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Over the last twenty years, patient opinions of the received healthcare services have emerged as a crucial quality indicator and a valuable instrument for evaluating the service quality of health organizations. However, many surveyors still utilized uncertain information for conducting this evaluation process. Whereas, in the past few years, the issues of inconsistency, indeterminacy, and uncertainty in data have been growing and have become a matter of concern in dealing with decision-making issues. This paper proposes an improved RAFSI method based on a single-valued trapezoidal neutrosophic number (SVTraNN) as a multi-attribute framework for dealing with a healthcare service quality evaluation. The proposed framework consists of two features: a feature for determining numerical criteria weights involving the procedures of the Ordinal Priority Approach (OPA) and a feature for selecting the best polyclinic through contributing our new SVTraNN Harmonic and arithmetic mean to yield criterion functions in the RAFSI method. This paper then compares the results obtained by the proposed method with other SVTraNN decision-making methods. A comparative analysis and rank reversal testing of the improved method demonstrated that the multi-attribute framework proffers the option of capability and stability in overcoming inconsistency, indeterminacy, and uncertainty information efficiently during the healthcare service quality evaluation. [ABSTRACT FROM AUTHOR]

• The centroid distance of PFNs is proposed and its properties are discussed. • Propose a score function based on the centroid distance and discuss its properties. • Applications of Pythagorean fuzzy clustering, ranking and MCDM are developed. • Some advantages of the proposed methods are showed through comparative analysis. By using Pythagorean fuzzy set (PFS), people can quantitatively describe and process information with fuzziness, and then make reasonable and effective judgments or decisions. In this process, distance measure often serves as a useful and important tool. The purpose of this paper is to explore some information processing methods and techniques in Pythagorean fuzzy environment. Firstly, the research progress of PFS is reviewed, and the main research directions and some hot issues in relevant research fields are discussed. Secondly, by analyzing the information of hesitation degree of Pythagorean fuzzy number (PFN), definitions of hesitation factor and centroid distance measure based on the representation of centroid coordinates of the hesitation regions are proposed, and properties of hesitation factor and centroid distance measure are discussed. Finally, the novel clustering algorithm, ranking method and multi criteria decision making (MCDM) method are developed in Pythagorean fuzzy environment, which are based on the new centroid distance measure. The effectiveness of the proposed algorithm and methods are verified through numerical examples and comparative analysis. The research results indicate that the centroid distance measure proposed in this paper can effectively characterize the distance between PFNs, thus making the clustering algorithm of PFNs, the ranking method of PFNs, and the Pythagorean fuzzy MCDM method have obvious superiorities and advantages. [ABSTRACT FROM AUTHOR]

Abstract: Many multi-criteria decision making (MCDM) methods have been proposed to handle uncertain decision making problems. Most of them are based on fuzzy numbers and they are not able to cope with risk in decision making. In recent years, some MCDM methods based on prospect theory to handle risk MCDM problems have been developed. In this paper, we propose a hybrid approach combining prospect theory and fuzzy numbers to handle risk and uncertainty in MCDM problems. So, it is possible to tackle more challenging MCDM problems. A case study involving oil spill in the sea illustrates the application of the novel method. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to develop a new approach for measuring the decision makers’ weights in group decision making setting, in which the decision information, provided by multiple decision makers, is expressed in interval-valued intuitionistic fuzzy numbers. There are two key issues being addressed in this approach. The first one is to develop an ideal decision of group, which is the mean of group decision. The second one is to select the similarity measure between each individual decision and the ideal decision according to the idea of the TOPSIS of . A numeric example is also given to clarify the developed approach and to demonstrate its effectiveness. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the expected values for intuitionistic trapezoidal fuzzy numbers and presented a handling method for intuitionistic trapezoidal fuzzy multicriteria decision-making problems, in which the preference values of an alternative on criteria and the weight values of criteria take the form of intuitionistic trapezoidal fuzzy numbers. Simple and exact formulas are proposed to determine the expected weight values of the criteria for an alternative and weighted expected value for an alternative. Therefore, the expected value method is extended for ranking alternatives and the most desirable one(s) can be selected according to the weighted expected values. Finally, an illustrative example shows that the proposed method is simple and effective. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to investigate the multiple attribute decision making problems with intuitionistic fuzzy information, in which the information about attribute weights is incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional gray relational analysis (GRA) method, by which the attribute weights can be determined. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. Then, based on the traditional GRA method, calculation steps for solving intuitionistic fuzzy multiple attribute decision-making problems with incompletely known weight information are given. Furthermore, we have extended the above results to an interval-valued intuitionistic fuzzy environment and developed modified GRA method for interval-valued intuitionistic fuzzy multiple attribute decision-making with incompletely known attribute weight information. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. [Copyright &y& Elsevier]