Soft set

From Wikipedia, the free encyclopedia
Jump to: navigation, search

Soft set theory is a generalization of fuzzy set theory, that was proposed by Molodtsov in 1999 to deal with uncertainty in a non-parametric manner.[1] Mathematically, a soft set, over a universal set X and set of parameters E is a pair (fA) where f is a function and A is a set such that f(e) is a subset of the universe X, where e is element of the set A. For each e the set f(e) is called the value set of e in (f, A).

One of the most important step for the new Theory of Soft Sets was to define mappings on soft sets, this was achieved in 2009 by mathematician Athar Kharal, though the results were published in 2011.[2] Soft sets have also been applied to the problem of medical diagnosis for use in medical expert systems. Fuzzy soft sets have also been introduced. Mappings on fuzzy soft sets were defined and studied in the ground breaking work of Kharal and Ahmad.[3]


  1. ^ Molodtsov, D. A. (1999). "Soft set theory—First results". Computers & Mathematics With Applications 37 (4): 19–31. doi:10.1016/S0898-1221(99)00056-5. 
  2. ^ Kharal, Athar; B. Ahmad (September 2011). "Mappings on Soft Classes". New Mathematics and Natural Computation 7 (3). doi:10.1142/S1793005711002025. 
  3. ^ Kharal, Athar; B. Ahmad (2009). "Mappings on Fuzzy Soft Classes". Advances in Fuzzy Systems 2009. doi:10.1155/2009/407890. 


  • Molodtsov D. A. A theory of soft sets. Moscow: Editorial URSS, 2004.
  • Matsievsky S. V. Sets, multisets, fuzzy and soft sets without universe. Vestnik IKSUR, 2007, N. 10, pp. 44–52.
  • Ahmad, B., Kharal, A.On Fuzzy Soft Sets. Advances in Fuzzy Systems Volume 2009 (2009), Article ID 586507, 6 pages doi:10.1155/2009/586507.