International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2516

Full Length Research Paper

A study of fuzzy Abel-Grassmann's groupoids

Madad Khan*, Saima Anis and Saeed Lodhi      
Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan.  
Email: [email protected]

  •  Accepted: 30 December 2011
  •  Published: 23 January 2012

Abstract

Fuzzy sets were first introduced by Zadeh in 1965 which have a wide range of applications in various fields of Engineering Sciences, Computer Science and Management Sciences. It is worth mentioning here that for applications of fuzzy sets mostly associative algebraic structures are used such as in 2003, Mordeson, Malik and Kuroki discovered the applications of fuzzy semigroups in fuzzy coding, fuzzy finite-state machines and fuzzy languages. Our aim in this paper is to apply fuzzy sets to non-associative algebraic structures and to develop some new related properties. Specifically we have characterized intra-regular Abel-Grassmann’s groupoids using generalized fuzzy bi-ideals.

 

Key words: Abel-Grassman's groupoid (AG-groupoid), intra-regular, fuzzy sets, fuzzy AG-groupoids,  -fuzzy ideals.