Informatica

One of the most recent innovations in the field of fuzzy sets has been continuous intuitionistic fuzzy sets (CINFUSs), where membership and non-membership degrees are defined by nonlinear functions, as a direct extension of intuitionistic fuzzy sets (IFSs). The membership and non-membership degrees of CINFUSs can account for uncertainty at every point since they are represented by continuous structures that change based on how the decision-maker responds to uncertainty. On the other hand, Pythagorean fuzzy sets (PFSs) allow for a more accurate representation of the data and a better way to handle uncertainty in decision issues by reflecting the hesitations of decision-makers over a larger range. Due to these superior advantages of CINFUSs and the fact that PFSs are more comprehensive than IFSs, in this study, continuous Pythagorean fuzzy sets (CPFUSs) have been aimed at introducing to define uncertainty more broadly and accurately by representing PFSs with a continuous structure as in IFSs. In this study, firstly, the basic principles and mathematical operators of CPFUSs have been developed and presented. Then, multi-attribute decision-making (MADM) models have been developed by considering different aggregation operators to indicate the feasibility and effectiveness of the continuous Pythagorean fuzzy (CPFU) extension. The developed CPFU-MADM models have been implemented to the solution of two different decision problems: green supplier selection and waste disposal site selection problems. In addition, sensitivity analyses have been conducted on criterion weights, expert weights and parameters in order to demonstrate the reliability and stability of the developed models. Furthermore, the validity and superiority of the developed models have been indicated by the comparative analysis conducted with IFSs and PFSs-based MADM models in the literature. MADM applications have shown that continuous Pythagorean fuzzy sets can successfully represent the expert decisions with different attitudes within the same model. It has been observed that the rankings of alternatives according to aggregation operators do not change even when there are differences in the score values of the alternatives.

The probabilistic linguistic terms set (PLTS) can reflect different importance degrees or weights of all possible linguistic terms (LTs) given by the experts for a specific object. The PROMETHEE II method is an important ranking method which can comprise preferences as well as indifferences, and it has a unique characteristic that can provide different types of preference functions. Based on the advantages of the PLTS and the PROMETHEE II method, in this paper, we extend the PROMETHEE II method to process the probabilistic linguistic information (PLI), and propose the PL-PROMETHEE II method with an improved possibility degree formula which can avoid the weaknesses from the original formula. Then concerning the multi-attribute decision making (MADM) problems with totally unknown weight information, the maximum deviation method is used to get the objective weight vector of the attributes, and net flows of the alternatives from the PROMETHEE II method are used to rank the alternatives. Finally, a numerical example is given to illustrate the feasibility of the proposed method.

In this study, we evaluated the effects of the normalization procedures on decision outcomes of a given MADM method. For this aim, using the weights of a number of attributes calculated from FAHP method, we applied TOPSIS method to evaluate the financial performances of 13 Turkish deposit banks. In doing this, we used the most popular four normalization procedures. Our study revealed that vector normalization procedure, which is mostly used in the TOPSIS method by default, generated the most consistent results. Among the linear normalization procedures, max-min and max methods appeared as the possible alternatives to the vector normalization procedure.