Generalized bipolar -soft sets, generalized bipolar-soft topology and their decision making algorithms

Abstract

Fatimah et al. <cite>del 21</cite> introduced the notion of N-soft set that is the extension of soft set introduced by Molodtsov <cite>del 43</cite>. Shabir et al. <cite>del 53</cite> studied the bipolarity of data within the soft set by defining the notion of bipolar soft set. During this paper, we have a tendency to encourage and introduce the concept of N-bipolar soft set as an extension of bipolar soft set and N-soft set. Some helpful algebraical definitions and properties are presented. Our concept is illustrated with real life examples, which have uncertainties in knowledge that may be properly captured by this structure. Also, we tend to introduce the notion of N-bipolar soft topology and its specific structures including N-bipolar soft neighborhood, N-bipolar soft interior, N-bipolar soft closure , and N-bipolar soft basis. Moreover, potential applications of N-bipolar soft sets in decision making are presented with algorithms. Finally, we present multi criteria group decision making (MCGDM) methods by utilizing N-bipolar soft set and N-bipolar soft topology to deal with uncertainties in the real world problems.