Multi-criteria Decision-making Problem Research Articles

Prioritizing Barriers Influencing Educators in Adoption of Augmented Reality in K-5 Education

Introduction: Indian education system still uses textbooks-based learning or some sort of digital modes for explaining the concepts to the children. These may benefit to some students, but young minds prefer learning in a fun way. Once they start learning complex concepts especially in mathematics, physics, or subjects like history they feel bored and hence they loose interest in the subject. Augmented Reality is a technology that bridges the gap between physical and virtual world and gives immersive experience to the user. Augmented Reality is widely used in higher education but the implementation at primary level is still limited. Therefore, the purpose of this research is to find the critical barriers to augmented reality technology in Indian education sector for K-5 school going children to allow its wider adoption. The objective is to identify the gaps and those hinderences to the wider usage so that obstacles can be handled before developing the AR applications. Objectives: The objective of this research is to find the influencing factors impacting the adoption of AR in education sector. The study also aims to find the important sub factors influencing the adoption of AR in education sector. Methods: The paper first identifies different factors influencing the adoption of AR in education sector of India for K-5 school children based on existing literature. After that, they were prioritized using AHP to determine their relative importance. The AHP is a multi-criteria decision making (MCDM) method that incorporates all aspects into a hierarchical model and bases its importance on pairwise comparisons using the Satty scale. Fifteen influencing factors were catergized into four main factors namely Pedagogy (P), Content (C), Technical Resources (TR) and Layout and Design (L&D). A survey containing pair-wise comparisons of factors and sub factors were collected from ten experts working in a higher position in different companies and in the education sector with a minimum of 10 years of experience. Results: Based on the result obtained, the findings reveal that “Pedagogy” and “Content” are the most important factors which influence the adoption of AR in education sector. Aditionnaly, simplicity/usability in AR mobile applications, proper content matching with school standards, teacher training for new advancements in the technology, and availability of resources are the important sub factors to considered before implementing AR applications for the school children. Conclusions: The study has given the conceptual model which has addressed several factors and sub factors to be taken care of for successful adoption of AR in education among school children. This research assist policymakers, industrialists, and institutional leaders in designing practical augmented reality (AR) initiatives. Originality/value: Most of the literature focuses on the factors influencing the adoption of AR in different industries and countries but very few studies have focused on K-5 class group children in India. This research plays vital role in those education setups where teaching using latest technoglies is mandatory. The present study also contributes to this area by formulating a research problem as an MCDM problem and by using AHP as a methodology to determine the weigths of factors and sub-factors infleucnign the adoption of AR in education sector.

Assessment of air purifiers for improving the air quality index using circular intuitionistic fuzzy Heronian means

The impact of airborne pollutants present in the environment, entering the body through breathing, can cause significant risks of respiratory and heart-related health problems for individuals. For this, different air purifiers are commonly used to eliminate delicate particulate matter PM2.5, and various studies have examined their effectiveness. This paper aims to analyze airborne pollutants and, by considering them, assess the performance of air purifiers in reducing the concentration of air pollutants in the environment. The aggregation operator (AO) plays a significant role in aggregating the multiple criteria and gives us a result in a singleton set, which assists us in decision-making (DM). So, considering this, the Heronian mean (HM) operator and its special cases such as averaging and geometric operators have been used in this paper. Moreover, circular intuitionistic fuzzy (C-IF) theory is more efficient and comprehensive than the intuitionistic fuzzy set (IFS), as the standard IFS cannot cope with the problems within a circular environment. So, the HM operator under the C-IF environment, such as circular intuitionistic fuzzy Heronian mean (C-IFHM) and it’s averaging and geometric operator, has been presented. Further, some prevalent and crucial properties and theorems have been defined. Then, an algorithm was developed to solve a multicriteria decision-making (MCDM) problem by using the proposed operators within the circular environment. To validate the effectiveness and priority, this paper presents a numerical example of MCDM, and a comparison analysis was conducted to verify the practicality of the proposed approach.

An integrated multi criteria decision making method using dual hesitant fuzzy sets with application for unmanned aerial vehicle selection

Unmanned aerial vehicles (UAVs) have gained widespread attention in recent years due to their expanding applications across various industrial sectors. Selecting the most suitable UAV for a given task is a critical decision-making challenge, which is typically modeled as a multi-criteria decision-making (MCDM) problem. However, expert assessments in such selection processes often involve considerable uncertainty and hesitation. To address this, this paper proposes a novel integrated MCDM framework that combines dual hesitant fuzzy sets (DHFSs), the best-worst method (BWM), and the MULTIMOORA method to evaluate and rank UAV alternatives. In the proposed method, DHFSs are employed to capture both membership and non-membership degrees of expert assessments under uncertainty, while expert weights are objectively determined based on the entropy of their assessments. Criteria weights are then calculated using an extended dual hesitant fuzzy BWM. Subsequently, the MULTIMOORA method is extended into the dual hesitant fuzzy environment, where UAV alternatives are evaluated from three perspectives: the ratio system, the extended reference point approach, and the full multiplicative form, and the evaluation results are aggregated to generate a comprehensive and reliable final ranking. To demonstrate the practicality and effectiveness of the proposed method, a case study on UAV selection for power line inspection is presented. The results show that the proposed approach effectively handles uncertainty, produces stable and consistent rankings, and offers reliable decision support under uncertain and fuzzy conditions. The proposed method provides a flexible and systematic decision-making tool that can assist decision-makers in solving UAV selection problems in complex, real-world scenarios.

A Hybrid Prospect–Regret Decision-Making Method for Green Supply Chain Management Under the Interval Type-2 Trapezoidal Fuzzy Environment

The concept of green supply chain management (GSCM) describes how to reduce the negative impact of the supply chain on the environment while balancing the economic and social benefits of a company being in the supply chain. Selecting the optimal multi-dimensional GSCM scheme, a typical multi-criteria decision-making (MCDM) problem, is a crucial step in implementing the GSCM concept. Therefore, this paper constructs a multi-dimensional GSCM index system for the comprehensive analysis of the important influencing factors of GSCM. Then, cross-entropy combining the interval type-2 trapezoidal fuzzy set (IT2TFS) is adopted to determine the weight distribution of GSCM indices, and a hybrid MCDM method integrating the IT2TFS prospect–regret method is proposed to analyze the psychological behaviors of decision makers who are selecting the best GSCM scheme. Moreover, the case study, comparative analysis, and sensitivity analysis are presented to verify the effectiveness and reasonableness of the proposed MCDM method. The results affirm the validity of the proposed MCDM method, with A4 identified as the optimal GSCM scheme, demonstrating its effectiveness and applicability in MCDM problems.

A Smart Decision Framework for Sustainable Managementof C&D Waste Using Picture Fuzzy Decision Model

Urbanization and rapid population growth have significantly accelerated the development of urban infrastructure, resulting in an unprecedented surge in construction and demolition (C&D) waste. The unregulated accumulation of this waste poses severe environmental and societal challenges, including greenhouse gas emissions, groundwater contamination, and land degradation. This issue is particularly critical in developing countries, where waste generation is directly linked to population density and industrialization. Given the limited availability of landfill space and the adverse environmental impacts of conventional dumping, the implementation of efficient and sustainable waste management strategies has become imperative. Although several waste treatment and recycling methods exist, selecting the most suitable alternative remains a complex multi-criteria decision-making (MCDM) problem due to the interplay of technical, environmental, and economic factors. This study proposes a systematic decision-making framework under a picture fuzzy MCDM environment to evaluate and rank sustainable C&D waste management solutions. A subjective weighting technique is utilized to determine the relative importance of each criterion, while a compromise ranking method is applied to identify the most promising alternative. The findings reveal that carbonation emerges as the optimal solution due to its potential for maximum waste reduction and enhanced sustainability. The proposed framework provides valuable insights for industry professionals and policymakers, facilitating effective C&D waste management practices and contributing to broader global sustainability objectives.

An integrated MCDM approach using double normalization: introducing the DN-WENSLO and DN-RPEM methods for socio-economic performance evaluation

This paper presents two significant additions to the scope of multi-criteria decision-making (MCDM) to assess socio-economic performance across various countries. The current study employed the Double Normalization Root-Proximity Evaluation Method (DN-RPEM), a refined integration approach. Furthermore, it was the first to implement the Double Normalization WENSLO (Weights by envelope and slope) (DN-WENSLO). With an architecture that integrates the RAM and the PIV approaches, the DN-RPEM is an integrated MCDM method for evaluating relative socio-economic performance in multiple countries. This integrated framework applies a linear and non-linear normalization approach to ensure the accuracy and validity of the decisions. At the same time, the DN-WENSLO method provides an advanced way to calculate criteria weights using weighted double normalization. Among the criteria, Unemployment, youth total (UYT) received the highest weight (0.1396), emphasizing its critical impact. At the same time, the mortality rate under 5 (MR) was assigned the lowest weight (0.0740), representing its relatively diminished influence in the analysis. Using the DN-RPEM method, Sweden was ranked as the top performer 1st rank (0.8131), while Pakistan was ranked as the least effective 12th rank (0.6415) among the evaluated countries. The DN-RPEM method outperforms TOPSIS, MOORA, CODAS, ARAS, WSM, and WASPAS in solving some of the best multi-criteria decision problems. Sensitivity analysis shows how rigid and flexible the DN-RPEM and DN-WENSLO methods are relevant to distinct case-specific situations, showing that they can be used for more than just socio-economic assessments.

Environmental Policy Selection Based on Linear-Times-Exponential One-Switch Utility Function and ELECTRE I Method

This paper examines how utility functions perform in tackling the multicriteria decision-making problem, especially one-switch utility function. Linear-times-exponential one-switch, exponential, and linear utility functions are implemented, which transforms corresponding criteria into utilities with ELECTRE I method. The detailed formulation of the decision model is presented. A numerical example about environmental policy selection is introduced to illustrate the use of the new decision model. With different wealth levels and utility functions for a policymaker, the inconsistent outranking policies illustrate the special characteristic of linear-times-exponential one-switch utility function whose initial wealth level has a significant impact on the outranking environmental policy. This study is also the first study applying one-switch utility function in address/ing multicriteria decision-making problem.

Explaining Results of Multi‐Criteria Decision‐Making

ABSTRACTTransparency in computing is an important precondition to ensure the trust of users. One concrete way of delivering transparency is to provide explanations of computing results. To this end, we introduce a method for explaining the results of various linear and hierarchical multi‐criteria decision‐making (MCDM) techniques such as the weighted sum model (WSM) and the analytic hierarchy process (AHP). The two key ideas are (A) to maintain a fine‐grained representation of the values manipulated by these techniques and (B) to derive explanations from these representations through merging, filtering, and aggregating operations. An explanation in our model presents a high‐level comparison of two alternatives in an MCDM problem, presumably an optimal and a non‐optimal one, illuminating why one alternative was preferred over the other. We show the usefulness of our techniques by generating explanations for two well‐known examples from the MCDM literature. Finally, we show their efficacy by performing computational experiments.

Evaluation of E-Banking Systems with Analytic Hierarchy Process Model

E-banking systems streamlines business processes and individual lives. A proper E-banking system helps to drive the economy of a country. However, there are several determinants that may affect customers’ adoption on the E-banking system. Since this is a multi-criteria decision-making problem, analytic hierarchy process (AHP) is used to study the adoption of E-banking among consumers in Malaysia. Risk, convenience, and accessibility are the three most important decision criteria influencing the adoption of E-banking in Malaysia, with weights of 0.2988, 0.2894, and 0.1927. Among the sub-criteria, all-day availability (0.1604), system security (0.1343), ease of understanding (0.1147), function coverage (0.0974), and privacy and confidentiality (0.0967) are the top determinants on the adoption of E-banking in Malaysia. Mobile banking has the highest local weights in terms of service fulfilment (0.4438), risk (0.4227), accessibility (0.4840), convenience (0.5554), and user interface (0.4812). Mobile banking is thus the most preferred E-banking system with regards to all the decision criteria with a global weight of 0.4800. This paper helps the government and banks to identify the most impactful main criteria and sub-criteria to help them improve on the E-banking system to increase customer adoption.

Picture Fuzzy Aczel-Alsina Power Geometric Aggregation Operators and Their Application to Multi Criteria Decision-Making

This paper develops a robust picture fuzzy (PF) decision-making framework by integrating power aggregation operators derived from Aczél-Alsina operations. The proposed power aggregation operators effectively capture intricate interrelationships among multiple criteria, thereby enhancing the precision and reliability of decision-making processes. In this study, the familiarity of decision makers with the evaluated objects is systematically incorporated into the PF framework alongside primary data, ensuring a more comprehensive assessment. Motivated by the operational principles of Aczél-Alsina functions, this research advances the theoretical foundation of PF Aczél-Alsina power-weighted and ordered-weighted geometric operators, seamlessly integrating decision makers’ expertise into the aggregation process. The structural properties and mathematical characteristics of these newly developed operators are rigorously analyzed. To validate their practical applicability, we employ the proposed operators to solve a complex multi-criteria decision-making (MCDM) problem within the food industry, a domain where uncertainty and nuanced judgments play a critical role. A comparative evaluation against existing operators highlights the superior performance of our approach in effectively managing uncertainty, refining decision accuracy, and enhancing adaptability to real-world decision-making challenges.

Pythagorean Fuzzy Overlap Functions and Corresponding Fuzzy Rough Sets for Multi-Attribute Decision Making

As a non-associative connective in fuzzy logic, the analysis and research of overlap functions have been extended to many generalized cases, such as interval-valued and intuitionistic fuzzy overlap functions (IFOFs). However, overlap functions face challenges in the Pythagorean fuzzy (PF) environment. This paper first extends overlap functions to the PF domain by proposing PF overlap functions (PFOFs), discussing their representable forms, and providing a general construction method. It then introduces a new PF similarity measure which addresses issues in existing measures (e.g., the inability to measure the similarity of certain PF numbers) and demonstrates its effectiveness through comparisons with other methods, using several examples in fractional form. Based on the proposed PFOFs and their induced residual implication, new generalized PF rough sets (PFRSs) are constructed, which extend the PFRS models. The relevant properties of their approximation operators are explored, and they are generalized to the dual-domain case. Due to the introduction of hesitation in IF and PF sets, the approximate accuracy of classical rough sets is no longer applicable. Therefore, a new PFRS approximate accuracy is developed which generalizes the approximate accuracy of classical rough sets and remains applicable to the classical case. Finally, three multi-criteria decision-making (MCDM) algorithms based on PF information are proposed, and their effectiveness and rationality are validated through examples, making them more flexible for solving MCDM problems in the PF environment.

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

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

Multi-objective optimization of a two-stage helical gearbox with double gears in second stage using saw technique to reduce bottom area and enhance efficiency

Two-stage helical gearboxes featuring two gears in the second stage are widely used across various industries. This gearbox design helps enhanced load capacity, increases consistent force distribution, and minimizes operational noise. One significant challenge in the design of this type of gearbox is the simultaneous optimization of multiple design criteria, including transmission efficiency and overall size. Optimizing gearbox design involves more than selecting an appropriate gear configuration; it necessitates a complete approach that balances performance with size, ensures sustainable operation, and minimizes manufacturing costs. This study was conducted to develop a method for solving the multi-objective optimization problem (MOOP) related to the design of a two-stage helical gearbox (TSHG) containing double gears in the second stage (DGSS). The primary focus is on two single-objective functions: maximizing gearbox efficiency and minimizing the gearbox bottom area. This study investigates three primary design parameters: the gear ratio of the first stage (u1), the gear width coefficient of the first stage (Xba1), and second stage (Xba2). The optimization process was carried out in two distinct stages. The initial phase focused on the single-objective optimization problem aimed at minimizing the gap among the variable levels. The second stage concentrated on dealing with the MOOP to identify the optimal design parameters. The Simple Additive Weighting (SAW) method was employed to solve the multi-criteria decision-making (MCDM) problem, while the MEREC technique was utilized to establish the weights of the criteria. The implementation of SAW in this context introduces a novel methodology that streamlines the identification of the optimal solution while enhancing the precision of the outcomes. Moreover, addressing the MOOP problem in a two-stage approach reduces the solution process and enhances the precision of the outcomes. The proposed optimized values of the primary design parameters aim to enhance gearbox efficiency and maximize installation space, thereby facilitating potential applications across diverse industries

How to select third-party library: harnessing visual insights and systematic evaluation for informed decisions

The subject of this study is a selection approach for third-party libraries in IT projects based on the collection and analysis of expert evaluations and solving optimization problems. The aim of this study is to minimize the key challenges associated with migrating third-party libraries, including high labor intensity and significant risks that could adversely affect project success. This study sets out several objectives: 1) to create a metric specification to guide evaluation data collection through a survey, focusing on technical metrics. Also, it needs to include recommendations for surveys development; 2) formalize a two-step method that enriches the outcomes and allows for their combined use, where the first step employs radial diagrams to visualize and simplify alternative assessments, and the second step applies the TOPSIS method to address the multi-criteria decision-making problem of selecting a third-party library; 3) the practical application of the proposed approach through illustrative samples. Results. The proposed metrics specification considers the essential technical metrics and offers a unified evaluation solution. We do not limit our approach to technical metrics or numeric data. It is both possible and recommended to include human and economic metrics and to use alternatives to numeric data. The combination of multi-criteria analysis and visual methodologies simplifies the assessment and comparison of libraries, making this approach valuable for developers in practical scenarios. The conclusions of this study emphasize that its findings may lay the groundwork for developing comprehensive decision-support systems focused on third-party library selection, thereby minimizing associated risks. Future developments will include the incorporation of other metrics for library selection, as well as consideration of uncertainty and data subjectivity.

The technique of fuzzy analytic hierarchy process (FAHP) based on the triangular q-rung fuzzy numbers (TR-q-ROFNS) with applications in best African coffee brand selection.

The African coffee market offers a rich and diverse range of coffee profiles. The coffee producers of Africa face numerous challenges like climate change, market fluctuations, diseases, soil degradation and limited access to finance. These challenges badly affect their productivity, quality and livelihood. There are different factors like social and cultural, which can affect the coffee production. This study aims to develop multi criteria decision making (MCDM) methods and their applications in coffee market specifically in identifying factors influencing consumers' coffee brand preferences in South Africa, which is known for its vibrant coffee culture. For this purpose, first we developed the technique of analytic hierarchy process (AHP) in the environment of triangular q-rung orthopair fuzzy numbers. The triangular q-rung fuzzy numbers can effectively handle the uncertainity. The AHP technique has widely been used in decision making due to its flexibility in assigning weights and dealing with vagueness. The weights of critera plays a very important role in an MCDM problem. The development of AHP technique in triangular q-rung orthopair fuzzy environment can improve the decision making (DM) by handling vagueness in data and by using the most appropriate weights. Furthermore this new proposed method improves accuracy and minimize the information loss. The newly peoposed method is applied to different MCDM problems and comparative analysis is conducted to check the validity of results.

Sustainable Model for Analyzing the Impact of Social Media on Customer Buying Behavior: A Case Study

In today's digital landscape, chatbots have become widely used across various applications, particularly in systems that provide intelligent assistance to users. To enhance user experience, these systems are often equipped with chatbots capable of processing user inquiries and delivering accurate, timely responses. This study proposes a structured framework for evaluating the impact of social media on customer buying behavior through a case study focused on selecting the most suitable Online Chatbot Platform (OCP). The selection of an optimal OCP is a complex multi-criteria decision-making (MCDM) problem, involving multiple interdependent and often conflicting factors. One of the key challenges in this process is the potential loss of critical decision information and underestimation of engagement complexity in a neutrosophic environment. To address this challenge, this paper introduces a hybrid MCDM framework that integrates Interval-Valued Neutrosophic Sets Analytical Hierarchy Process (IVNSs-AHP) with Weighted Aggregated Sum Product Assessment (WASPAS). The IVNSs-AHP method is employed to determine the relative importance of the evaluation criteria, while WASPAS is used to rank different OCP options. A comprehensive set of assessment criteria, grounded in the principles of sustainable development, was established through an extensive literature review and expert consultations to ensure the practical applicability of the proposed MCDM model.

CoCoSo method based on generalized distance measure with trapezoidal fuzzy multi-numbers for solving multi-criteria decision-making method problems

Abstract In this study, the authors develop the Combined Compromise Solution (CoCoSo) method on trapezoidal fuzzy multi-numbers, where all the decision information takes the form of trapezoidal fuzzy multi-numbers. To construct the method, generalized distance measures between two trapezoidal fuzzy multi-numbers are presented. Finally, a real example is introduced and compared with different methods to show the applicability and feasibility of the proposed multi-attribute decision-making method.

Evaluation on the Preference of Courier Services Using Integrated AHP-TOPSIS Model

Courier services are businesses that deliver documents, parcels and heavy products from one place to another. Courier services are gaining popularity nowadays due to their efficient and reliable delivery. However, the existence of many courier service companies today has led to fierce commercial competition both domestically and globally. Since there are many decision alternatives and criteria to consider, consumers face a significant challenge in choosing the best courier service. As a result, selecting the optimal courier service involves a process of Multi-Criteria Decision Making (MCDM). The objective of this study is to determine the preferred courier service based on undergraduates’ preferences using an integrated AHP-TOPSIS model. The AHP-TOPSIS model is proposed in this study to tackle the MCDM problem as choosing the optimal courier service involves various decision criteria. In this research, AHP is proposed to identify the priority of decision criteria, whereas TOPSIS is utilized to determine the ranking of the courier service providers. Additionally, this study aims to determine the priority of decision criteria. As a result of this research, GD Express was identified as the most preferred courier service provider, followed by DHL, FedEx, Skynet Express, PosLaju, and City-Link Express. Furthermore, the top three influencing factors are freight rates, timeliness and reliability. The significance of this study lies in identifying the most preferred courier service and the most influential decision criterion in the decision-making process. The study can serve as a reference for the less popular courier service companies, assisting them in identifying weaknesses and making enhancements according to the decision criteria’ ranking.

A hybridized Pythagorean fuzzy AHP and WASPAS method for airline new route selection: case study of Turkish Airline

Purpose This study aims to provide a practical and novel solution for the complex multi-criteria decision-making (MCDM) problem of airline route selection, which is characterized by conflicting criteria, alternative routes, and complex judgments. Design/methodology/approach This study proposes a hybrid MCDM approach using Interval-valued Pythagorean Fuzzy AHP and Interval-valued Pythagorean Fuzzy weighted aggregated sum product assessment (WASPAS) methods. Decision analysis is applied to select a new route between different alternatives through selection criteria. Pythagorean Fuzzy AHP is used for weighting criteria, and Pythagorean Fuzzy WASPAS is used for assessing alternatives. The pair-wise linguistic comparisons of selection criteria are transferred into Pythagorean fuzzy numbers (PFNs) to weigh each criterion’s importance. Findings The pair-wise linguistic comparisons of selection criteria are transferred into PFNs to weigh each criterion’s importance. The results of these comparisons show that the main criteria, cost (43% weight) and demand (33% weight), impact route selection decisions more than social/economic conditions (15% weight) and competitiveness (9% weight). Regarding the criteria, the five routes alternative were evaluated by the route development experts, and the best route was selected with Pythagorean Fuzzy WASPAS. Practical implications The proposed model is used for a route selection problem of Turkish Airlines, the airline that flies to the most countries in the world. Originality/value To the best of the authors’ knowledge, this study is the first to use the Interval-valued Pythagorean Fuzzy AHP combined with Interval-valued Pythagorean Fuzzy WASPAS to solve the route selection problem. This hybrid MCDM methodology presents a novel and feasible solution for selecting the new route for airlines.

Evaluating the Impact of Weighting Methods on the Stability of Scores for Alternatives in Multi-Criteria Decision-Making Problems

Criteria weights play a crucial role in Multi-Criteria Decision Making (MCDM) problems when selecting the best alternative from a set of options. This study aims to compare three objective weighting methods: MEthod based on the Removal Effects of Criteria (MEREC), Entropy, and Symmetry Point of Criterion (SPC). These methods were applied to a case study involving the ranking of eight sustainable energy development alternatives, each characterized by seventeen criteria. Four representative MCDM methods, the Simple Additive Weighting (SAW), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Proximity Indexed Value (PIV), and Root Assessment Method (RAM), were also deployed. The results revealed that the Entropy method provided the most stable and consistent performance, followed by the MEREC method, with the SPC method showing the least stability.