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Top1. Introduction
The fuzzy set (FS) has announced by the mid of the sixties by (Zadeh, 1965). It has been extensively considered, developed, and effectively applied to several grounds. Fuzzy sets and numbers can offer very good solutions in multi attributes in decision making (MADM) cases (Bellman & Zadeh, 1970; Yager, 1977). However, fuzzy sets failed to represent uncertain data being of several types owing to its limitation in convey information by only a single value that lies in [0, 1] so that the soft set (SS) came to overcome this limitation (Molodtsov, 1999). Further researches have shown strong attention in this method and several applications in MADM (Maji, et al. 2002; 2003; Ali et al., 2009; 2011;2012; Sezgin & Atagün, 2011; Jiang, et al., 2011; Min, 2012; Aktas & Çağman, 2007; Acar et al., 2010; Gong et al., 2010; Babitha & Sunil, 2010; Çağman & Engino’glu, 2010; Feng & Çağman, 2012). Due to the complication caused by the fuzzy nature of parameters in many situations, SS and FS were combined to formalize fuzzy soft sets (FSS) to deal with these situations (Maji et al., 2001). Therefore, some operations, new order relation, and decomposition finite value spaces of FSS are discussed (Borah et al., 2012; Guan et al., 2012; Feng et al., 2014).
One more combination, bipolar fuzzy set (BFS) (Zhang, 1994) and SS innate a new notion named bipolar fuzzy soft set (BFSS) (Abdullaha et al., 2014) and they introduced fundamental properties and operations on the BFSS. An application and an algorithm of BFSS to solve decision-making problems were studied (Abdullaha et al., 2014). The bipolar fuzzy set (Zhang, 1994) has an exclusive property, which is the representing bipolar information “two-sided” about the given set (for instance: positive and negative, possible and impossible, Male and female, effect and side effect, etc.). The notion of BFS is an extension to FS (Zhang, 1994), in which the membership is extended from membership of degree in 
to a membership of degree in 
to indicate that the element satisfies somewhat an interesting property (Zhang et al., 2003;2004;2005;2006;2007;2009). Recently, some generalizations and applications in MADM, TOPSIS and VIKOR method were studied and genralized by using Bipolar fuzzy sets, Bipolar Fuzzy Soft Sets, Linear Diophantine Fuzzy Soft Rough Sets, and Linear Diophantine Fuzzy Sets see (Tehrim & Riaz, 2019; Riaz et. al., 2020; Riaz & Raza, 2019; Riaz &Tehrim, 2019; Riaz & Tehrim 2020, Mandal, 2021; Ali G, 2019; Tahir Mahmood. 2020).