Applied Mathematical Sciences, Vol. 5, 2011, no. 72, 3561 - 3573 Soft Multisets Theory Shawkat Alkhazaleh School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia 43600 UKM Bangi, Selangor DE, Malaysia shmk 79@yahoo.com Abdul Razak Salleh School of Mathematical Sciences, Faculty of Science and Technology Universiti Kebangsaan Malaysia 43600 UKM Bangi, Selangor DE, Malaysia Nasruddin Hassan School of Mathematical Sciences, Faculty of Science and Technology Universiti Kebangsaan Malaysia 43600 UKM Bangi, Selangor DE, Malaysia Abstract In 1999 Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. The solutions of such problems involve the use of mathematical principles based on uncertainty and imprecision. In this paper we recall the definition of a soft set, its properties and its operations. As a generalization of Molodtsov’s soft set we introduce the definitions of a soft multiset, its basic operations such as complement, union and intersection. We give examples for these concepts. Basic properties of the operations are also given. Keywords: soft set; soft multiset 1 Introduction Most of the problems in engineering, medical science, economics, environments etc. have various uncertainties. Molodtsov [6] initiated the concept of soft set theory as a mathematical tool for dealing with uncertainties which is free