Binary Soft Fuzzy approximation space

In this work devoted to study Binary soft fuzzy probability, probabilistic interpretation of Binary soft fuzzy, relationship between BSF reliability and classical reliability in addition to that BSF reliability is presented in view of BSF approximation, consider reliability as probability according to definition and consider BSF in the result according to our belief in current study.The Soft Fuzzy set is a new field of development and with its help not only new decision-making models and problems via the interactive soft computing complexity and time analysis but new mathematical models may be evolved which will be incentive to the natural sciences such as information systems, biomathematics and other. The novel structure of binary soft fuzzy approximation space is introduced in this paper. An attempt has been made to discuss some of the basic notions and concepts. the purpose of this paper is just to introduce the theorem and there are many opportunities for investigation for the researchers in this area, i. e. this is starting of some new kind of soft fuzzy approximation space structure and the such concepts like binary soft fuzzy lower and BSF upper and another basic concepts as, separation principles, and other things can be diverse about this new type of soft fuzzy reliability.