Cardinality inverse soft matrix theory and its applications in multicriteria group decision making

The main objective of this paper is to present a novel decision making algorithm using matrix representation of the inverse soft set defined in [10]. Therefore, we first introduce cardinality inverse soft matrix theory and its operations, products and algebraic structures in detail. Afterwards, an algorithmic solution employing the cardinality inverse soft matrix to find the optimum object and the ranking order of objects is proposed. The performance of algorithm named soft sum-row decision making algorithm is demonstrated by solving various decision problems. Also, we compare it with existing algorithms based on the soft set theory, soft matrix theory and inverse soft set theory. Moreover, we give Scilab codes of the algorithm and argue that this codes make the process of decision making composed of many objects, criteria and decision makers faster and easier.