The join of fuzzy algebraic substructures of a group and their lattices

Fuzzy Sets and Systems

Volumn 99, Issue 2, 1998, Pages 213-224

  Ajmal, Naseem ^a,c   Thomas, K V ^b  

^a UNIVERSITY OF DELHI   (India)

^b UNIVERSITY OF DELHI   (India)

^c NONE   (India)

Author keywords

Complete lattice; Fuzzy algebra; Fuzzy invariant subgroup; Fuzzy subgroup; Fuzzy subgroupoid; Lattice; Level subset; Modular lattice; Quasinormality; Set product

Indexed keywords

ALGEBRA; SET THEORY; THEOREM PROVING;

COMPLETE LATTICE; FUZZY INVARIANT SUBGROUP; FUZZY SUBGROUP; FUZZY SUBGROUPOID; LEVEL SUBSET; MODULAR LATTICE; QUASINORMALITY; SET PRODUCT;

FUZZY SETS;

EID: 0032188692     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0114(96)00395-8     Document Type: Article

References (24)

1. M.T. Abu Osman, On the direct product of fuzzy Subgroups, Fuzzy Sets and Systems 19 (1986) 177-191.
2. N. Ajmal, Set product and fuzzy subgroups, Proc. IFSA World Cong. (1991) 4-7.
3. N. Ajmal, Homomorphism of fuzzy groups, correspondence Theorem fuzzy quotient groups, Fuzzy Sets and systems 61 (1994) 329-339.
4. N. Ajmal, K.V. Thomas, Quasinormality and fuzzy subgroups, Fuzzy Sets and Systems 58 (1993) 217-225.
5. N. Ajmal, K.V. Thomas, The lattices of fuzzy subgroups and fuzzy normal subgroups. Inform. Sci. 76 (1994) 1-11.
6. N. Ajmal, K.V. Thomas, A complete study of the lattices of fuzzy congruences and fuzzy normal subgroups. Inform. Sci., 82 (1995) 197-218.
7. J.M. Anthony, H. Sherwood, Fuzzy groups redefined, J. Math. Anal. Appl. 69 (1979) 124-130.
8. P.S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl. 84 (1981) 264-269.
9. A. Deluca, S. Termini, Algebraic properties of fuzzy sets, J. Math Anal. Appl. 40 (1972) 373-386.
10. W.E. Deskins, On quasinormal subgroups of finite groups, Math. Z. 82 (1963) 125-132.
11. J.A. Goguen, L-fuzzy sets, J. Math. Anal. Appl. 18 (1967) 145-174.
12. K.C. Gupta, S. Ray, Modularity of the quasihamiltonian fuzzy subgroups, Inform. Sci. 79 (1994) 233-250.
13. R. Kumar, Fuzzy subgroups, fuzzy ideals, and fuzzy costs: some properties, Fuzzy Sets and Systems 48 (1992) 267-274.
14. N. Kuroki, Fuzzy congruences and fuzzy normal subgroups, Inform. Sci. 60 (1992) 247-259.
15. W.J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems 8 (1992) 133-139.
16. D.S. Malik, J.N. Moderson, P.S. Nair, Fuzzy normal subgroups in fuzzy subgroup, J. Korean Math Soc. 29 (1992) 1-8.
17. x, Fuzzy Sets and Systems 41 (1991) 101-111.
18. C.V. Negoita D.A. Ralescu, Applications of Fuzzy Sets to Systems Analysis, Wiley, New York, 1975, pp 54-59.
19. O. Ore, Contributions to the theory of groups of finite order, Duke Math. J. 5 (1939) 431-460.
20. A. Rosenfeld, Fuzzy groups. J. Math. Anal. Appl. 35 (1971) 512-517.
21. F.I. Sidky, M. Atif Mishref, Fuzzy cosets and cyclic and Adelian fuzzy subgroups, Fuzzy Sets and Systems 43 (1991) 241-250.
22. S.E. Stonehewar, Permutable subgroups of infinite groups, Math. Z. 125 (1972) 1-16.
23. N.L. Youssef, K.A. Dib, A new approach to fuzzy subgroups, Fuzzy Sets and Systems 49 (1992) 253-282.
24. B. Yuan, W. Wu, Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems 35 (1990) 231-240.