%0 Journal Article
%T An Investigation on Algebraic Structure of Soft Sets and Soft Filters over Residuated Lattices
%A S. Rasouli
%A B. Davvaz
%J ISRN Algebra
%D 2014
%R 10.1155/2014/635783
%X We introduce the notion of soft filters in residuated lattices and investigate their basic properties. We investigate relations between soft residuated lattices and soft filter residuated lattices. The restricted and extended intersection (union), and -intersection, cartesian product, and restricted and extended difference of the family of soft filters residuated lattices are established. Also, we consider the set of all soft sets over a universe set and the set of parameters with respect to , ( ), and we study its structure. 1. Introduction In economics, engineering, environmental science, medical science, and social science, there are complicated problems which to solve them methods in classical mathematics may not be successfully used because of various uncertainties arising in these problems. Alternatively, mathematical theories such as probability theory, fuzzy set theory [1], rough set theory [2, 3], vague set theory [4], and the interval mathematics [5] were established by researchers to modelling uncertainties appearing in the above fields. In 1992, Molodtsov [6] introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainties. In soft set theory, the problem of setting the membership function does not arise, which makes the theory easily applied to many different fields. At present, works on soft set theory are progressing rapidly. Some authors, for example, Maji et al. [7], discussed the application of soft set theory to a decision making problem. Chen et al. [8] presented a new definition of soft set parametrization reduction and compared this definition to the related concept of attributes reduction in rough set theory. In theoretical aspects, Maji et al. [9] and Ali et al. [10] defined and studied several operations on soft sets. The algebraic structure of the soft sets has been studied by some authors. Akta£ż and £ża£żman [11] studied the basic concepts of soft set theory and compared soft sets to the related concepts of fuzzy sets and rough sets. Soft set relations are defined and studied in [12] and some new operations are introduced in [13]. Jun et al. [14] introduced and investigated the notion of soft -algebras. Zhan and Jun [15] studied soft BL-algebras on fuzzy sets. Also, Feng et al. [16] combined soft sets theory, fuzzy sets, and rough sets. Feng et al. [17] studied deeply the relation between soft set theory and rough set theory. Recently, Yamak et al. in [18] introduce and study the notion of soft hyperstructure. Residuated lattices were introduced in by Krull in [19] who discussed
%U http://www.hindawi.com/journals/isrn.algebra/2014/635783/