Year 2019,
Volume: 9 Issue: 2, 257 - 266, 01.06.2019
Abstract
In this paper, the notion of mutant fuzzy sets that by adhering to the classical sense in any semigroups has been introduced and its some of structural properties have been studied. In addition to this, the concept of t-norm based mutation for fuzzy sets on any crisp set has been given, and some of results have been investigated.
Keywords
References
- Zadeh, L. A., (1965), Fuzzy sets, Inform. Control, 8, pp. 338–353.
- Rosenfeld, A., (1971), Fuzzy groups, J. Math. Anal. Appl., 35, pp. 512–517.
- Mullin, A. A., (1961), Properties of mutants, Bull. Amer. Math. Soc., 67, pp. 82.
- Mullin, A. A., (1962), On mutant sets, Bull. Math. Biol., 24, pp. 209–215.
- Mullin, A. A., (1962), Some theorems on the structure of mutant sets and their applications to group
- and ring theory, Notre Dame J. Form. Log., 3 (3), pp. 148–151.
- Iseki, K., (1962), On (m, n)−mutant sets in semigroups, Proc. Japan Acad., 38 (6), pp. 269–270.
- Iseki, K., (1962), On mutant sets in semigroup, Proc. Japan Acad., 38 (8), pp. 478–479.
- Kim, J. B., (1969), Mutants in semigroups, Czech. Math. Jour., 19, pp. 86–90.
- Mordeson, J. N., Malik, D.S. and Kuroki N., (2003), Fuzzy semigroups, Springer-Verlag, pp. 303.
- Mordeson, J. N., Bhutani, K. R. and Rosenfeld, A., (2005), Fuzzy Group Theory, Springer-Verlag, pp. 300.
- Howie, J. M., (1995), Fundamentals of Semigroup Theory, Oxford University Press Inc., pp. 364.
- Zimmermann, H. J., (1996), Fuzzy Set Theory and Its Applications 3rd Ed., Kluwer Academic Pub., pp. 435.
- Klement, E. P., Mesiar, R. and Pap, E., (2000), Triangular Norms, Springer, pp. 385.
- Bandemer, H. and Gottwald, S., (1995), Fuzzy Sets, Fuzzy Logic, Fuzzy Methods with Applications, Wiley and Sons Ltd., pp. 239.
- Liu, W. J., (1982), Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8, pp. 133– 139.
- Zahedi, M. M., (1991), A characterization of L-fuzzy prime ideals, Fuzzy Sets and Systems, 44, pp. 147–160.
Year 2019,
Volume: 9 Issue: 2, 257 - 266, 01.06.2019
Abstract
References
- Zadeh, L. A., (1965), Fuzzy sets, Inform. Control, 8, pp. 338–353.
- Rosenfeld, A., (1971), Fuzzy groups, J. Math. Anal. Appl., 35, pp. 512–517.
- Mullin, A. A., (1961), Properties of mutants, Bull. Amer. Math. Soc., 67, pp. 82.
- Mullin, A. A., (1962), On mutant sets, Bull. Math. Biol., 24, pp. 209–215.
- Mullin, A. A., (1962), Some theorems on the structure of mutant sets and their applications to group
- and ring theory, Notre Dame J. Form. Log., 3 (3), pp. 148–151.
- Iseki, K., (1962), On (m, n)−mutant sets in semigroups, Proc. Japan Acad., 38 (6), pp. 269–270.
- Iseki, K., (1962), On mutant sets in semigroup, Proc. Japan Acad., 38 (8), pp. 478–479.
- Kim, J. B., (1969), Mutants in semigroups, Czech. Math. Jour., 19, pp. 86–90.
- Mordeson, J. N., Malik, D.S. and Kuroki N., (2003), Fuzzy semigroups, Springer-Verlag, pp. 303.
- Mordeson, J. N., Bhutani, K. R. and Rosenfeld, A., (2005), Fuzzy Group Theory, Springer-Verlag, pp. 300.
- Howie, J. M., (1995), Fundamentals of Semigroup Theory, Oxford University Press Inc., pp. 364.
- Zimmermann, H. J., (1996), Fuzzy Set Theory and Its Applications 3rd Ed., Kluwer Academic Pub., pp. 435.
- Klement, E. P., Mesiar, R. and Pap, E., (2000), Triangular Norms, Springer, pp. 385.
- Bandemer, H. and Gottwald, S., (1995), Fuzzy Sets, Fuzzy Logic, Fuzzy Methods with Applications, Wiley and Sons Ltd., pp. 239.
- Liu, W. J., (1982), Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8, pp. 133– 139.
- Zahedi, M. M., (1991), A characterization of L-fuzzy prime ideals, Fuzzy Sets and Systems, 44, pp. 147–160.
There are 17 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Publication Date | June 1, 2019 |
| Published in Issue | Year 2019 Volume: 9 Issue: 2 |