I-Vague Groups

Authors: Zelalem Teshome Wale

Abstract:

The notions of I-vague 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]. Moreover, various operations and properties are established.

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

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332338

References:

[1] K. T. Atanassov, Intutionistic fuzzy sets, Fuzzy Sets and Systems, vol. 20, 1986, pp. 87-96.
[2] R. Biswas, Vague groups, International Journal of Computational Cognition, vol. 4(2), 2006, pp. 20-23.
[3] H. Bustince and P. Burillo, Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 79, 1996, pp. 403-405.
[4] C. C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math.Soc., vol. 88, 1958, pp. 467-490.
[5] M. Demirci, Vague groups, Jou. Math. Anal. Appl., vol. 230, 1999, pp.142-156.
[6] W. L. Gau and D. J. Buehrer, Vague sets, IEEE Transactions on Systems, Man and Cybernetics, vol. 23, 1993, pp. 610-614.
[7] G. Gratzer, General Lattice Theory, Acadamic press Inc, 1978.
[8] H. Khan, M. Ahmad and R. Biswas, On vague groups, International Journal of Computational Cognition , vol.5(1), 2007, pp.27-30.
[9] J. Rach İunek, MV-algebras are categorically equivalent to a class of DRl1(i)-semigroups, Math. Bohemica, vol.123, 1998, pp.437-441.
[10] N. Ramakrishna, Vague groups and vague weights, International Journal of Computational Cognition, vol.6(4), 2008, pp.41-44.
[11] N. Ramakrishna and T. Eswarlal, Boolean vague sets, International Journal of Computational Cognition, vol.5(4), 2007, pp.50-53.
[12] N. Ramakrishna, A Study of Vague Groups, Vague Universal Algebras and Vague Graphs, Doctoral Thesis, Andhra University, Visakhapatnam, India, March 2009.
[13] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. vol.35, 1971, pp. 512-517.
[14] K. L. N. Swamy, Dually residuated lattice ordered semigroups, Math. Annalen, vol. 159, 1965, pp. 105 -114.
[15] K. L. N. Swamy, Dually residuated lattice ordered semigroups II, Math. Annalen, vol.160, 1965, pp. 64 -71.
[16] K. L. N. Swamy, Dually residuated lattice ordered semigroups III, Math. Annalen, vol.167, 1966 , pp.71-74.
[17] L. A. Zadeh, Fuzzy sets, Information and Control, vol. 8, 1965, pp. 338-353.
[18] T. Zelalem, I-Vague Sets and I-Vague Relations, International Journal of Computational Cognition, vol.8(4), 2010, pp.102-109.
[19] T. Zelalem, A Theory of I-Vague Sets, Doctoral Thesis, Andhra University, Vishakapatnam, India, July 2010.