International Journal of Pure and Applied Mathematics Volume 77 No. 4 2012, 549-563 ISSN: 1311-8080 (printed version) url: http://www.ijpam.eu P A ijpam.eu POSSIBILITY VAGUE SOFT SET AND ITS APPLICATION IN DECISION MAKING Khaleed Alhazaymeh 1 , Nasruddin Hassan 2 § 1,2 School of Mathematical Sciences Universiti Kebangsaan Malaysia 43600 UKM, Bangi Selangor, MALAYSIA Abstract: We introduce the concept of possibility vague soft sets and its operations. We give applications of this theory in solving a decision-making problem. We also introduce the similarity measure of two possibility vague soft sets and discuss their application in a medical diagnosis problem. AMS Subject Classification: 03B52, 03E72 Key Words: possibility fuzzy soft set, soft set, vague soft set 1. Introduction Fuzzy set was introduced by Zadeh in [1] as a mathematical tool to solve the problem and vagueness in everyday life. Molodtsov [2] mentioned a soft set as a mathematical way to represent and solve these problems with uncertain- ties which traditional mathematical tools cannot handle. He has proved several applications of his theory in solving problem in economics, engineering, environ- ment, social science, medical science and business management. Roy and Maji used this theory to solve some decision-making problems [3]. Alkhazaleh et al [4] introduced the concept of soft multiset as a generalization of Molodtsov’s soft set. They [5] also introduced possibility fuzzy soft set and some proposi- tions of possibility fuzzy soft set with application in decision making. Salleh et Received: March 1, 2012 c  2012 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author