We introduce the concept of vague ideals in a distributive implication groupoid and investigate their properties. The vague ideals of a distributive implication groupoid are also characterized.
[2] P. Bhattacharya and N.P. Mukherjee, Fuzzy relations and fuzzy groups, Inform. Sci. 36 (1985), 267-282. doi: 10.1016/0020-0255(85)90057-X
[3] R. Biswas, Vague groups, International Journal of Computational Cognition 4 (2) (2006), 20-23. http://www.yangsky.com/ijcc/pdf/ijcc423.pdf
[4] I. Chajda and R. Hala, Congruences and ideals in Hilbert algebras, Kyungpook Math. J. 39 (1999), 429-432 (preprint).
[5] I. Chajda and R. Hala R, Distributive implicaiton groupoids, Central European Journal of Mathematics 5 (3) (2007), 484-492. doi: 10.2478/s11533-007-0021-5
[6] W.A. Dudek and Y.B. Jun, On fuzzy ideals in Hilbert algebras, Novi Sad J. Math. 29 (2) (1999), 193-207. ftp://ftp.gwdg.de/pub/EMIS/journals/NSJOM/Papers/29_2/NSJOM_29_2_193_207.pdf
[7] W.L. Gau and D.L. Buehrer, Vague sets, IEEE Transactions on systems-Man and Cybernetics 23 (1993), 610-614. doi: 10.1109/21.229476
[8] Y.B. Jun and S.M. Hong, On fuzzy deductive systems of Hilbert algebras, Indian Journal of Pure and Applied Mathematics 27 (2) (1996), 141-151. http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_2/20005a24_141.pdf.
[9] Y.B. Jun and C.H. Park, Vague ideals of subtraction algebra, International Mathematical Forum 2 (2007), 2919-2926. http://www.m-hikari.com/imf-password2007/57-60-2007/parkIMF57-60-2007-1.pdf.
[10] J.N. Mordeson and D.S. Malik, Fuzzy Commutative algebra, World Scientific Publishing Co. pvt. Ltd, Singapore, 1998. http://www.worldscientific.com/worldscibooks/10.1142/3929.
[11] L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X