The research entitled “N-soft Sets and Their Decision-Making Algorithms” was conducted by **Fatia Fatimah** under the guidance of Dr.rer.nat., Dedi Rosadi, S.Si., M.Sc., and Dr. Raden Bagus Fajriya Hakim, S.Si., M.Si. in 2018.

The following is the abstract of this research.

**ABSTRACT**

*Decision-making uncertainty has been applied in various fields. Soft set is one of the theories that can handle the decision-making problems under uncertainty where its parameters as the benchmark of decision making. The parameters may be real numbers, words, sentences, functions and so on. Therefore, it is flexible in representing individual needs. In everyday life, data sets can be found in the form of probabilities or rankings. Unfortunately, there is no literature in soft sets for handling decision-making problems using probabilities or N ary rankings. Thus, this research discusses about decision-making approach using probabilistic soft sets and N-soft sets. The results are as follows. First, probabilistic soft sets is useful for decision making where its probability distributions based on parameters. Seven decision-making algorithms are proposed i.e., Probabilistic Soft Sets-Choice Values, Probabilistic Soft Sets-Minimax, Probabilistic Soft Sets-Opportunity Cost, Probabilistic Soft Sets-Weighted Choice Values, Probabilistic Soft Sets-Weighted Minimax, Probabilistic Soft Sets Weighted Opportunity Costs, and Probabilistic Soft Sets Positive Matrices. Second, dual probabilistic soft sets, as an adaptation of probabilistic soft sets, is necessary for handling decision-making problems where its probability distributions based on objects. Dual Probabilistic Soft Sets Positive Matrices algorithm is presented. Third, N-soft sets can handle decision making with binary or non-binary rankings. Three decision-making algorithms are introduced i.e., Extended Choice Values, Extended Weight Choice Values, and T-Extended Choice Values. They are applied to a real case study. Fourth, graded soft set, a special case of N-soft set, draws a bridge between decision making in soft set and social choice theory. Its decision-making mechanism using choice values coincides with the Borda count in voting.* read more