Multi-criteria Decision-making Problem Research Articles

Determining the Best Design Factors of a Two-stage Helical Gearbox with Two Gear Sets in the First Stage to Increase Efficiency and Reduce Volume using the SAW Method

This study describes the outcomes of employing the Simple Additive Weighting (SAW) approach to address the Multi-Objective Optimization Problem (MOOP) of a two-stage helical gearbox with two gear sets at the first stage. Its objective is to determine the key design variables that can reduce the volume of the gearbox while simultaneously maximizing its efficiency. For this investigation, three key design parameters were selected, namely the coefficients of the wheel face width of the first and second stages (Xba1 and Xba2), and the gear ratio of the first stage u1. In addition, the SAW technique was deployed to deal with the problem of Multi-Criteria Decision Making (MCDM), while the Method based on the Removal Effects of Criteria (MEREC) was employed to determine the weight criterion for addressing the MOOP. The obtained results are valuable for defining the optimal values for three primary design factors, which are essential for the development of a two-stage helical gearbox with two gear sets at the first stage.

Interactive Preference Elicitation under Noisy Preference Models: an Efficient Non-Bayesian Approach

The development of models that can cope with noisy input preferences is a critical topic in artificial intelligence methods for interactive preference elicitation. A Bayesian representation of the uncertainty in the user preference model can be used to successfully handle this, but there are large costs in terms of the processing time which limit the adoption of these techniques in real-time contexts. A Bayesian approach also requires one to assume a prior distribution over the set of user preference models. In this work, dealing with multi-criteria decision problems, we consider instead a more qualitative approach to preference uncertainty, focusing on the most plausible user preference models, and aim to generate a query strategy that enables us to find an alternative that is optimal in all of the most plausible preference models. We develop a non-Bayesian algorithmic method for recommendation and interactive elicitation that considers a large number of possible user models that are evaluated with respect to their degree of consistency of the input preferences. This suggests methods for generating queries that are reasonably fast to compute. We show formal asymptotic results for our algorithm, including the probability that it returns the actual best option. Our test results demonstrate the viability of our approach, including in real-time contexts, with high accuracy in recommending the most preferred alternative for the user.

Fuzzy set-based decision support system for hydrogen sulfide removal technology selection in natural gas processing: a sustainability and efficiency perspective.

Removing hydrogen sulfide (H2S) toxic and corrosive gas from the natural gas processing and utilization industry is a challenging problem for managers of these industries. This problem involves different economic, environmental, and health issues. Various technologies have been employed to remove the H2S gas from these industries, and choosing appropriate H2S removal technologies is a complex multi-criteria decision-making (MCDM) problem. In this regard, the present research work aims at developing a novel decision support system (DSS) by integrating MCDM techniques based upon the (best worst method) BWM and (alternative ranking order method accounting for two-step normalization) AROMAN methods under the decomposed fuzzy set theory. The DSS is used to assess technologies for removing H2S gas and then choose the best scenario for implementing among these technologies. Fourteen criteria in four environmental, social, economic, and efficiency aspects and five technologies of fixed-bed activated carbon technology (A_h2s1), biotrickling filter technology (A_h2s2), scavenger technology (A_h2s3), chemical oxidation scrubber technology (A_h2s4), and liquid redox technology (A_h2s5) have been chosen for evaluation. The final value of each technology is obtained as A_h2s1 (0.5550), A_h2s2 (0.5262), A_h2s3 (0.5809), A_h2s4 (0.6357), and A_h2s5 (0.5790). The results reveal that the chemical oxidation scrubber technology (A_h2s4) and biotrickling filter technology (A_h2s2) with the values of 0.6357 and 0.5262 are respectively the best and worst scenario for the removal of H2S produced by the natural gas processing and utilization plants of Iran. Therefore, the DSS is feasible and applicable and gives reliable and robust findings for acquiring the optimal H2S removal technology.

Optimum selection of nature-inspired texture pattern for cutting tool surface using an integrated multi-criteria decision-making approach: a comparative analysis

Purpose This paper aims to focus on the selection of an appropriate nature-inspired texture pattern for cutting tool tribological surface. The selection process uses the recognized skin textures of different snakes scrolling on highly rough and projected surface conditions to analyze suitability of texture based on the texture geometry and machining conditions. The work also aims to propose a texture pattern selection process to incorporate on cutting tool tribological surface. Design/methodology/approach The selection of alternative nature-inspired texture patterns based on the texture pattern geometry and machining properties leads to a multi-criteria decision-making problem. Thirteen criteria are considered for selecting an appropriate texture pattern among 14 alternatives, i.e. nature-inspired texture patterns. In the present work, an integrated analytical hierarchy process (AHP)-TOPSIS, AHP-multi-objective optimization on the basis of ratio analysis (MOORA) and AHP-Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) approaches have been proposed for the selection of an appropriate nature-inspired texture pattern. AHP is used for the formulation of decision-making matrix and criteria weight calculations and ranking of alternatives is done by three methods. Spearman’s correlation compared and found positive relations between rank assigned by methods. Experimental validation is done in Lathe for selected texture effects. Findings The texture parameters C-1 (Width of texture) and C-2 (Depth of texture) are found significant, while T-2 (Blended Krait) and T-6 (Banded Racer-1) texture is found optimal to generate on cutting tool surface. Research limitations/implications Only some nature-inspired texture patterns have been recognized before the selection; an infinite number of textures are available in nature. The size of the texture pattern is difficult to identify by the selection process because each texture pattern may have different effects on tribological surfaces. Practical implications The proposed selection methodology of nature-inspired texture patterns will help identify optimal texture geometry for specific tribological applications. The nature-inspired texture patterned tool has a significant impact on the cutting force and temperature due to its tribological effect on the cutting tool surface; it decreases the power required for machining. The machining characteristics like roughness are found to decrease by using nature-inspired texture patterned tools. Social implications Various nature-inspire texture studies to generate specific effects on the tribological surfaces may be started study for the surface of aircraft, ships, bearings, etc. Small and big fabrication industries may benefit by decreasing the cost of machining using nature-inspired texture-patterned tools. Research society will pay attention to nature’s inspiration. Originality/value Novel snake-skin-inspired texture patterns are recognized and hybrid MCDM methods are proposed to select optimal texture pattern. Proposed method used single time normalization to effectively rank the alternatives. The insights gained from this research can be extrapolated to address similar challenges in selecting nature-inspired textures for various applications. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-05-2024-0163/

Selection of the Optimum Material for Prefabricated Structures by AHP

The construction sector is known as the least digitalized sector after the hunting and agriculture sectors among 22 sectors. The beginning of the industrialization process in the construction sector has entered our lives with prefabrication. Prefabricated systems accelerate the construction process and enable faster production. The emerging prefabricated construction technology contributes to faster, easier, and more cost-effective construction of buildings. Today, interest and demand for prefabricated structures have increased. Multi-criteria decision-making (MCDM) is a method that helps to determine the best choice by evaluating various criteria together. The use of AHP (Analytic Hierarchy Process), which is one of the MCDM methods, is frequently preferred in solving multi-criteria decision-making problems. Within the scope of the article; it is aimed to be an interdisciplinary study by evaluating prefabricated structures, which are accepted as the beginning of industrialization in the construction sector, and MCDM methods together. In this article, alternative materials used in prefabricated building systems and sub-criteria affecting the materials were analyzed. AHP was used as the methodology in the study and the selection of the optimum material for prefabricated structures was carried out. In order to apply the method, appropriate criteria were determined and then the criteria were scored by experts in the field. Then, the values of 3 types of materials (alternatives) for prefabricated buildings were determined. After the AHP method was applied, it was found that the optimum material among the alternatives was steel.

A new probabilistic linguistic decision-making process based on PL-BWM and improved three-way TODIM methods

Probabilistic linguistic term sets (PLTSs) provide a flexible tool to express linguistic preferences, which allow decision-makers to label linguistic information with different probabilities. In this paper, a method based on a PLTS is proposed to address multi-criteria decision-making problems (MCDM). We develop the theory of PLTSs and put forward a novel best–worst method (BWM), termed PL-BWM, based on PLTS. Our method fully reflects the preference information of decision-makers and accurately provides the importance level of the criteria. The combined weight of the criteria is obtained by merging PL-BWM-based subjective weights and similarity minimization-based objective weights. Upon introducing a three-way decision system to improve the TODIM method, a novel three-way TODIM method is proposed and showcased on an optimal new energy vehicle selection problem. The effectiveness and accuracy of the proposed method are verified by sensitivity analysis and comparative analysis. Our approach paves the way for new developments in solving MCDM problems and for novel applications in otherwise difficult ranking problems.

Interval-valued q-rung orthopair fuzzy complex proportional assessment-based approach and its application for evaluating the factors of blockchain technology in various domains

Blockchain technology (BT) is a digitally decentralized, distributed and public ledger, which considers a secure and viable solution for storing and accessing the record transactions in a public or private peer-to-peer network and assures a smart world of automation of complex services. This paper aims to evaluate the factors persuading the BT adoption and also to assess the possible application areas for the adoption of BT. Implementation of the BT process considers multiple criteria and alternatives with uncertain information; therefore, it can be considered as an uncertain multi-criteria decision-making problem. In this context, a hybrid approach is proposed based on the criteria interaction through inter-criteria correlation (CRITIC) and the complex proportional assessment (COPRAS) methods with interval-valued q-rung orthopair fuzzy set (IVq-ROFS) named as the “IVq-ROF-CRITICCOPRAS” framework. In this approach, the significance values of the factors are computed through novel score function-based CRITIC model, whereas the CRITIC-based COPRAS model is employed to rank different domains/application areas for the adoption of BT under IVq-ROFSs environment. In this regard, a novel score function is introduced with its desirable characteristics. Further, the developed model is executed on a case study of BT adoption considering 14 factors, which confirms the efficiency and applicability of introduced approach. Based on the results, the healthcare BT alternative is most appropriate among the others. To evaluate its permanence, sensitivity analysis with regard to various ratings of decision strategic coefficient is presented under IVq-ROFS context. The strength of the developed approach is emphasized by comparing it with some of the former models under the context of IVq-ROFSs. The proposed extension of the COPRAS approach can be utilized to solve other complex group decision-making problems with uncertainties.

Applications of T-spherical fuzzy aczel-alsina power muirhead mean operators in identifying the most effective water purification process for commercial purpose

One of the key areas of research in ambiguous and inconsistent problems with decision-making is T-spherical multiple-attribute decision making (TSP-FMADM). The TSP-F number (TSP-FN), which is an extension of the fuzzy number, an intuitionistic fuzzy number, and other fuzzy structures, may deal with problems involving a significant amount of incorrect, incomplete, and inconsistent data. Being an extension of various fuzzy structures, the TSP-F sets (TSP-FSs) provide decision-makers greater freedom to voice their actual opinions and offer a broader range of acceptable membership grades. The Muirhead mean (MM) operator and power aggregation (PA) operators are illustrations of standard aggregation operators. They are better because they can reproduce the relationships amongst input qualities and eliminate the negative influence of obstinate data. Since its publication in 1982, Aczel and Alsina's t-norms have proven to be a highly effective and popular technique for generating aggregation operators of any kind. Furthermore, the parameter belongs to (0,+∞) converts the Aczel-Alsina t-norms into a specific instance of the algebraic t-norms. In this article, novel aggregation operators (AGOs) are suggested, considering the advantages of the TSP-FN, to handle the multi-criteria decision-making problems. These new AGOs consider how various input data are related to one another and can mitigate the impact of inaccurate data at the same time. To strengthen the adaptability of these new AGOs, this article proposes the T-spherical fuzzy Aczel-Alsina power Muirhead mean (TsP-FAAPMM) operator, T-spherical fuzzy Aczel-Alsina power dual Muirhead mean (TsP-FAAPDMM) operator which combines the Aczel-Asina operational rules with the power average/geometric operator and the Muirhead/dual Muirhead mean operators. A variety of fundamental characteristics and special cases with respect to the parameters are explored and it is retrieved that various existing AGOs are special cases of these newly initiated AGOs. Further, weighted forms of these AGOs are established. Then, we set up the multiple attribute decision making (MADM) technique using these AGOs that are suggested to solve MADM problems. We then give a numerical example about industrial water purification selection and compare it to other related MADM techniques that are already in use in the TsP-FN information to demonstrate the effectiveness and appropriateness of the anticipated technique.

The Development of IV-VIKOR Method Under Hesitant Fuzzy Sets in MCDM

Due to its solution correctness and ease of evaluation, the VIKOR approach has already established itself as a popular multi-criterion decision-making (MCDM) method. This strategy focuses on picking and ranking from a list of viable options in order to assist the decision-maker in determining a final course of action. Additionally, it looks for a middle ground to resolve a problem with competing demands. It produces a ranking list of compromises based on a precise measurement of distance from the ideal response. The hesitant fuzzy set (HFS) has furthermore come under increased study because of its potency and ability in capturing ambiguity and uncertainty. This paper introduces the inversion of VIKOR method (IV-VIKOR) to take uncertain fuzzy conditions into account. These novel concepts serve as the foundation for an IV-VIKOR method that we suggest, and a real-world application is given to demonstrate how well our method works when dealing with MCDM problem with hesitant fuzzy preference data.

Evaluation of sustainable hydrogen production technologies by fuzzy AHP analysis with bootstrapping

The concept of a hydrogen economy has received increasing attention worldwide. Hydrogen is a promising energy carrier that contributes to the development of a sustainable and reliable energy sector. Selection of the most sustainable hydrogen production technology (HPT) plays a significant role in promoting a hydrogen economy. However, it is regarded as a multi-criteria decision-making (MCDM) problem with several incompatible evaluation criteria. In this study, we develop an MCDM approach based on Fuzzy Analytic Hierarchy Process (FAHP) for prioritizing HPT alternatives, focusing on Egypt as a case study. Our contributions are twofold. First, to combat the issue of a small number of subject matter experts, a bootstrap method is employed to validate the main criteria weights in FAHP. Second, we conduct a comparative FAHP analysis from a broad perspective of the national experts from a developing country and the international experts from developed countries. Our results show that PV electrolysis is the most preferable technology option from the perspectives of both the national and international experts. Since the FAHP approach proposed is a flexible framework that can be applied to countries other than Egypt, it will support global policymakers and industry stakeholders in their decision making toward a sustainable and efficient hydrogen economy strategy.

Group decision-making with hesitant fuzzy linguistic preference relations in view of worst and average indexes

To address the situation where Multi-criteria group decision-making (MCGDM) problems with hesitant fuzzy linguistic preference relations (HFLPRs), this study introduces a group decision-making (GDM) method in view of the worst additive consistency index (WACI) and average additive consistency index (AACI) simultaneously. First, several optimization models are constructed for deriving the WACI and AACI. The main characteristic of the constructed optimization models is that it takes into accounted the personalized individual semantics (PISs). And then the concept of acceptable additive consistent HFLPRs is developed based on the proposed WACI and AACI. Second, several optimization models are constructed for improving the consistency of HFLPRs. Two predefined thresholds for the WACI and AACI are considered in the proposed optimization models. It requires the consistency levels of all the linguistic preference relations (LPRs) associated with HFLPR meet the threshold of WACI, and the average consistency level of all LPRs reaches the threshold of AACI. Third, an algorithm is designed for deriving priority weights from acceptable consistent HFLPRs. Finally, the presented models are validated using a numerical example and extensive comparative analyses.

Health Insurance Provider Selection Through Novel Correlation Measure of Neutrosophic Sets Using TOPSIS

Risk monitoring aims to recognize and control potential threats to our assets or health activities. Insurance is vital, as it compensates for any unexpected loss of property or life. Clients selecting the best health insurance provider must consider various factors and their relative significance to their circumstances. Multi-criteria decision-making (MCDM) helps people analyze and compare policy alternatives to find the best option. This research aims to assist potential health policy purchasers by addressing the selection of health insurance providers as an MCDM problem. The correlation coefficient is useful for identifying the importance of several conflicting criteria. The idea of correlation coefficients is extended in a neutrosophic context to capture the indeterminacy and incomplete information in the relationship among the criteria. The technique for order preference by similarity to an ideal solution (TOPSIS) approach is a useful and straightforward approach to solving MCDM problems. However, it often became ambiguous to researchers due to its involvement in the distance measure technique. The proposed neutrosophic correlation measure may also replace the ambiguity of using a suitable distance measure in the TOPSIS approach. This study extends the TOPSIS method by using the proposed neutrosophic correlation coefficient on single-valued neutrosophic sets (SVNSs). The criteria preferences are computed using a method based on the removal effects of the criteria (MEREC) approach. Some valuable concepts, like the weighted closeness measure of type I and type II and the weighted index parameter, are introduced with their properties to establish the proposed neutrosophic TOPSIS approach. An MCDM approach for health insurance providers has been constructed to illustrate the proposed approach numerically. The proposed method suggest that the health insurance provider ϒ2 is the most beneficial alternative, whereas ϒ1 is the least suitable. The client considers the terms and conditions for non-coverage and the facilities provided for pediatric and maternity care while buying health insurance. The comparative analysis of the suggested technique demonstrates the merit of the research in terms of consistency. The sensitivity analysis demonstrates the flexibility and robustness of the obtained results.

Optimisation problem of China’s supply chain transportation issues in European logistics

The paper highlights the importance and validity of the research problem: the major consequence for logistics arising from China’s logistics market due to its effective short-term and long-term strategies and developing transportation wholesale. The presented viewpoint helps to clearly understand the international perspective of the vastly enlarging China’s supply chain market due to its strong links with logistics centres. In recent years, much scientific research and studies have been conducted in China and Europe regarding China’s transport evolution era, from the production stage to the physical distribution stage, involving multiple steps until loads are in customers’ hands. The article considers the optimisation problem of a supply chain with multiple periods and diverse means of transportation. The considered problem can be formulated as a dynamic multi-criteria decision-making problem, in which the criteria are minimising the total cost, minimising the carbon footprint, and minimising the average transporting time.

A new virtual water qualimeter with a changeable broken linear pointer based on a quadrant circular constellation graph

ABSTRACT As water is a very important natural resource for humans and its quality is closely related to human health, water quality evaluation (WQE) is very important for the protection of human health, livelihoods, environment, and management of water. Although various WQE methods have been developed and used, a common drawback is that the methods lack visualization of the WQE results and require additional complicated graphical techniques. The Pointer meter is an analogue measuring device with a pointer indicating the measured value with its location. A constellation graph (CG) enables to map multi-dimensional data on a two-dimensional plane. By introducing the pointer meter and CG for WQE, this paper proposes a new visualized pointer meter-type virtual water qualimeter (VWQ-meter) based on a quadrant circular constellation graph (QCCG). It has a changeable broken linear pointer with variable lengths and shapes, while the traditional pointer meters have straight-line pointers with a fixed length and a straight-line shape. It evaluates the water quality not only quantitatively but also intuitively as in the pointer meters. To demonstrate its effectiveness, it is applied to one example of WQE. It could be widely applied to not only WQE but also various multi-criteria decision-making (MCDM) problems arising in water pollution evaluation, water resource management, water supply, and wastewater treatment.

Site Selection Decision-Making for Offshore Wind-to-Hydrogen Production Bases Based on the Two-Dimensional Linguistic Cloud Model

Offshore wind-to-hydrogen production is an effective means of solving the problems of large-scale grid-connected consumption and high power transmission costs of offshore wind power. Site selection is a core component in planning offshore wind-to-hydrogen facilities, involving careful consideration of multiple factors, and is a classic multi-criteria decision-making problem. Therefore, this study proposes a multi-criteria decision-making method based on the two-dimensional linguistic cloud model to optimize site selection for offshore wind-to-hydrogen bases. Firstly, the alternative schemes are evaluated using two-dimensional linguistic information, and a new model for transforming two-dimensional linguistic information into a normal cloud is constructed. Then, the cloud area overlap degree is defined to calculate the interaction factor between decision-makers, and a multi-objective programming model based on maximum deviation-minimum correlation is established. Following this, the Pareto solution of criteria weights is solved using the non-dominated sorting genetic algorithm II, and the alternatives are sorted and selected through the cloud-weighted average operator. Finally, an index system was constructed in terms of resource conditions, planning conditions, external conditions, and other dimensions, and a case study was conducted using the location of offshore wind-to-hydrogen production bases in Shanghai. The method proposed in this study demonstrates strong robustness and can provide a basis for these multi-criteria decision-making problems with solid qualitative characteristics.

Similarity Measures of Probabilistic Interval Preference Ordering Sets and Their Applications in Decision-Making

The concept of probabilistic interval preference ordering sets (PIPOSs) provides a scientific and intuitive framework for solving real-life multi-criteria group decision-making problems. In some areas such as investment decision-making and supplier selection, PIPOSs have a wider application space, and the development of similarity and distance measures based on PIPOSs holds great significance. Similarity measure is a basic and prominent tool for dealing with imperfect and ambiguous information in fuzzy sets, but it can also be used to deal with uncertain information in preference ordering. These metrics play an important role in the actual decision-making process, as they effectively quantify the degree of similarity between two PIPOSs, and further allow for the prioritization of different scenarios. In this article, we sort out the definitions and arithmetic rules of PIPOSs, and creatively propose several new similarity measures based on PIPOSs. Then, we propose a group decision-making method based on similarity measures and conduct a comparative study with three existing similarity measures to illustrate its advantages over existing metrics. Finally, we confirm its validity through numerical illustrations in the case study, and also conduct a comparative assessment to verify the scientific validity and effectiveness of the newly introduced measure against the existing metrics.

Development of the rough Defining Interrelationships Between Ranked criteria II method and its application in the MCDM model

Although numerous methods of multi-criteria decision-making have been developed so far, there are still those that have not been improved by different theories that deal well with uncertainties and inaccuracies that are a normal occurrence in everyday life. The goal of this research is the development of the Rough Defining Interrelationships Between Ranked Criteria II (Rough DIBR II) method and the presentation of its application in the multi-criteria decision-making (MCDM) problem, specifically in human resource management (HRM). The paper presents the subject-developed method and its practical application in the MCDM model with the Rough Additive Ratio Assessment (Rough ARAS) method. In order to check the consistency and validity of the proposed methodology, a sensitivity analysis and a comparative analysis were performed. The conclusions of this research indicate a stable and valid proposed methodology, as well as the possible application of the Rough DIBR II method for defining weighting coefficients of criteria in real-life decision-making problems.

Empowering decentralized identity systems for Web 3.0 in complex spherical fuzzy knowledge

The Web 3.0 network system, the next generation of the world wide web, incorporates new technologies and algorithms to enhance accessibility, decentralization, and security, mimicking human comprehension and enabling more personalized user interactions. The key component of this environment is decentralized identity management (DIM), embracing an identity and access management strategy that empowers computing devices and individuals to manage their digital personas. Aggregation operators (AOs) are valuable techniques that facilitate combining and summarizing a finite set of imprecise data. It is imperative to employ such operators to effectively address multicriteria decision-making (MCDM) issues. Yager operators have a significant extent of adaptability in managing operational environments and exhibit excellent effectiveness in addressing decision-making (DM) uncertainties. The complex spherical fuzzy (CSF) model is more effective in capturing and reflecting the known unpredictability in a DM application. This research endeavors to enhance the DM scenario of the Web 3.0 environment using Yager aggregation operators within the CSF environment. We present two innovative aggregation operators, namely complex spherical fuzzy Yager-ordered weighted averaging (CSFYOWA) and complex spherical fuzzy Yager-ordered weighted geometric (CSFYOWG) operators. We elucidate some structural characteristics of these operators and come up with an updated score function to rectify the drawbacks of the existing score function in the CSF framework. By utilizing newly proposed operators under CSF knowledge, we develop an algorithm for MCDM problems. In addition, we adeptly employ these strategies to handle the MCDM scenario, aiming to identify the optimal approach for ensuring the privacy of digital identity or data in the evolving landscape of the Web 3.0 era. Moreover, we undertake a comparative study to highlight the veracity and proficiency of the proposed techniques compared to the previously designed approaches.

Auditing road safety achievement using MEREC–ARAS–QBKM model: an empirical study for APEC member economies

Progress monitoring and action recalibrations are advocated as promising methods for improving road safety, which significantly relates to economic stability and social development. To achieve this, an auditing framework that can evaluate road safety and aid in policymaking is urgently required. To this end, this study developed a systemic decision model that integrates the method based on the removal effects of criteria (MEREC), additive ratio assessment (ARAS), and quantile-based k-means clustering (QBKM), termed MEREC–ARAS–QBKM, with the aim of auditing road safety achievements and providing corresponding policy suggestions with substantial reliability. In particular, the performance of the traditional k-means clustering model was improved by implanting quantiles to determine the initial clustering, which overcomes the uncertainty of k-means clustering owing to the variety of initial cluster centers. Multiple comparisons of empirical results based on a case study of the Asia-Pacific Economic Cooperation (APEC) member economies verified the robustness of the proposed model, demonstrating its applicability, practicability, and reliability in handling real-world multi-criteria decision-making problems in the field of road safety. The empirical findings show that road safety developments among the APEC countries are of class differentiation, suggesting an urgent regional benchmarking. Overall, the proposed methodology empowers decision-makers and policymakers in APEC to swiftly formulate effective action plans, countermeasures, and investment schemes, ultimately contributing to the enhancement of road safety performance and socio-economic benefit across APEC members.

Generalized picture fuzzy Frank aggregation operators and their applications

Picture fuzzy sets with four-dimensional features are widely used in decision-making as a mathematical tool because they can capture the uncertainty of data. However, the methods and techniques based on matrix theory are difficult to solve the decision problem involving high-dimensional data in a picture fuzzy setting. Therefore, operators that can identify high-dimensional data in a picture fuzzy environment are proposed to address this challenge. In this paper, firstly, by integrating the Frank operators into the picture fuzzy tensor, the generalized picture fuzzy Frank weighted arithmetic (GPFFWA) and generalized picture fuzzy Frank weighted geometric (GPFFWG) operators are defined. Their specific expressions are discussed, and the idempotency, order-preservation, boundedness, and commutativity of the proposed operators are also given. Then, combining the GPFFWA and GPFFWG operators, an algorithm is designed to solve the multi-criteria decision-making problem with high-dimensional data features in the picture fuzzy environment. Finally, a numerical example and related analysis demonstrate the effectiveness, superiority, and flexibility of the suggested technique. This work provides new theoretical and methodological support for developing and practicing the decision-making discipline.