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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 350603, 20 pages
Research Article

Fuzzy Soft Multiset Theory

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Selangor DE, 43600 UKM Bangi, Malaysia

Received 23 January 2012; Revised 22 March 2012; Accepted 28 March 2012

Academic Editor: P. J. Y. Wong

Copyright © 2012 Shawkat Alkhazaleh and Abdul Razak Salleh. 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.


In 1999 Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Alkhazaleh et al. in 2011 introduced the definition of a soft multiset as a generalization of Molodtsov's soft set. In this paper we give the definition of fuzzy soft multiset as a combination of soft multiset and fuzzy set and study its properties and operations. We give examples for these concepts. Basic properties of the operations are also given. An application of this theory in decision-making problems is shown.