multi attribute decision making

As the digital landscape continues to evolve, the selection of an appropriate online shop-ping platform has become increasingly crucial for both consumers and businesses. This paper introduces a novel approach that combines the Fermatean fuzzy set theory with the triangular divergence distance measure in Compromise Ranking of Alternatives from Distance to Ideal Solution (CRADIS) method to streamline the decision-making process in online platform selection. Through a comprehensive example, we illustrate the application of this approach in evaluating and ranking four distinct online shopping latforms based on multiple criteria. Through this integrated approach, decision-makers can gain valuable insights into the rela-tive merits of each online shopping platform, allowing them to make informed choices aligned with their preferences and requirements. Furthermore, by accommodating uncertainty and imprecision, the Fermatean fuzzy set theory enhances the robustness of the decision-making process, minimizing the risk of making suboptimal decisions. Overall, this paper demon-strates the practical applicability of Fermatean fuzzy set theory in decision support systems for online platform selection. To demonstrate the proposed method’s applicability, we have compared the results with existing Multi-attribute decision making (MADM) methods. To establish its stability, we conducted a sensitivity analysis. By leveraging the CRADIS method alongside Fermatean fuzzy set theory, decision-makers can navigate the complex landscape of online shopping platforms with greater confidence and efficiency, ultimately leading to more satisfactory outcomes for both consumers and businessesalike.

Healthcare services supply chain performance evaluation in hospitals that deal with society's well-being has significant importance on their performance improvement. The purpose of this research was to evaluate healthcare services supply chain performance using a neutrosophic multiple attribute decision-making technique in Tehran’s hospitals. Comprehensive performance evaluation was conducted by applying both objective attributes that focused on the outcome along subjective attributes that were based on the judgment of evaluators. In this regard, neutrosophic logic has been deployed to face uncertainties in the expert’s judgment for determining the priority of attributes over each other explained via linguistic variables in the form of trapezoidal neutrosophic numbers. Eigenvector-power as one of the multiple attribute decision-making techniques concerned with evaluating and choosing the best option among the available ones based on diverse and conflicting attributes was used to ascertain attributes’ importance in addition to guaranteeing obtainment of the largest eigenvalue of the characteristic polynomial, has led to reduction of calculations. Neutrosophic algebraic operations embedded in the eigenvector-power technique after efficiency confirmation of the technique was acquired. In order to gap analysis, a paired t-test was exploited to discover the existence of differences between the current and desired performance of attributes. Then, attributes’ weighted performance gaps were calculated by multiplying the weight of each attribute by its performance gap which smoothed attributes’ performance gap criticality definition by applying quartiles. ``Staff job satisfaction" and ``response to demands" attributes were categorized as very highly critical, ``treatment branding" and ``proportion of service with cost" attributes were classified as highly critical, ``technological comfort" and ``stakeholder’s interests" attributes were grouped as moderately critical and ``access" and ``treatment plan fulfilment" attributes were relegated as low critical, respectively according to the weighted performance gap.

Multi-Attribute Decision Making (MADM) process is the most well-known branch of decision making and it is one of the most important tasks that have received a lot of attention in many areas. In solving MADM issues, the parameters of decision-making are often faced with problems, such as imprecise, vague, uncertain, or incomplete information which lead to inaccurate decision-making. To cope with these problems, the researchers apply fuzzy set theory as the best-developed approach. Among different fuzzy methods, the fuzzy rule-based system (FRBS) due to its flexibility, simplicity, and experts' knowledge modeling is an adequate technique for solving MADM problems. The main objective of this study is to apply experts' opinions by Z-numbers in MADM issues to enhance the accuracy of the decision-making process. The fundamental issue in solving MADM problems is that inadequate information in the experts' opinions leads to some degree of uncertainty in decisions. Indeed, in FRBS research to ranking, the reliability level (Z-numbers) in experts' opinions within the decision-making process has not been taken into account. Whereas, the Z-numbers play a key role in the decision-making process to reach more precise decisions affecting the final ranking results. In the proposed approach (Z-FRBS), by considering experts' opinions in the form of Z-numbers to deal with inadequate information and modeling experts' knowledge through FRBS, the process of making a decision is performed without using conventional techniques which resulted in a more accurate solving MADM problems. The effectiveness and validity of the proposed method was approved with an illustrative example, sensitivity analysis, and comparison with three other validated method.

Picture fuzzy set is an extension of intuitionistic fuzzy set, which can deal with inconsistent and uncertain information more accurately. Similarity measure, as an important  mathematical tool to evaluate the degree of similarity between picture fuzzy sets, has been widely used to deal with multi-attribute decision-making problems. But there are unreasonable  and counter-intuitive cases due to  a few undesirable properties. In order to handle these unreasonable cases, this paper proposes a parametric similarity measure based on three parameters $m_1, m_2$ and $m_3$, in which decision makers with different decision styles can  obtain  the appropriate similarity measure by adjusting parameters $m_1, m_2$ and $m_3$. Moreover, we  analyze some existing similarity measures from the perspective of mathematics and show that the proposed similarity measure is effective by   numerical examples. In the end, we use the proposed similarity measure to solve the problems of multi-attribute decision-making. Through the  comparison and analysis, we find that the proposed similarity measure is more effective  than some existing similarity measures between picture fuzzy sets.