest ordinary set of a fuzzy set : a rough theoretic construction” , Bull. Polish. Acad. Sci. Math.
[7] Kankana Chakrabarty, Ranjit Biswas, Sudarshan Nanda, “ Union and intersection of fuzzy sets” , Bull. Pour Sous. Ens. Flous. Appl. (BUSEFAL)
[8] Tridiv Jyoti Neog, Dusmanta Kumar Sut, “On Union and Intersection of Fuzzy Soft Sets” Int.J. Comp. Tech. Appl., Vol 2 (5), 1160-1176
[9] Chandana Goswami, Dusmanta Kumar Sut, “ Union and Intersection of Fuzzy Soft Sets”, Indian Journal of Social Science and Sciences Vol 1, No 2, pp 243 – 246
[10] L.A. Zadeh, “Fuzzy Sets”, Information and Control, 8, pp. 338-353, 1965

Keywords
Soft Set, Fuzzy Soft Set, Union of Fuzzy Soft Sets, Intersection of Fuzzy Soft Sets.