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Keywords = extended TOPSIS technique

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34 pages, 2795 KB  
Article
Development of a Decision Support System for Biomaterial Selection Based on MCDM Methods
by Dušan Lj. Petković, Miloš J. Madić and Milan M. Mitković
Appl. Sci. 2025, 15(16), 9198; https://doi.org/10.3390/app15169198 - 21 Aug 2025
Viewed by 690
Abstract
The material selection process can be viewed as a multi-criteria decision-making (MCDM) problem with multiple objectives, which are often conflicting and of different importance. The selection of the most suitable biomaterial is considered as a very complex, important, and responsible task that is [...] Read more.
The material selection process can be viewed as a multi-criteria decision-making (MCDM) problem with multiple objectives, which are often conflicting and of different importance. The selection of the most suitable biomaterial is considered as a very complex, important, and responsible task that is influenced by many factors. In this paper, a procedure for biomaterial selection based on MCDM is proposed by using a developed decision support system (DSS) named MCDM Solver. Within the framework of the developed DSS, the complete procedure for selecting the criteria weights was developed. Also, in addition to the adapted standard MCDM methods such as TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) and VIKOR (VIšekriterijumsko KOmpromisno Rangiranje), an extended WASPAS (Weighted Aggregated Sum Product Assessment) method was developed, enabling its application for considering target-based criteria in solving biomaterial selection problems. The proposed MCDM Solver enables a structured decision-making process helping decision-makers rank biomaterials with respect to multiple conflicting criteria and make rational and justifiable decisions. For the validation of the developed DSS, two case studies, i.e., the selection of a plate for internal bone fixation and a hip prosthesis, were presented. Finally, lists of potential biomaterials (alternatives) in the considered case studies were ranked based on the selected criteria, where the best-ranked one presents the most suitable choice for the specific biomedical application. Full article
(This article belongs to the Special Issue Application of Decision Support Systems in Biomedical Engineering)
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18 pages, 2842 KB  
Article
Optimization of In Vitro Shoot Culture Parameters for Enhanced Biomass and Rosmarinic Acid Production in Salvia atropatana
by Wiktoria Ejsmont, Anna K. Kiss and Izabela Grzegorczyk-Karolak
Molecules 2025, 30(12), 2654; https://doi.org/10.3390/molecules30122654 - 19 Jun 2025
Cited by 1 | Viewed by 683
Abstract
Salvia atropatana is a medicinal plant native to Middle Eastern countries. It has been traditionally used in Turkish and Iranian folk medicine to treat infections, wounds, inflammatory diseases, spastic conditions, and diabetes. Its therapeutic potential has been attributed to its essential oil, polyphenolic [...] Read more.
Salvia atropatana is a medicinal plant native to Middle Eastern countries. It has been traditionally used in Turkish and Iranian folk medicine to treat infections, wounds, inflammatory diseases, spastic conditions, and diabetes. Its therapeutic potential has been attributed to its essential oil, polyphenolic acid, flavonoid, and diterpenoid content. The aim of the study was to determine the optimal conditions of in vitro S. atropatana shoot culture to enhance proliferation and secondary metabolite production. It examined the effects of various cytokinins and culture duration on culture growth parameters and phenolic compound accumulation. Exogenous cytokinin supplementation significantly enhanced shoot proliferation, with the highest proliferation ratio (6.3) observed with 1 and 2 mg/L 6-benzylaminopurine (BAP). Biomass accumulation was the highest at 0.5 mg/L BAP, followed by 1 and 2 mg/L meta-toplin (mTOP). Phenolic profiling identified nine compounds, with rosmarinic acid (RA) as the dominant metabolite. The highest RA content (16 mg/g dry weight) was achieved with 1 and 2 mg/L BAP and 0.5 mg/L of its ryboside. The TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method identified 1 mg/L BAP as the optimal treatment, balancing high proliferation, biomass, and polyphenol accumulation. Extending culture duration to 50 days increased biomass and phenolic content reaching 19.25 mg/g dry weight. However, morphological changes, including apical necrosis, were observed, and a significantly longer cultivation period was needed, questioning the value of the procedure. This study provides a basis for scalable in vitro production of bioactive compounds in S. atropatana. Full article
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19 pages, 354 KB  
Article
Customer Clustering and Marketing Optimization in Hospitality: A Hybrid Data Mining and Decision-Making Approach from an Emerging Economy
by Maryam Deldadehasl, Houra Hajian Karahroodi and Pouya Haddadian Nekah
Tour. Hosp. 2025, 6(2), 80; https://doi.org/10.3390/tourhosp6020080 - 9 May 2025
Cited by 2 | Viewed by 1617
Abstract
This study introduces a novel Recency, Monetary, and Duration (RMD) model for customer classification in the hospitality industry. Using a hybrid approach that integrates data mining with multi-criteria decision-making techniques, this study aims to identify valuable customer segments and optimize marketing strategies. This [...] Read more.
This study introduces a novel Recency, Monetary, and Duration (RMD) model for customer classification in the hospitality industry. Using a hybrid approach that integrates data mining with multi-criteria decision-making techniques, this study aims to identify valuable customer segments and optimize marketing strategies. This research applies the K-means clustering algorithm to classify customers from a hotel in Iran based on RMD attributes. Cluster validation is performed using three internal indices, and hidden patterns are extracted through association rule mining. Customer segments are prioritized using the TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method and Customer Lifetime Value (CLV) analysis. The outcomes revealed six distinct customer clusters, identified as new customers; loyal customers; collective buying customers; potential customers; business customers, and lost customers. This study helps hotels to be aware of different types of customers with particular spending patterns, enabling hotels to tailor services and improve customer retention. It also provides managers with appropriate tools to allocate resources efficiently. This study extends the traditional Recency, Frequency, and Monetary (RFM) model by incorporating duration, an overlooked dimension of customer engagement. It is the first attempt to integrate data mining and multi-criteria decision-making for customer segmentation in Iran’s hospitality industry. Full article
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31 pages, 1306 KB  
Article
Evaluation of Adjustment Effects of Highway Guide Signs Based on the TOPSIS Method
by Jin Ran, Meiling Li, Jian Rong, Ding Zhao, Ahmetjan Kadir and Qiang Luo
Appl. Sci. 2025, 15(9), 4949; https://doi.org/10.3390/app15094949 - 29 Apr 2025
Viewed by 647
Abstract
With the rapid expansion of highway networks, the demand for timely and reliable road information has steadily increased. However, some guide signs on newly built or extended highways in China have not been updated or adjusted in time, resulting in incomplete information and [...] Read more.
With the rapid expansion of highway networks, the demand for timely and reliable road information has steadily increased. However, some guide signs on newly built or extended highways in China have not been updated or adjusted in time, resulting in incomplete information and non-standard setups. These issues not only affect drivers’ navigation experience but may also negatively impact road safety and traffic efficiency. Therefore, it is crucial to establish a scientifically sound evaluation system and a comprehensive assessment model for highway guide signs. This study selected a representative highway (G2 Expressway in China) as the research subject and combined questionnaire surveys with field investigations to identify common issues such as vague information and irregular placement of guide signs. Through an in-depth analysis of travel demand, the core requirements of drivers were summarized as safety, efficiency, and comfort. Based on these insights, the study proposes four key design principles for guide signs: standardization, readability, continuity, and consistency. A set of quantifiable evaluation indicators was developed through a comprehensive analysis of key factors affecting signage performance, and factor analysis was applied to verify the independence and rationality of the indicators. On this basis, an evaluation model was constructed using the technique for order preference by similarity to ideal solution (TOPSIS) to scientifically quantify the effectiveness of guide signs. The model was applied in a field study on the Hebei section of the G2 Expressway in China (with comprehensive traffic sign coverage, high traffic volume, and more traffic sign issues), with results demonstrating the feasibility and practicality of the proposed evaluation system and model. This research offers a systematic solution to enhance the service quality of highway guide signs and provides essential references for future highway planning and management practices. It aims to comprehensively improve drivers’ travel experiences and promote the development of sustainable and intelligent transportation networks, offering valuable insights for building integrated urban systems. Full article
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31 pages, 6835 KB  
Article
Identification of Critical Track Sections in a Railway Station Using a Multiplex Networks Approach
by Pengfei Gao, Wei Zheng, Jintao Liu and Daohua Wu
Mathematics 2025, 13(7), 1151; https://doi.org/10.3390/math13071151 - 31 Mar 2025
Cited by 1 | Viewed by 403
Abstract
Railway stations serve as critical nodes within transportation networks, and the efficient management of in-station track sections is vital for smooth operations. This study proposes an integrated method for identifying critical track sections, which refers to track sections with the highest static occupancy [...] Read more.
Railway stations serve as critical nodes within transportation networks, and the efficient management of in-station track sections is vital for smooth operations. This study proposes an integrated method for identifying critical track sections, which refers to track sections with the highest static occupancy rates (HiSORTS), in railway station yards using a multiplex network framework. By modeling the station as a Railway Station Multiplex Network (RSMN) that incorporates train routes (TRs), extended routes (ERs), and shunting routes (SRs), the proposed approach overcomes the limitations of single-layer, single-metric analyses and effectively captures complex operational characteristics. Classical network metrics, including Degree Centrality (DC), Betweenness Centrality (BC), Closeness Centrality (CC), Katz Centrality (KC), and PageRank (PR), along with a custom Fusion Centrality (FC), are used to quantify track section importance. Principal Component Analysis (PCA) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) are applied to generate rankings, which are further analyzed using SHapley Additive exPlanations (SHAP)-based matrics contributions analysis. The results indicate that TR metrics contribute the most (50.3%), followed by ER (25.5%) and SR (24.2%), with KC and FC being the most influential metrics. The findings provide a robust decision-support framework for railway operations, facilitating targeted maintenance, congestion mitigation, and efficiency optimization. Full article
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29 pages, 7569 KB  
Article
Enhancing User Experience in Smart Tourism via Fuzzy Logic-Based Personalization
by Konstantina Chrysafiadi, Aristea Kontogianni, Maria Virvou and Efthimios Alepis
Mathematics 2025, 13(5), 846; https://doi.org/10.3390/math13050846 - 3 Mar 2025
Cited by 3 | Viewed by 2676
Abstract
In the era of smart tourism, providing seamless and personalized experiences has become significant for enhancing user satisfaction and engagement. This paper presents a novel fuzzy logic-based application system designed to enhance personalization in smart tourism. The proposed system integrates real-time user data [...] Read more.
In the era of smart tourism, providing seamless and personalized experiences has become significant for enhancing user satisfaction and engagement. This paper presents a novel fuzzy logic-based application system designed to enhance personalization in smart tourism. The proposed system integrates real-time user data and delivers customized services to each particular user. In particular, the proposed system incorporates a recommendation mechanism that combines TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) with fuzzy logic to assess multiple criteria and user preferences and provide accurate and well-rounded personalized travel destination recommendations. By employing fuzzy logic, the system effectively overcomes challenges associated with uncertainty and subjectivity in user data, enabling precise and adaptable decision-making and ensuring more accurate service recommendations. Through case studies and simulations, the paper evaluates the system’s impact on enhancing user satisfaction and the overall tourism experience. Furthermore, preliminary evaluation results demonstrate the system’s ability to generate meaningful and seamless personalized recommendations that enhance the provided tourism services. This work contributes to the growing field of smart tourism by offering a scalable and user-centric solution. The scalability of the system is ensured through its efficient handling of multidimensional data, adaptability to diverse user profiles, and extendability to various tourism applications, including destination ranking, activity recommendations, and hotel selection. Additionally, its integration potential with existing travel platforms highlights its applicability in real-world scenarios, making it a robust tool for enhancing smart-tourism experiences. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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16 pages, 2132 KB  
Article
Piping Material Selection in Water Distribution Network Using an Improved Decision Support System
by Xing Wei, Ming Wang, Qun Wei and Xiangmeng Ma
Water 2025, 17(3), 342; https://doi.org/10.3390/w17030342 - 25 Jan 2025
Cited by 1 | Viewed by 1796
Abstract
This study introduces an integrated Multi-Criteria Decision Making (MCDM) methodology combining the Analytic Hierarchy Process (AHP), Entropy Weight Method (EWM), and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to optimize the selection of municipal water supply pipeline materials. A [...] Read more.
This study introduces an integrated Multi-Criteria Decision Making (MCDM) methodology combining the Analytic Hierarchy Process (AHP), Entropy Weight Method (EWM), and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to optimize the selection of municipal water supply pipeline materials. A comprehensive evaluation system encompassing thirteen criteria across technical, economic, and safety dimensions was developed to ensure balanced decision-making. The method employs a weight determination model based on Jaynes’ maximum entropy theory to harmonize subjective AHP-derived weights with objective EWM-derived weights, addressing inconsistencies in traditional evaluation approaches. This framework was validated in a case study involving a DN400 pipeline project in Jiaxing, Zhejiang Province, China, where five materials—steel, ductile iron, reinforced concrete, High-Density Polyethylene (HDPE), and Unplasticized Polyvinyl Chloride (UPVC)—were assessed using quantitative and qualitative criteria. Results identified HDPE as the most suitable material, followed by UPVC and reinforced concrete, with steel ranking lowest. Comparative analysis with alternative MCDM techniques demonstrated the robustness of the proposed method in balancing diverse factors, dynamically adjusting to project-specific priorities. The study highlights the flexibility of this approach, which can extend to other infrastructure applications, such as drainage systems or the adoption of innovative materials like glass fiber-reinforced plastic (GFRP) mortar pipes. By integrating subjective and objective perspectives, the methodology offers a robust tool for designing sustainable, efficient, and cost-effective municipal water supply networks. Full article
(This article belongs to the Section Water, Agriculture and Aquaculture)
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21 pages, 1238 KB  
Article
A Consensus Framework for Evaluating Dispute Resolution Alternatives in International Law Using an Interval-Valued Type-2 Fuzzy TOPSIS Approach
by Ibrahim Yilmaz and Hatice Kubra Ecemis Yilmaz
Appl. Sci. 2024, 14(23), 11046; https://doi.org/10.3390/app142311046 - 27 Nov 2024
Cited by 4 | Viewed by 1531
Abstract
This research is motivated by the arbitrary nature of decision-making environments and the dynamic changes in decision patterns, particularly in international dispute resolution. These challenges introduce uncertainties that could be effectively managed by fuzzy logic, which provides a robust framework for evaluating alternatives [...] Read more.
This research is motivated by the arbitrary nature of decision-making environments and the dynamic changes in decision patterns, particularly in international dispute resolution. These challenges introduce uncertainties that could be effectively managed by fuzzy logic, which provides a robust framework for evaluating alternatives under multiple criteria. In this study, an Interval-Valued Type-2 Fuzzy TOPSIS approach is proposed to assess various dispute resolution methods, including negotiation, good offices, mediation, international inquiry, conciliation, international organization, arbitration, and international jurisdiction. Common criteria are determined by examining academic literature and by interviewing relevant experts.—cost-efficiency, duration, impartiality, binding nature, and generalizability are considered essential in determining the best resolution method. The proposed method allows for a nuanced evaluation by incorporating both primary and secondary levels of uncertainty, enabling decision-makers to determine the best alternative solution more reliably. This method’s application extends not only to the international law field but also to industrial engineering, where complex, uncertain decision environments require similarly sophisticated multicriteria decision-making tools. By systematically analyzing these resolution methods, this study aims to provide a structured, quantifiable approach that enhances the decision-making process for both international legal practitioners and engineers working with uncertain and dynamic systems. The results of this study ultimately contribute to improved decision-making outcomes and greater efficiency in multidisciplinary problem solving. The assessments of experts in international law, international relations, and political science in their respective fields of expertise have been gathered to form a consensus. This study contributes to the literature as it is the pioneering application of fuzzy multicriteria decision-making techniques in the field of international law. The results of this study imply that the best option from the different decision-maker evaluations is international jurisdiction. Consequently, the utilization of multicriteria decision-making tools can result in more informed and effective decisions in complex and uncertain situations, which is advantageous to both legal practitioners and engineers. Additionally, incorporating different disciplines can help streamline the decision-making process and improve overall efficiency in solving multidisciplinary problems. Full article
(This article belongs to the Special Issue Applications of Fuzzy Systems and Fuzzy Decision Making)
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35 pages, 7180 KB  
Article
Metaheuristic Optimization of the Agricultural Biomass Supply Chain: Integrating Strategic, Tactical, and Operational Planning
by Seyed Mojib Zahraee, Nirajan Shiwakoti and Peter Stasinopoulos
Energies 2024, 17(16), 4040; https://doi.org/10.3390/en17164040 - 14 Aug 2024
Cited by 3 | Viewed by 1846
Abstract
Biomass supply chain (BSC) activities have caused social and environmental disruptions, such as climate change, energy security issues, high energy demand, and job opportunities, especially in rural areas. Moreover, different economic problems have arisen globally in recent years (e.g., the high costs of [...] Read more.
Biomass supply chain (BSC) activities have caused social and environmental disruptions, such as climate change, energy security issues, high energy demand, and job opportunities, especially in rural areas. Moreover, different economic problems have arisen globally in recent years (e.g., the high costs of BSC logistics and the inefficiency of generating bioenergy from low-energy-density biomass). As a result, numerous researchers in this field have focused on modeling and optimizing sustainable BSC. To this end, this study aims to develop a multi-objective mathematical model by addressing three sustainability pillars (economic cost, environmental emission, and job creation) and three decision levels (i.e., strategic (location of facilities), tactical (type of transportation and routing), and operational (vehicle planning). A palm oil BSC case study was selected in the context of Malaysia in which two advanced evolutionary algorithms, i.e., non-dominated sorting genetic algorithm II (NSGA-II) and Multiple Objective Particle Swarm Optimization (MOPSO), were implemented. The study results showed that the highest amounts of profit obtained from the proposed supply chain (SC) design were equal to $13,500 million and $7000 million for two selected examples with maximum emissions. A better target value was achieved in the extended example when 40% profit was reduced, and the minimum emissions from production and transportation in the BSC were attained. In addition, the results demonstrate that more Pareto solutions can be obtained using the NSGA-II algorithm. Finally, the technique for order of preference by similarity to the ideal solution (TOPSIS) was adopted to balance the optimum design points obtained from the optimization algorithm solutions through two-objective problems. The results indicated that MOPSO worked more efficiently than NSGA-II, although the NSGA-II algorithm succeeded in generating more Pareto solutions. Full article
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18 pages, 2408 KB  
Article
Implication of the EU Countries’ Energy Policy Concerning Scenarios Affecting the Air Quality Improvement
by Marta Skiba, Maria Mrówczyńska, Agnieszka Leśniak, Natalia Rzeszowska, Filip Janowiec, Małgorzata Sztubecka, Wioleta Błaszczak-Bąk and Jan K. Kazak
Energies 2024, 17(16), 3892; https://doi.org/10.3390/en17163892 - 7 Aug 2024
Viewed by 1328
Abstract
Energy policy has a significant impact on the state of the environment and, therefore, on residents’ health and life expectancy, especially in highly urbanized areas. Reducing emissions is currently one of the necessary actions that must be taken at the scale of individual [...] Read more.
Energy policy has a significant impact on the state of the environment and, therefore, on residents’ health and life expectancy, especially in highly urbanized areas. Reducing emissions is currently one of the necessary actions that must be taken at the scale of individual countries to ensure sustainable development. The article aims to identify the best ways to shape energy policy by evaluating development scenarios for air protection and their environmental impact. The realization of the goal is based on the data included in three groups: (1) Economic factors, Health factors, and Demographic factors; (2) Clima-e related economic losses, Renewable Energy sources in electricity, heating, and cooling, Premature deaths due to exposure to fine particulate matter (PM2.5), Health impacts of air pollution, Population change; (3) Demographic balance and crude rates at the national level, GDP per capita in purchasing power PPS, GDP, and principal components; covering 36 EU countries in 2019 and 2021. The study proposes an advanced methodology for assessing development strategies by integrating the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and Bayesian networks (BN) and incorporating them into a multicriteria decision-making (MCDM) support system. The TOPSIS model based on BN allowed for the illustration of the features of many criteria and the identification of relationships between scenarios, allowing for selecting the best way to develop energy policy. The results showed a 60.39% chance of achieving success in extending the life of residents by five years. At the same time, the most favorable development path was the scenario promoting activities aimed at reducing air pollution by introducing renewable energy sources to produce energy used for lighting and preparing domestic hot water urban areas. By presenting possible scenarios and the probability of success, it is possible to achieve the goal of practical energy policy at the level of the country and individual European cities and also by extending the life of city inhabitants, as presented by the authors in this study. Full article
(This article belongs to the Section C: Energy Economics and Policy)
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22 pages, 2790 KB  
Article
An Integrated Group Decision-Making Framework for the Evaluation of Artificial Intelligence Cloud Platforms Based on Fractional Fuzzy Sets
by Saleem Abdullah, Saifullah and Alaa O. Almagrabi
Mathematics 2023, 11(21), 4428; https://doi.org/10.3390/math11214428 - 25 Oct 2023
Cited by 9 | Viewed by 1651
Abstract
Due to the rapid development of machine learning and artificial intelligence (AI), the analysis of AI cloud platforms is now a key area of research. Assessing the wide range of frameworks available and choosing the ideal AI cloud providers that may accommodate the [...] Read more.
Due to the rapid development of machine learning and artificial intelligence (AI), the analysis of AI cloud platforms is now a key area of research. Assessing the wide range of frameworks available and choosing the ideal AI cloud providers that may accommodate the demands and resources of a company is mandatory. There are several options, all having their own benefits and limitations. The evaluation of artificial intelligence cloud platforms is a multiple criteria group decision-making (MCGDM) process. This article establishes a collection of Einstein geometric aggregation operators (AoPs) and a novel Fractional Fuzzy VIKOR and Fractional Fuzzy Extended TOPSIS based on the entropy weight of criteria in fractional fuzzy sets (FFSs) for this scenario. The FFSs provide an evaluation circumstance containing more information, which makes the final decision-making results more accurate. Finally, this framework is then implemented in a computational case study for the evaluation of artificial intelligence cloud platforms and comparison of this model with other existing approaches, such as the extended GRA approach, to check the consistency and accuracy of the proposed technique. The most optimal artificial intelligence cloud platform is I1 Full article
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24 pages, 2064 KB  
Article
Determining Priorities in Infrastructure Management Using Multicriteria Decision Analysis
by Ana Bošnjak and Nikša Jajac
Sustainability 2023, 15(20), 14953; https://doi.org/10.3390/su152014953 - 17 Oct 2023
Cited by 3 | Viewed by 2377
Abstract
This paper aims to form a concept of infrastructure management based on a multicriteria approach to determining management priorities. As the complexity of infrastructure construction and maintenance management requires looking at this problem from different aspects, the proposed multicriteria approach in this paper [...] Read more.
This paper aims to form a concept of infrastructure management based on a multicriteria approach to determining management priorities. As the complexity of infrastructure construction and maintenance management requires looking at this problem from different aspects, the proposed multicriteria approach in this paper is based on the application of a two-phase analytical hierarchy process (AHP) method and technique for order of preference by similarity to ideal solution (TOPSIS) method. Using the two-phase AHP method, the process of determining the relative weights of the criteria is improved with the aim of providing better management of stakeholders as one of the essential preconditions for the success of the entire management process. In this way, it is desired to simulate the decision-making process as realistically as possible, in which the opinions and interests of all stakeholders are respected, but the key decision-maker is responsible for the final decision. Furthermore, with the help of the TOPSIS method, a ranking list of maintenance management priorities is formed, based on which it is possible to distribute limited financial resources intended for annual maintenance more rationally. The stability of the TOPSIS results was confirmed by a sensitivity analysis when changing the relative weights of the criteria. The proposed allocation of financial resources represents the basis for a better design of the maintenance management plan of the analyzed infrastructure elements, thus completing the observed gap in the existing literature. The aim of the above is to improve the planning function and at the same time to improve the implementation, monitoring, and control management functions, which creates a more efficient management system that can preserve the value of the analyzed infrastructure elements and extend their lifetime. Full article
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13 pages, 1073 KB  
Article
Intuitionistic Fuzzy Sets with Ordered Pairs and Their Usage in Multi-Attribute Decision Making: A Novel Intuitionistic Fuzzy TOPSIS Method with Ordered Pairs
by Cengiz Kahraman, Selcuk Cebi, Basar Oztaysi and Sezi Cevik Onar
Mathematics 2023, 11(18), 3867; https://doi.org/10.3390/math11183867 - 10 Sep 2023
Cited by 20 | Viewed by 2007
Abstract
Intuitionistic Fuzzy Sets with Ordered Pairs (IFSOP) are the recent extension of intuitionistic fuzzy sets by incorporating functional and dysfunctional points of view into the definition of membership functions. This paper extends the Technique of Order Preference Similarity to the Ideal Solution (TOPSIS) [...] Read more.
Intuitionistic Fuzzy Sets with Ordered Pairs (IFSOP) are the recent extension of intuitionistic fuzzy sets by incorporating functional and dysfunctional points of view into the definition of membership functions. This paper extends the Technique of Order Preference Similarity to the Ideal Solution (TOPSIS) method to the Intuitionistic Fuzzy TOPSIS (IF TOPSIS) with ordered pairs method and applies it to a multi-criteria risk-based supplier selection problem under fuzziness. IF TOPSIS with ordered pairs involves finding a positive ideal solution and a negative ideal solution, and measuring the distance between each alternative and these solutions. The final ranking of the alternatives is obtained based on the proportion of distances between the positive and negative ideal solutions. By asking functional and dysfunctional questions in this ranking process, the developed IF TOPSIS with ordered pairs method incorporates the accuracy and consistency of expert judgments, enhancing the decision-making process. A sensitivity analysis is also presented in order to show the robustness of the rankings obtained by IF TOPSIS with ordered pairs. Full article
(This article belongs to the Special Issue 40 Years of Intuitionistic Fuzzy Sets)
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13 pages, 291 KB  
Article
Distance-Based Knowledge Measure and Entropy for Interval-Valued Intuitionistic Fuzzy Sets
by Chunfeng Suo, Xuanchen Li and Yongming Li
Mathematics 2023, 11(16), 3468; https://doi.org/10.3390/math11163468 - 10 Aug 2023
Cited by 8 | Viewed by 1783
Abstract
The knowledge measure or uncertainty measure for constructing interval-valued intuitionistic fuzzy sets has attracted much attention. However, many uncertainty measures are measured by the entropy of interval-valued intuitionistic fuzzy sets, which cannot adequately reflect the knowledge of interval-valued intuitionistic fuzzy sets. In this [...] Read more.
The knowledge measure or uncertainty measure for constructing interval-valued intuitionistic fuzzy sets has attracted much attention. However, many uncertainty measures are measured by the entropy of interval-valued intuitionistic fuzzy sets, which cannot adequately reflect the knowledge of interval-valued intuitionistic fuzzy sets. In this paper, we not only extend the axiomatic definition of the knowledge measure of the interval-valued intuitionistic fuzzy set to a more general level but also establish a new knowledge measure function complying with the distance function combined with the technique for order preference by similarity to ideal solution (TOPSIS). Further, we investigate the properties of the proposed knowledge measure based on mathematical analysis and numerical examples. In addition, we create the entropy function by calculating the distance from the interval-valued fuzzy set to the most fuzzy point and prove that it satisfies the axiomatic definition. Finally, the proposed entropy is applied to the multi-attribute group decision-making problem with interval-valued intuitionistic fuzzy information. Experimental results demonstrate the effectiveness and practicability of the proposed entropy measure. Full article
26 pages, 1515 KB  
Article
GRA-Based Dynamic Hybrid Multi-Attribute Three-Way Decision-Making for the Performance Evaluation of Elderly-Care Services
by Fan Jia, Yujie Wang and Yiting Su
Mathematics 2023, 11(14), 3176; https://doi.org/10.3390/math11143176 - 19 Jul 2023
Cited by 3 | Viewed by 1597
Abstract
As an important branch of modern decision-making theory, multi-attribute decision-making (MADM) plays an important role in various fields. Classic MADM methods can provide a ranking of alternatives, and decision-makers need to evaluate the level subjectively based on the ranking results. Because of the [...] Read more.
As an important branch of modern decision-making theory, multi-attribute decision-making (MADM) plays an important role in various fields. Classic MADM methods can provide a ranking of alternatives, and decision-makers need to evaluate the level subjectively based on the ranking results. Because of the limitation of knowledge, this is likely to lead to potential individual losses. Three-way decision (3WD) theory has good classification ability. Therefore, this paper proposes a dynamic hybrid multi-attribute 3WD (MA3WD) model. First, a new scheme for constructing loss functions is proposed from the perspective of gray relational analysis (GRA), which is an accurate and objective way to describe the relationship between loss functions and attribute values. Then, conditional probabilities are determined by employing the gray relational analysis technique for order preference by similarity to the ideal solution (GRA-TOPSIS). With these discussions, a GRA-based hybrid MA3WD model for a single period is proposed by considering multi-source information. Furthermore, by extending the single-period scenario to a multi-period one, we construct a dynamic hybrid MA3WD model, which can obtain the final three-way decision rules as well as the results of each period and each attribute. Finally, the proposed method is applied to the case of performance evaluation of elderly-care services to demonstrate the effectiveness of the method, and comparative analyses are given to verify the superiority of the proposed method. Full article
(This article belongs to the Special Issue Mathematical Methods for Decision Making and Optimization)
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