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The Scientific World Journal
Volume 2014 (2014), Article ID 275947, 9 pages
http://dx.doi.org/10.1155/2014/275947
Research Article

A Novel Approach toward Fuzzy Generalized Bi-Ideals in Ordered Semigroups

1Department of Mathematics and Statistics, University of Swat, Swat, Khyber Pakhtunkhwa 19130, Pakistan
2Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, UTM, 81310 Johor Bahru, Johor, Malaysia

Received 26 August 2013; Accepted 6 November 2013; Published 27 April 2014

Academic Editors: Y.-T. Li and S. Pérez-Díaz

Copyright © 2014 Faiz Muhammad Khan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In several advanced fields like control engineering, computer science, fuzzy automata, finite state machine, and error correcting codes, the use of fuzzified algebraic structures especially ordered semigroups plays a central role. In this paper, we introduced a new and advanced generalization of fuzzy generalized bi-ideals of ordered semigroups. These new concepts are supported by suitable examples. These new notions are the generalizations of ordinary fuzzy generalized bi-ideals of ordered semigroups. Several fundamental theorems of ordered semigroups are investigated by the properties of these newly defined fuzzy generalized bi-ideals. Further, using level sets, ordinary fuzzy generalized bi-ideals are linked with these newly defined ideals which is the most significant part of this paper.