The Relations between Soft L-fuzzy Topogenous Orders and Soft L-fuzzy Pre-uniformities

Recently, Molodtsov [12] introduced the soft set as a mathematical tool for dealing information as the uncertainty of data in engineering, physics, computer sciences and many other diverse field. Presently, the soft set theory is making progress rapidly [1,3]. Pawlak’s rough set [13,14] can be viewed as a special case of soft rough sets [3]. The topological structures of soft sets have been developed by many researchers [2,7-10,15-18]. On the other hand, Hájek [4] introduced a complete residuated lattice which is an algebraic structure for many valued logic. It is an important mathematical tool for algebraic structures [5,7-10]. Kim [8] introduced a fuzzy soft F : A → L as an extension as the soft F : A → P (U) where L is a complete residuated lattice. Kim [7-10] introduced the soft topological structures, L-fuzzy quasiuniformities and soft L-fuzzy topogenous orders in complete residuated lattices.