Iranian Journal of Fuzzy Systems Vol. 8, No. 3, (2011) pp. 137-147 137 FUZZY SOFT SET THEORY AND ITS APPLICATIONS N. C . A ˘ GMAN, S. ENGINO ˘ GLU AND F. C . ITAK Abstract. In this work, we define a fuzzy soft set theory and its related properties. We then define fuzzy soft aggregation operator that allows con- structing more efficient decision making method. Finally, we give an example which shows that the method can be successfully applied to many problems that contain uncertainties. 1. Introduction Molodtsov [23] introduced the concept of soft sets that can be seen as a new mathematical theory for dealing with uncertainty. Molodtsov applied this theory to several directions [23, 24, 25], and then formulated the notions of soft number, soft derivative, soft integral, etc. in [26]. The soft set theory has been applied to many different fields with great success. Maji et al. [20] worked on theoretical study of soft sets in detail, and [19] presented an application of soft set in the decision making problem using the reduction of rough sets [29]. Chen et al. [6] proposed parametrization reduction of soft sets, and then Kong et al. [16] presented the normal parametrization reduction of soft sets. Recently, many scholars study the properties and applications on the soft set theory. Xiao et al. [34] studied synthetically evaluating method for business com- petitive capacity and also Xiao et al. [35] gave a recognition for soft information based on the theory of soft sets. Pei and Miao [30] showed that the soft sets are a class of special information systems. Mushrif et al. [27] presented a new algorithm based on the notions of soft set theory for classification of the natural textures. Kovkov et al. [17] considered the optimization problems in the framework of the theory of soft sets which is directed to formalization of the concept of approximate object description. Zou and Xiao [42] presented data analysis approaches of soft sets under incomplete information. Majumdar and Samanta [21] studied the similarity measure of soft sets. Ali et al. [1] introduced the analysis of several operations on soft sets. The algebraic structure of soft set theory dealing with uncertainties has also been studied in more detail. Aktas . and C . a˘ gman [2] introduced a definition of soft groups, and derived their basic properties. Park et al. [28] worked on the notion of soft WS-algebras, soft subalgebras and soft deductive systems. Jun [9] dealt with the algebraic structure of BCK/BCI-algebras by applying soft set theory. Jun Received: January 2010; Accepted: July 2010 Key words and phrases: Fuzzy sets, Soft sets, Fuzzy soft sets, Soft aggregation, Fuzzy soft aggregation, Aggregate fuzzy set.