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This research presents a novel hybrid portfolio optimization framework that combines the Hierarchical Risk Parity (HRP) algorithm with two Multi-Criteria Decision-Making (MCDM) methods, MEREC and WEDBA, specifically to overcome fundamental shortcomings in the standard HRP model. The central goal is to alleviate the chaining problem and resolve HRP’s difficulty in identifying the optimal number of clusters, issues known to negatively affect portfolio diversification and risk allocation. To achieve this structural improvement, the Elbow method is integrated directly into the HRP process, ensuring a robust cluster structure is defined before any weight allocation occurs. The MEREC method is then utilized to calculate objective criterion weights, while the WEDBA approach is employed to assess the financial performance of individual assets within each cluster generated by HRP. This HRP–MCDM algorithm is tested using daily closing price data for stocks on the BIST 100 Index covering the 2018–2022 period. The performance of portfolios generated across seven distinct linkage methods (Ward, single, complete, average, weighted, centroid, and median) is rigorously benchmarked against the outcomes from the traditional HRP approach. Findings demonstrate that the HRP–MCDM framework significantly boosts both return levels and risk-adjusted metrics, especially when using the single and Ward linkage method, thereby surpassing the standard HRP algorithm in the majority of test cases. By strategically blending machine-learning-based risk clustering with objective, multi-criteria evaluation, this study makes a vital methodological contribution to the portfolio optimization domain, equipping investors with a more stable, transparent, and performance-focused asset allocation instrument.

The Best-Worst Method (BWM) is a recently introduced, innovative multi-criteria decision-making (MCDM) technique used to determine criterion weights for selection processes. However, another method is needed to complete the selection of the most preferred alternative. In this research, we propose a group decision-making methodology based on the multiplicative BWM to make this selection. Furthermore, we give new models that allow for groups with different best and worst criteria to exist. This capability is crucial in reconciling the differences among experts from various geographical locations with diverse evaluation perspectives influenced by social and cultural disparities. Our work contributes significantly in three ways: (1) we propose a BWM-based methodology for evaluating alternatives, (2) we present new linear models that facilitate decision-making for groups with different best and worst criteria, and (3) we develop a dissimilarity ratio to quantify the differences in expert opinions. The methodology is illustrated via numerical experiments for a global car company deciding which car model alternative to introduce in its markets.

This paper proposes a new multi-criteria group decision-making (MCGDM) method utilizing q-rung orthopair fuzzy (qROF) sets, improved power weighted operators and improved power weighted Maclaurin symmetric mean (MSM) operators. The power weighted averaging operator and power weighted Maclaurin symmetric mean (MSM) operator used in the existing MCGDM methods have the drawback of being unable to distinguish the priority order of alternatives in some scenarios, especially when one of the qROF numbers being considered has a non-belongingness grade of 0 or a belongingness grade of 1. To address this limitation of existing MCGDM methods, four operators, namely qROF improved power weighted averaging (qROFIPWA), qROF improved power weighted geometric (qROFIPWG), qROF improved power weighted averaging MSM (qROFIPWAMSM) and qROF improved power weighted geometric MSM (qROFIPWGMSM), are proposed in this paper. These operators mitigate the effects of erroneous assessment of information from some biased decision-makers, making the decision-making process more reliable. Following that, a group decision-making methodology is developed that is capable of generating a reasonable ranking order of alternatives when one of the qROF numbers considered has a non-belongingness grade of 0 or a belongingness grade of 1. To investigate the applicability of the proposed approach, a case study is also presented and a comparison-based investigation is used to demonstrate the superiority of the approach.

Consensus creation is a complex challenge in decision making for conflicting or quasi-conflicting evaluator groups. The problem is even more difficult to solve, if one or more respondents are non-expert and provide uncertain or hesitant responses in a survey. This paper presents a methodological approach, the Interval-valued Spherical Fuzzy Analytic Hierarchy Process, with the objective to handle both types of problems simultaneously; considering hesitant scoring and synthesizing different stakeholder group opinions by a mathematical procedure. Interval-valued spherical fuzzy sets are superior to the other extensions with a more flexible characterization of membership function. Interval-valued spherical fuzzy sets are employed for incorporating decision makers’ judgements about the membership functions of a fuzzy set into the model with an interval instead of a single point. In the paper, Interval-valued spherical fuzzy AHP method has been applied to public transportation problem. Public transport development is an appropriate case study to introduce the new model and analyse the results due to the involvement of three classically conflicting stakeholder groups: passengers, non-passenger citizens and the representatives of the local municipality. Data from a real-world survey conducted recently in the Turkish big city, Mersin, help in understanding the new concept. As comparison, all likenesses and differences of the outputs have been pointed out in the reflection with the picture fuzzy AHP computation of the same data. The results are demonstrated and analysed in detail and the step-by-step description of the procedure might foment other applications of the model.

The aim of this manuscript is to propose a new extension of the MULTIMOORA method adapted for usage with a neutrosophic set. By using single valued neutrosophic sets, the MULTIMOORA method can be more efficient for solving complex problems whose solving requires assessment and prediction, i.e. those problems associated with inaccurate and unreliable data. The suitability of the proposed approach is presented through an example.