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Filters of residuated lattices based on soft set theory

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Strong uni-soft filters and divisible uni-soft filters in residuated lattices are introduced, and several properties are investigated. Characterizations of a strong and divisible uni-soft filter are discussed. Conditions for a uni-soft filter to be divisible are established. Relations between a divisible uni-soft filter and a strong uni-soft filter are considered.

Abstract

Strong uni-soft filters and divisible uni-soft filters in residuated lattices are introduced, and several properties are investigated. Characterizations of a strong and divisible uni-soft filter are discussed. Conditions for a uni-soft filter to be divisible are established. Relations between a divisible uni-soft filter and a strong uni-soft filter are considered.

참고문헌 (14)

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  2. N. C¸ aˇgman, "Soft set theory and uni-int decision making", European J. Oper. Res, 207(2), pp.848~855 (2010)
  3. F. Esteva, "Monoidal t-norm based logic: towards a logic for left-continuous t-norms", Fuzzy Sets and Systems, 124(3), pp.271~288 (2001)
  4. P. H´ajek, "Metamathematics of Fuzzy Logic" (1998), Kluwer Academic Press
  5. Y. B. Jun, "Classes of int-soft filters in residuated lattices", The Scientific World J, 2014, pp.12~ (2014)
  6. Y. B. Jun, "Uni-soft filters and uni-soft G-filters in residuated lattices", J. Comput. Anal. Appl
  7. Z. M. Ma, "Characterizations and new subclasses of I-filters in residuated lattices", Fuzzy Sets and Systems, 247, pp.92~107 (2014)
  8. P. K. Maji, "Soft set theory", Comput. Math. Appl, 45(4-5), pp.555~562 (2003)
  9. D. Molodtsov, "Soft set theory – First results", Comput. Math. Appl, 37(4-5), pp.19~31 (1999)
  10. J. G. Shen, "On filters of residuated lattice", Chinese Quart. J. Math, 21(3), pp.443~447 (2006)
  11. E. Turunen, "BL-algebras of basic fuzzy logic", Mathware Soft Comput, 6(1), pp.49~61 (1999)
  12. E. Turunen, "Boolean deductive systems of BL-algebras", Arch. Math. Logic, 40(6), pp.467~473 (2001)
  13. X. H. Zhang, "IMTL(MV)-filters and fuzzy IMTL(MV)-filters of residuated lattices", J. Intell. Fuzzy Systems, 26(2), pp.589~596 (2014)
  14. Y. Q. Zhu, "On filter theory of residuated lattices", Inform. Sci, 180(19), pp.3614~3632 (2010)

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