PENGAMBILAN KEPUTUSAN DENGAN PENDEKATAN PROBABILISTIC SOFT SETS DAN N-SOFT SETS

FATIA FATIMAH, Prof. Dr.rer.nat. Dedi Rosadi, S.Si., M.Sc. ; Dr. Raden Bagus Fajriya Hakim, S.Si., M.Si.

2018 | Disertasi | S3 Matematika

Pengambilan keputusan uncertainty telah diterapkan di berbagai bidang diantaranya statistika, ekonomi, sosial, medis dan sebagainya. Soft set merupakan salah satu teori yang dapat menangani masalah pengambilan keputusan uncertainty dengan parameter sebagai tolak ukur pengambilan keputusan. Parameter soft set dapat berupa angka, kata, kalimat, fungsi atau bentuk lainnya sehingga fleksibel dalam merepresentasikan kebutuhan individu. Dalam kehidupan sehari-hari dapat dijumpai himpunan data berupa probabilitas dan pemeringkatan. Namun penelitian terkait pengambilan keputusan soft set hanya membahas penilaian biner dan interval [0;1] akan tetapi bukan probabilitas. Oleh karena itu, penelitian ini membahas tentang bagaimana bentuk pengambilan keputusan dengan pendekatan probabilistic soft sets dan N-soft sets. Berikut temuan hasil penelitian. Probabilistic soft sets berguna untuk pengambilan keputusan dimana distribusi probabilitas per parameter. Algoritma pengambilan keputusannya yaitu Probabilistic Soft Sets-Choice Values, Probabilistic Soft Sets-Minimax, Probabilistic Soft Sets-Opportunity Cost, Probabilistic Soft SetsWeighted Choice Values, Probabilistic Soft Sets-Weighted Minimax, Probabilistic Soft Sets�Weighted Opportunity Cost, dan Probabilistic Soft Sets-Positive Matrices. Dual probabilistic soft sets perlu untuk pengambilan keputusan dimana distribusi probabilitas per objek. Algoritma pengambilan keputusannya yaitu Dual Probabilistic Soft Sets-Positive Matrices. N-soft set dapat menangani pengambilan keputusan dengan pemeringkatan biner maupun non-biner. Algoritma pengambilan keputusannya yaitu Extended Choice Values, Extended Weight Choice Values, dan T-Extended Choice Values diterapkan pada data nyata. Graded soft set menjembatani keterhubungan pengambilan keputusan antara teori soft set dengan teori social choice. Pengambilan keputusan graded soft set sesuai dengan aturan Borda pada sistem voting.

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 decisionmaking 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.

Kata Kunci : Pengambilan keputusan, Probabilistics soft sets, N-soft set