Hindawi Publishing Corporation Discrete Dynamics in Nature and Society Volume 2013, Article ID 602959, 8 pages http://dx.doi.org/10.1155/2013/602959 Research Article Int-Soft Filters of -Algebras Sun Shin Ahn, 1 N. O. Alshehri, 2 and Young Bae Jun 3 1 Department of Mathematics Education, Dongguk University, Seoul 100-715, Republic of Korea 2 Department of Mathematics, Faculty of Science for Girls, King Abdulaziz University, Jeddah, Saudi Arabia 3 Department of Mathematics Education, Gyeongsang National University, Jinju 660-701, Republic of Korea Correspondence should be addressed to N. O. Alshehri; nalshehrie@kau.edu.sa Received 7 August 2013; Accepted 2 November 2013 Academic Editor: Cengiz C ¸ inar Copyright © 2013 Sun Shin Ahn et al. Tis 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. Te notion of int-sof flters ofa -algebra is introduced, and related properties are investigated. Characterization of an int-sof flter is discussed. Te problem of classifying int-sof flters by their -inclusive flter is solved. 1. Introduction In 1966, Imai and Is´ eki [1] and Is´ eki [2] introduced two classes of abstract algebras: BCK-algebras and BCI-algebras. It is known that the class of BCK-algebras is a proper subclass of the class of BCI-algebras. As a generalization of a BCK- algebra, H. S. Kim and Y. H. Kim [3] introduced the notion of a -algebra and investigated several properties. In [4], Ahn and So introduced the notion of ideals in -algebras. Tey gave several descriptions of ideals in -algebras. Various problems in system identifcation involve char- acteristics which are essentially nonprobabilistic in nature [5]. In response to this situation Zadeh [6] introduced fuzzy set theory as an alternative to probability theory. Uncertainty is an attribute of information. In order to suggest a more general framework, the approach to uncertainty is outlined by Zadeh [7]. To solve complicated problem in economics, engineering, and environment, we cannot successfully use classical methods because of various uncertainties typical for those problems. Tere are three theories: theory of probability, theory of fuzzy sets, and the interval mathematics which we can consider as mathematical tools for dealing with uncertainties. But all these theories have their own difculties. Uncertainties cannot be handled using traditional mathematical tools but may be dealt with using a wide range of existing theories such as probability theory, theory of (intuitionistic) fuzzy sets, theory of vague sets, theory of interval mathematics, and theory of rough sets. However, all of these theories have their own difculties which are pointed out in [8]. Maji et al. [9] and Molodtsov [8] suggested that one reason for these difculties may be due to the inadequacy of the parametrization tool of the theory. To overcome these difculties, Molodtsov [8] introduced the concept of sof set as a new mathematical tool for dealing with uncertainties that is free from the difculties that have troubled the usual theoretical approaches. Molodtsov pointed out several directions for the applications of sof sets. At present, works on the sof set theory are progressing rapidly. Maji et al. [9] described the application of sof set theory to a decision-making problem. Maji et al. [10] also studied several operations on the theory of sof sets. Chen et al. [11] presented a new defnition of sof set parametrization reduction and compared this defnition to the related concept of attributes reduction in rough set theory. Te algebraic structure of set theories dealing with uncertainties has been studied by some authors. C ¸a ̆ gman et al. [12] introduced fuzzy parameterized (FP) sof sets and their related properties. Tey proposed a decision-making method based on FP-sof set theory and provided an example which shows that the method can be successfully applied to the problems that contain uncertainties. Feng [13] considered the application of sof rough approximations in multicriteria group decision- making problems. Aktas ¸ and C ¸a ̆ gman [14] studied the basic concepts of sof set theory and compared sof sets to fuzzy and rough sets, providing examples to clarify their diferences. Tey also discussed the notion of sof groups. In this paper, we introduce the notion of int-sof flter ofa -algebra and investigate its properties. We