Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SOFT WS-ALGEBRAS

  • Published : 2008.07.31
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Abstract

Molodtsov [8] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of subtraction algebras. The notion of soft WS-algebras, soft subalgebras and soft deductive systems are introduced, and their basic properties are derived.

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References

  1. J. C. Abbott, Sets, Lattices and Boolean Algebras, Allyn and Bacon, Boston 1969
  2. D. Chen, E. C. C. Tsang, D. S. Yeung, and X. Wang, The parametrization reduction of soft sets and its applications, Comput. Math. Appl. 49 (2005), 757-763 https://doi.org/10.1016/j.camwa.2004.10.036
  3. Y. B. Jun, Y. H. Kim, and K. J. Lee, Weak forms of subtraction algebras, Bull. Korean Math. Soc. 45 (2008), no. 3, 419-426 https://doi.org/10.4134/BKMS.2008.45.3.437
  4. Y. B. Jun, H. S. Kim, and E. H. Roh, Ideal theory of subtraction algebras, Sci. Math. Jpn. 61 (2005), no. 3, 459-464
  5. Y. B. Jun, C. H. Park, and E. H. Roh, Order systems, ideals and right fixed maps of subtraction algebras, Commun. Korean Math. Soc. 23 (2008), no. 1, 1-10 https://doi.org/10.4134/CKMS.2008.23.1.001
  6. P. K. Maji, R. Biswas, and A. R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003), 555-562 https://doi.org/10.1016/S0898-1221(03)00016-6
  7. P. K. Maji, A. R. Roy, and R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44 (2002), 1077-1083 https://doi.org/10.1016/S0898-1221(02)00216-X
  8. D. Molodtsov, Soft set theory - First results, Comput. Math. Appl. 37 (1999), 19-31 https://doi.org/10.1016/S0898-1221(99)00056-5
  9. L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353 https://doi.org/10.1016/S0019-9958(65)90241-X

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