×

Fuzzy Lie ideals and fuzzy Lie subalgebras. (English) Zbl 0922.17018

Summary: The authors have tried to apply the concepts of fuzzy sets to Lie algebra, to define some concepts related to fuzzy sets and to discuss their properties and the relations among them.

MSC:

17B99 Lie algebras and Lie superalgebras
03E72 Theory of fuzzy sets, etc.
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Das, P. S., Fuzzy groups and level subgroups, J. Math. Anal. Appl., 84, 264-269 (1981) · Zbl 0476.20002
[2] Dixit, V. N.; Kumar, R.; Ajmal, N., Level subgroups and union of fuzzy subgroups, Fuzzy Sets and Systems, 37, 359-371 (1990) · Zbl 0728.20061
[3] Dixit, V. N.; Kumar, R.; Ajmal, N., Fuzzy ideals and fuzzy prime ideals of a ring, Fuzzy Sets and Systems, 44, 127-138 (1991) · Zbl 0772.16002
[4] Dixit, V. N.; Kumar, R.; Ajmal, N., On fuzzy rings, Fuzzy Sets and Systems, 49, 205-213 (1992) · Zbl 0771.13012
[5] Humphreys, J. E., Introduction to Lie Algebras and Representation Theory (1972), Springer: Springer New York · Zbl 0254.17004
[6] Jacobson, N., Lie Algebras (1962), Wiley: Wiley New York · JFM 61.1044.02
[7] Katsaras, A. K.; Liu, D. B., Fuzzy vector spaces and fuzzy topological vector spaces, J. Math. Anal. Appl., 58, 135-146 (1977) · Zbl 0358.46011
[8] Kumar, R., Fuzzy irreducible ideals in rings, Fuzzy Sets and Systems, 42, 369-379 (1991) · Zbl 0745.16002
[9] Kumar, R., Homomorphism and fuzzy subgroups, Fuzzy Sets and Systems, 44, 165-168 (1991) · Zbl 0761.20028
[10] Kumar, R., Fuzzy subgroups, fuzzy ideals and fuzzy cosets: some properties, Fuzzy Sets and Systems, 48, 267-274 (1992) · Zbl 0798.20065
[11] Liu, W. J., Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8, 133-139 (1982) · Zbl 0488.20005
[12] Liu, W. J., Operations on fuzzy ideals, Fuzzy Sets and Systems, 11, 31-41 (1983) · Zbl 0522.06013
[13] Nanda, S., Fuzzy fields and fuzzy linear spaces, Fuzzy Sets and Systems, 19, 89-94 (1986) · Zbl 0602.15002
[14] Rosenfeld, A., Fuzzy groups, J. Math. Anal. Appl., 35, 512-517 (1971) · Zbl 0194.05501
[15] Zadeh, L. A., Fuzzy sets, Inform. and Control, 8, 338-353 (1965) · Zbl 0139.24606
[16] Zimmermann, H. J., Fuzzy set theory and its applications (1985), Kluwer-Nijhoff: Kluwer-Nijhoff Dordrecht, Boston · Zbl 0578.90095
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.