Possibilistic simulation based interactive fuzzy MAGDM under discrimination q-rung picture linguistic information. Application in educational programs efficiency evaluation

Abstract

In certain Multi-Attribute Group Decision-Making (MAGDM) approaches an aggregation of decision-making matrices of experts’ evaluations/ratings of possible alternatives by their attributes into an etalon decision-making matrix is an important task. Based on possible great experience and deep knowledge of the subject, the expert tries to dominate other experts in the decision-making process. Besides, every expert has a possibility of a certain degree to influence on the decision-making process. In such cases experts’ evaluations aggregation into an etalon matrix by the additive or linear aggregation instruments is unacceptable. We present a new two-stage MAGDM approach to solve this task. On the first stage: In the evidence theory environment the connection between experts’ pair interaction indexes and possibility levels of their influence on decision-making process is constructed. For this, a Monte-Carlo simulation algorithm is created, the result of which is the estimated class of associated probabilities of the possibility distribution. Experts’ evaluations in decision-making matrixes are represented by the q-rung orthopair fuzzy numbers (q-ROFNs). Before aggregation of experts’ data into an etalon decision-making matrix, evaluations are transformed into discrimination q-rung picture linguistic numbers (q-RPLNs). New definitions are introduced for the Score and Accuracy functions of the q-rung picture linguistic numbers. q-rung picture linguistic numbers contain as well quantitative as qualificative information on experts’ reflections on objects, while discrimination q-rung picture linguistic numbers describe interactive phenomena between arguments. Based on constructed possibility distribution on the experts’ group, the ordered weighted averaging (OWA) and Choquet averaging (CA) aggregation operators under q-rung picture linguistic environment are extended (q-RPLOWA and q-RPLCA, respectively). By the q-RPLOWA and q-RPLCA operators decision-making matrices of experts’ evaluations/ratings are condensed into an etalon decision-making matrix. On the second stage: The concept of Euclidean distance and the entropy of De Luca–Termini are defined for q-rung picture linguistic set. The new relative closeness parameter for the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) approach under q-rung picture linguistic information is also defined. The technique for the TOPSIS approach for the ranking of possible alternatives in MAGDM by aggregating discrimination q-rung picture linguistic data of etalon matrix is developed. For illustration of the obtained results, Educational Programs Efficiency Evaluation problem is considered. Our constructed MAGDM approach complies with the principle of expertise in educational programs evaluation commission. The numerical results obtained for the q-RPLNs environment and the ranking of alternatives are compared with the numerical results and the ranking of alternatives obtained by the same approach for the initial expert data in q-ROFNs environment. A comparison with the results obtained by other existing methods is given.