Şahin, Rıdvan

In order to handle simultaneously the cardinal and ordinal information in decision-making process, QUALIFLEX (QUALItative FLEXible multiple criteria method) is a very well-known decision-making approach. In this work, we extend the classical QUALIFLEX method to neutrosophic environment and develop a neutrosophic QUALIFLEX (N-QUALIFLEX) method that uses the newly defined distance-based comparison approach. It is highly effective in solving multi-criteria decision problems in which both ratings of alternatives on criteria and weights of criteria are single-valued neutrosophic numbers (SVNNs), and their aggregated values are single-valued neutrosophic hesitant fuzzy numbers (SVNHFNs). A neutrosophic hesitancy index (NHI) of a SVNHN is introduced based on degrees of the truth-membership, indeterminacy-membership and falsity-membership, which is used to measure the degree of hesitancy of SVNHN. Considering the NHIS of SVNHFNs, we propose a distance-based comparison approach to determine the magnitude of the SVNHFNs. Then, we apply the comparison approach to define the concordance/discordance index, the weighted concordance/discordance index and the comprehensive concordance/discordance index that are steps of the developed N-QUALIFLEX. By taking all possible permutations of alternatives with respect to the level of concordance/discordance into account, we determine the order of alternatives in final decision. Finally, a practical example on antivirus mask selection over the COVID-19 pandemic is provided to present the effectiveness and applicability of the proposed method, and a comparative study is conducted to show the advantages of the proposed method over other existing methods.

Altun, Fatma; Şahin, Rıdvan; Güler, Coşkun

Probabilistic simplified neutrosophic set (PSNS) is an important tool to describe the vagueness existing in the real life. In this study, we define a PSNS and discuss some of theoretical set operations of PSNSs. Also we propose the concepts of module on PSNSs, as well as inner product and projection operator between two PSNSs. In relation to this new set, we introduce a probabilistic simplified neutrosophic number (PSNN). A PSNN has three components which is called probabilistic-valued truth membership degree, probabilistic-valued indeterminacy membership degree and probabilistic-valued falsity membership degree, respectively. We give some of algebraic operational rules, a score function and an accuracy function on PSNNs. Furthermore, we introduce two aggregation operators called the probabilistic simplified neutrosophic weighted arithmetic average operator and the probabilistic simplified weighted geometric average operator on PSNNs. Furthermore, we determine weights of criteria with a method that is based on fuzzy measure and develop a method based on preference function to determine weight of each decision maker. We present an extended PROMETHEE method based on PSNSs for group decision problems. Finally, as an application of this theory, we give a practice on a multi-criteria group decision making problem based on PSNNs by using extended PROMETHEE method to ensure stability of the proposed method.