I-Vague Normal Groups

Authors: Zelalem Teshome Wale

Abstract:

The notions of I-vague normal groups with membership and non-membership functions taking values in an involutary dually residuated lattice ordered semigroup are introduced which generalize the notions with truth values in a Boolean algebra as well as those usual vague sets whose membership and non-membership functions taking values in the unit interval [0, 1]. Various operations and properties are established.

Keywords: Involutary dually residuated lattice ordered semigroup, I-vague set, I-vague group and I-vague normal group.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1074383

References:

[1] R. Biswas, Vague groups, International Journal of Computational Cognition, vol. 4(2), 2006, pp. 20-23. Systems, vol. 79, 1996, pp. 403-405.
[2] M. Demirci, Vague groups, Jou. Math. Anal. Appl., vol. 230, 1999, pp. 142-156.
[3] N. Ramakrishna, A Study of Vague Groups, Vague Universal Algebras and Vague Graphs, Doctoral Thesis, Andhra University, Visakhapatnam, India, March 2009.
[4] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. vol.35, 1971, pp. 512- 517.
[5] K. L. N. Swamy, Dually residuated lattice ordered semigroups, Math. Annalen, vol. 159, 1965, pp. 105 -114.
[6] K. L. N. Swamy, Dually residuated lattice ordered semigroups II, Math. Annalen, vol. 160, 1965, pp. 64 -71.
[7] K. L. N. Swamy, Dually residuated lattice ordered semigroups III, Math. Annalen, vol. 167, 1966 , pp.71-74.
[8] L. A. Zadeh, Fuzzy sets, Information and Control, vol. 8, 1965, pp. 338- 353.
[9] T. Zelalem, I-Vague Groups, submitted for publication to the International Journal of Computational and Mathematical Sciences.
[10] T. Zelalem, A Theory of I-Vague Sets, Doctoral Thesis, Andhra University, Vishakapatnam, India, July, 2010.