Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ε-FUZZY CONGRUENCES ON SEMIGROUPS

  • Published : 2008.10.31
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Abstract

We define an $\epsilon$-fuzzy congruence, which is a weakened fuzzy congruence, find the $\epsilon$-fuzzy congruence generated by the union of two $\epsilon$-fuzzy congruences on a semigroup, and characterize the $\epsilon$-fuzzy congruences generated by fuzzy relations on semigroups. We also show that the collection of all $\epsilon$-fuzzy congruences on a semigroup is a complete lattice and that the collection of $\epsilon$-fuzzy congruences under some conditions is a modular lattice.

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References

  1. J. A. Goguen, L-fuzzy sets, J. Math. Anal. Appl. 18 (1967), 145-174 https://doi.org/10.1016/0022-247X(67)90189-8
  2. K. C. Gupta and R. K. Gupta, Fuzzy equivalence relation redefined, Fuzzy Sets and Systems 79 (1996), 227-233 https://doi.org/10.1016/0165-0114(95)00155-7
  3. V. Murali, Fuzzy equivalence relation, Fuzzy Sets and Systems 30 (1989), 155-163 https://doi.org/10.1016/0165-0114(89)90077-8
  4. C. Nemitz, Fuzzy relations and fuzzy function, Fuzzy Sets and Systems 19 (1986), 177-191 https://doi.org/10.1016/0165-0114(86)90036-9
  5. M. Samhan, Fuzzy congruences on semigroups, Inform. Sci. 74 (1993), 165-175 https://doi.org/10.1016/0020-0255(93)90132-6
  6. E. Sanchez, Resolution of composite fuzzy relation equation, Inform. and Control 30 (1976), 38-48 https://doi.org/10.1016/S0019-9958(76)90446-0
  7. R. T. Yeh, Toward an algebraic theory of fuzzy relational systems, Proc. Int. Congr. Cybern. (1973), 205-223
  8. L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353 https://doi.org/10.1016/S0019-9958(65)90241-X

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