Soft discernibility matrix and its applications in decision making

Graphical abstractDisplay Omitted HighlightsThe aim of this paper is to solve the problem of decision makings by introducing soft discernibility matrix in soft sets.The notion of soft discernibility matrix is firstly introduced in soft sets.An novel algorithm based on the soft discernibility matrix is proposed to solve the problems of decision making.The algorithm can output an order relation of all the objects easily by scanning the soft discernibility matrix at most one time.The weighted soft discernibility matrix is introduced in soft sets and its application to decision making is also investigated. In this paper, we aim to solve the problems of decision making by introducing soft discernibility matrix in soft sets. Firstly, the notion of soft discernibility matrix is introduced in soft sets, and some properties associated with the soft discernibility matrix are researched. Secondly, an novel algorithm based on soft discernibility matrix is proposed to solve the problems of decision making. It can find not only the optimal choice object, but also an order relation of all the objects easily by scanning the soft discernibility matrix at most one time, rather than calculating the choice value. Finally, the weighted soft discernibility matrix is introduced in soft sets and its application to decision making is also investigated.

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