Multi-criteria Decision-making Problem Research Articles

Modified VIKOR-GP approach by considering the Leopold Matrix for optimal water reuse allocation

ABSTRACT The global water resource crisis caused by population growth, and increasing water demand has led to using treated wastewater in many regions. Effective distribution of wastewater treatment across various consumer sectors is crucial for sustainable environmental practices and resource management. Wastewater Allocation (WA) is a multi-criteria decision-making problem, and this study used modified VIKOR (VIekriterijumsko KOmpromisno Rangiranje) method in the combination with GP (Goal Programming) technique to optimize WA in Iran. The environmental effects were evaluated using Leopold Matrix results. The proposed approach resulted in an allocation of 6912 m3/day for urban green space irrigation 10,368 m3/day for the agricultural irrigation, and 2592 m3/day for industrial water demand at the Shahreza wastewater treatment plant. The research shows that better recommendations for resource allocation may be developed by combining quantitative assessment, optimization, and mathematical models. This approach has proven successful in maximizing the reuse of wastewater for a variety of uses.

Novel picture fuzzy power partitioned Hamy mean operators with Dempster-Shafer theory and their applications in MCDM

In some multi-criteria decision-making (MCDM) scenarios, decision makers must address challenges like handling uncertain and incomplete information, managing biases in criteria values, and assessing interrelationships among criteria based on their partitioning as per their characteristics. To tackle these challenges, a picture fuzzy set (PFS) can be utilized to quantify vague information, Hamy mean (HM) can be used to consider criteria interrelationships while the power average (PA) mitigates any kind of biasness. Also, to overcome the limitations of persistence and invariantess in algebraic operations, Dempster-Shafer theory (DST) is employed. By integrating the conventional HM with the traditional PA under partitioning, this paper first introduced the novel power partitioned Hamy mean (PPtHMq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$PPtHM^q$$\\end{document}) operator. Then, this operator is extended for picture fuzzy numbers (PFNs) with DST and two novel operators are introduced, which are named as picture fuzzy power partitioned Hamy mean (PFPPtHMDSTq)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(PFPPtHM^q_{DST})$$\\end{document} and picture fuzzy weighted power partitioned Hamy mean (PFWPPtHMDSTq)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(PFWPPtHM^q_{DST})$$\\end{document} with some desirable properties. Moreover, based on these operators, a new method for MCDM in the PFS environment has been designed. The paper illustrates their application in selecting the best hotel among four alternatives (B1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_1$$\\end{document}, B2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_2$$\\end{document}, B3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_3$$\\end{document}, B4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_4$$\\end{document}) based on five criteria, which are partitioned into two sets. Results indicate that the best and worst alternatives under these operators are hotels B1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_1$$\\end{document} and B4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_4$$\\end{document}, respectively. Sensitivity analysis explores the impact of granularity parameter variations, and comparative analysis demonstrates the effectiveness of the presented operators. Overall, the study concludes that these operators offer flexibility, generality, and consistency for analyzing MCDM problems in PFS environments.

A Robust Decision-Making Model for Medical Supplies via Selecting Appropriate Unmanned Aerial Vehicle

Recently, Unmanned Aerial Vehicles (UAVs) have been used in many fields, including the field of health care, especially in delivering the necessary medical equipment and supplies, due to the many advantages they have compared to other traditional methods and the presence of different types of UAVs, to improve healthcare and provide it with the medical supplies and equipment necessary to save the lives of patients. Choosing the appropriate UAV for a specific situation represents a problem facing decision-makers, which is considered a multi-criteria decision-making problem. Since the decision-making process is cumbersome and complex, and deals with uncertainty and ambiguity. In this research, we proposed multi-criteria decision-making (MCDM) model using CRITERIA (Criteria Importance through Intercriteria Correlation) and MARICA (Multi-Attribute Rating Analysis with Ideal Concepts) methods integrated with neutrosophic logic, which is considered a powerful tool in dealing with uncertainty and ambiguity. The CRITIC method calculates the weight of criteria, whereas it takes into account the correlations and relationships between the criteria, whether they are positive or negative, unlike other methods that consider the criteria separately, which allows for a more accurate and comprehensive analysis of the decision problem. The MARICA method is used also to rank the alternatives. It allows decision-makers to evaluate alternatives according to how well they perform across multiple criteria by considering several factors at once. This helps increase the effectiveness of judgments by taking into account all relevant factors. Moreover, MARICA is a user-friendly method that doesn't require complex mathematical calculations, making it accessible to anyone who wants to make sound choices. The UAV with the highest ranking is the one that will be chosen and represents the best among the alternatives. The proposed model proved its effectiveness by applying it to an experimental case.

A study of entrepreneur and innovative university index by entropy-based grey relational analysis and PROMETHEE

In recent years, the concept of entrepreneurial and innovative universities has gained widespread prominence. Many universities have been paying more attention to being entrepreneurial and innovative by improving their organizational systems, advancing their infrastructure, and increasing financial support. Since numerous criteria with different weights exist, ranking universities based on entrepreneurial and innovative performance can be considered a multi-criteria decision-making (MCDM) problem. This article aims to investigate how different multi-criteria decision-making methods with different criterion weights can affect university rankings and to highlight the reasons that contribute to these differences. In this scope, Grey Relational Analysis (GRA) and Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) methods were used to rank and compare the universities in Türkiye according to the 2022 Entrepreneur and Innovative University Index (EIUI). In addition to the current weights of each EIUI dimension, entropy-based weights and equal weights were used in MCDM methods. Three ranking approaches with varying weights provided different rankings for universities. The effect of criterion weights was found to be more important in the ranking difference than the method used. The ranks for universities coded U1 and U2 as the most entrepreneurial and innovative universities remained the same. In addition, the performance of each university according to each dimension was evaluated graphically using the GAIA plane to enable them to identify areas for improvement in their rankings.

A Decision Model for High School Students' Summer job Choices: a Study Combining Hierarchical Analysis and Entropy Power Methods

As summer vacation approaches, high school students face an annual opportunity: choosing a summer job. These job opportunities not only provide a way to earn money, but also help students explore their career interests, develop key skills, and prepare them for future educational and career paths. However, high school students often have difficulty in finding the right job. To solve this, we have constructed a decision model that combines the hierarchical analysis of hierarchy (AHP) and entropy weighting method, aiming to find the best match among the many choices for high school students. The problem is essentially a multi-criteria decision-making problem that involves a number of decision-making factors, which need to be taken into account, along with the job characteristics and the applicant's profile and preferences. In our research, summer jobs are evaluated on a total of eight criteria: income, safety risk, job purpose, working conditions, and work. The model takes into account the job characteristics and the user's profile/preferences, and is therefore able to recommend the best job that matches the user's profile/preferences. In this paper, the AHP is used to determine the relative importance of these criteria for each individual, while the entropy weighting method is used to determine the relative importance of these criteria from an objective perspective. The model works as expected by validating it against nineteen types of job and ten fictional characters. Not only can we recommend the best jobs with the highest scores, but we can also rank all candidate jobs according to the calculated priority, providing users with a wider range of job options.

Insurance Risk Assessment Model based on Game Theory-Combined Weighting-TOPSIS

With the increasingly severe climate change and intensifying severity of weather events and natural disasters, ensuring the sustainable development of the property insurance industry becomes particularly important. The policy distribution of insurance companies has become a key issue. This paper proposes a novel Game Theory-Combined Weighting-TOPSIS model, which weights indicators using The Entropy Weight Method and the CRITIC method, combines the weights of the former two through game-based combined weighting, and leverages the advantages of the TOPSIS method in handling multi-criteria decision-making problems. Among them, taking China as an example and applying the model, it is found that southeastern China and coastal areas have higher scores and are suitable for insurance. Through this approach, we can scientifically and reasonably assess the risk levels in different regions, provide decision support for property insurance companies to optimize policy distribution, and promote the healthy development of the insurance industry.

Use of measurement results from a mobile laboratory in the diagnostics of anthropogenic environment - linear ordering of objects using the TOPSIS method

The measurements of the concentrations of gaseous and dust pollutants in the anthropogenic environment are an important element of environmental monitoring and for determining directions of preventive activities in the field of health protection. The article presents the results involving the concentrations of suspended dust and gaseous pollutants in the outdoor air, which were recorded at three measuring stations of air quality in the Silesian and Opole voivodeships (Wodzisław Śląski, Zabrze, Kędzierzyn-Koźle). The results were supplemented with the values recorded by the mobile laboratory located at the Center for Continuing Education - Branch of the Silesian University of Technology in Rybnik. The research results were used for a synthetic assessment of the threat level to the anthropogenic environment. In the computational layer, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was employed, which is included in the group of methods for solving multi-criteria decision-making problems (Multi Attribute Decision Making).

Extended Dombi–Hamy mean operator and Gaussian likelihood-based ranking approach for solving MCDM problems in interval-valued neutrosophic environment

The contrivance of this paper is two-dimensional. The first is to formulate an extended Dombi-Hamy mean operator in an interval-valued neutrosophic environment for assembling inter-related multiple parameters. The second one is to develop a new ranking procedure named as GLF ranking by introducing the concept of Gaussian likelihood function for solving multi-criteria decision-making problems in an interval-valued neutrosophic circumstance. Also, we have proposed a novel algorithm named Gaussian likelihood function based algorithm or GLF algorithm in solving multi-criteria decision-making problem from the field of medical science to find out the vital cause responsible for the occurrence of cancer in India. Finally, we have verified the flexibility and etiquette of GLF method by comparing it with the existing multi-criteria decision-making methods such as Aiwu’s method and Jun Ye’s method.

Sustainable Afforestation Strategies: Hybrid Multi-Criteria Decision-Making Model in Post-Mining Rehabilitation

This article describes an effective approach for selecting suitable plant species for afforestation in post-mining rehabilitation. The research was conducted in the Western Black Sea region of Turkey. The aim of the research is to perform accurate criteria weighting and species prioritization for afforestation in post-mining degraded areas. This helps to ensure consistent conditions for the future use of the site as a forest, sustainability of nature, and selection of appropriate species adapted to the difficult post-mining conditions. In this study, which is a multi-criteria decision-making problem (MCDM), the weights of the criteria were determined by stepwise weight assessment ratio analysis (SWARA), and the priority ranking of the species was determined by the analytic hierarchy process (AHP). Analyses were carried out with 10 afforestation criteria and five tree species. According to the analysis, the top three ranked criteria are Economic Efficiency > Carbon Stock and Credit > Reducing Afforestation Cost. The five species’ priority ranking is Robinia pseudoacacia L. (0.456) > Alnus glutinosa subsp. glutinosa (0.248) > Populus nigra subsp. nigra (0.146) > Salix alba L. (0.103) > Quercus robur subs. robur (0.048). The hybrid approach is expected to increase the effectiveness of post-mining rehabilitation works.

Wind farm site selection using GIS-based mathematical modeling and fuzzy logic tools: a case study of Burundi

Introduction: The electricity generated from nuclear plants and petroleum-based products has a negative influence on the environment as a whole. It has shown the utility to search out and promote the utilization of renewable, environmentally friendly, and sustainable energy sources such as solar, wind, and geothermal. Nowadays, Wind energy resource has quickly emerged as the world’s fastest-growing energy source.Methods: However, the selection of the most suitable places for developing a wind farm is a crucial challenge that can be seen as a problem of site selection, which involves numerous conflicting variables. Therefore, it is classified as an MCDM (multi-criteria decision-making) problem. The main objective of this research is to determine the best locations in Burundi for the installation of wind farms. The Fuzzy Analytic Hierarchy Process (FAHP) was used to weigh the criteria considering their relative importance. This study considers several key factors when determining the optimal location for a wind farm. These factors include wind speed, slope, proximity to the grid network, distance to roads, and land use/land cover (LULC). Furthermore, a geographic information system (GIS) is utilized to generate the final suitability wind farm locations map.Results and Discussion: The obtained results indicate that 20.91% of the whole study area is suitable nevertheless, only 1.96% is tremendously suitable for wind turbine placement. The western part of Burundi is the optimal area for constructing a wind farm, and the most is in Lake Tanganyika.

A Few Similarity Measures on the Class of Trapezoidal-Valued Intuitionistic Fuzzy Numbers and Their Applications in Decision Analysis

Similarity measures on trapezoidal-valued intuitionistic fuzzy numbers (TrVIFNs) are functions that measure the closeness between two TrVIFNs, which has a lot of applications in the area of pattern recognition, clustering, decision-making, etc. Researchers around the world are proposing various similarity measures on the generalizations of fuzzy sets. However, many such measures do not satisfy the condition that “the similarity between two fuzzy numbers is equal to 1 implies that both the fuzzy numbers are equal” and this gives a pathway for the researchers to introduce different similarity measures on various classes of fuzzy sets. Also, all of them try to find out the similarity by using a single function, and in the present study, we try to propose a combined similarity measure principle by using four functions (four similarity measures). Thus, the main aim of this work is to introduce a few sets of similarity measures on the class of TrVIFNs and propose a combined similarity measure principle on TrVIFNs based on the proposed similarity measures. To do this, in this paper, firstly, we propose four distance-based similarity measures on TrVIFNs using score functions on TrVIFNs and study their mathematical properties by establishing various propositions, theorems, and illustrations, which is achieved by using numerical examples. Secondly, we propose the idea of a combined similarity measure principle by using the four proposed similarity measures sequentially, which is a first in the literature. Thirdly, we compare our combined similarity measure principle with a few important similarity measures introduced on various classes of fuzzy numbers, which shows the need for and efficacy of the proposed similarity measures over the existing methods. Fourthly, we discuss the trapezoidal-valued intuitionistic fuzzy TOPSIS (TrVIF-TOPSIS) method, which uses the proposed combined similarity measure principle for solving a multi-criteria decision-making (MCDM) problem. Then, we discuss the applicability of the proposed modified TrVIF-TOPSIS method by solving a model problem. Finally, we discuss the sensitivity analysis of the proposed approaches by using various cases.

Using SMART Method for Multi-criteria Decision Making: Applications, Advantages, and Limitations

The applications of multi-criteria decision-making (MCDM) techniques are numerous. Simple Multi-Attribute Rating Technique (SMART) is a popular method for addressing MCDM problems with several criteria. The research investigates the SMART approach discussing how it is used, and its benefits and drawbacks, in decision-making situations. It looks at how it can be applied in choosing technology, improving healthcare systems, and managing the environment. SMART simplifies decision-making by comparing options based on factors. Yet it also has drawbacks such as biases in assigning weights and may not fully address the intricacies of certain decisions. The goal of the study is to enhance comprehension of SMART advocate for its use and propose combining it with intricate decision frameworks. Even though the SMART method is now widely used there is a lack of a thorough understanding of the method to identify its various applications. This paper aims to provide a comprehensive guide and a thorough overview of the SMART method to aid in decision-making and ranking in multi-attribute scenarios.

Bipolar valued probabilistic hesitant fuzzy sets based on Generalized Hybrid Operators in multi-criteria decision-making problems based on TOPSIS

This paper aims to present Bipolar valued probabilistic hesitant fuzzy sets (BVPHFSs) by combining bipolar fuzzy sets and probabilistic hesitant fuzzy sets (PHFSs). PHFSs are a strong version of hesitant fuzzy sets (HFSs) in terms of evaluated as probabilistic of each element. Probabilistic hesitant fuzzy sets (PHFSs) are a set structure that argues that each alternative should be evaluated probabilistically. In this framework, the proposed cluster allows probabilistic evaluation of decision- makers’ opinions as negative. Thus, this case proposes flexibility about selection of an element and aids to overcome with noise channels. Furthermore, some new aggregation operators are discussed called bipolar valued probabilistic hesitant fuzzy weighted average operator (BVPHFWA), Generalized bipolar valued probabilistic hesitant fuzzy weighted average operator (GBVPHFWA), bipolar valued probabilistic hesitant fuzzy weighted geometric operator (BVPHFWG), Generalized bipolar valued probabilistic hesitant fuzzy weighted geometric operator (GBVPHFWG), bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric operator (BVPHFHWAG) and Generalized bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric (GBVPHFHWAG) and some basic properties are presented. A score function is defined ranking alternatives. Moreover, two different algorithms are put forward with helping to TOPSIS method and by using aggregation operators over BVPHFSs. The validity of proposed operators are analyzed with an example and results are compared in their own.

Rough Neutrosophic Shapley Weighted Einstein Averaging Aggregation Operator and its Application in Multi-Criteria Decision-Making Problem

The study of aggregation operators has played a crucial role in various decision-making methods. The primary function of the aggregation operator is to combine multiple numbers into a single value. While Einstein operators offer a compact notation and can handle complex and large datasets, they do not consider the interaction involved in determining the criteria weights or account for imprecise and indeterminate data. To overcome this limitation, this paper introduces an improved aggregation operator, the rough neutrosophic Shapley weighted Einstein averaging aggregation operator. The rough neutrosophic sets offer a method for effectively managing the fuzziness and uncertainty that commonly occur in real-world scenarios and the Shapley fuzzy measure helps us understand the importance or value of different elements in each scenario. This operator combines the Shapley fuzzy measure with Einstein operators under rough neutrosophic sets, which are an effective tool for handling incomplete, indeterminate, and inconsistent information. The proposed operator satisfies essential algebraic properties such as idempotency, boundedness, and monotonicity. This paper also presents a decision-making methodology based on the proposed operator, with attribute values derived from the rough neutrosophic set. Finally, the applicability of the suggested aggregation operator is illustrated with a numerical example.

Testing the suitability of vector normalization procedure in topsis method: application to wheel loader selection

The object of the research consists of testing the suitability of the vector normalization procedure (NP) in the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) method. One of the most problematic steps of the Multi-Criteria Decision Making (MCDM) process is related to the application of NPs by default to transform different measurement units of criteria into a comparable unit. This is because of the absence of a universal agreement that defines which NP is the most suitable for a given MCDM method. In the literature, there are thirty-one available NPs, each one of them has its strengths and weaknesses and, accordingly, can efficiently be applied to an MCDM method and even worst to another. Let’s note that many NPs (e. g., NPs of sum, max-min, vector, and max) have been used by default (i. e., without suitability study) in the TOPSIS method. Consequently, outcomes of multi-criteria evaluation and rankings of alternatives considered in the decision problems could have led to inconsistent solutions, and, therefore, decision-makers could have made irrational or inappropriate decisions. That’s why suitability studies of NPs become indispensable. Moreover, a description of the methodology, proposed in this research, is outlined as follows: 1) method of weighting based on an ordinal ranking of criteria and Lagrange multiplier (for determining criteria weights); 2) TOPSIS method (for ranking considered alternatives); 3) a statistical approach with 3-estimate (for comparing effects generated by the used NPs). In the research, twelve different NPs are compared to each other in the TOPSIS method via a numerical example, which deals with the wheel loader selection problem. The results of the comparison indicate that, amongst the twelve different NPs analyzed in this suitability study, vector NP has the lesser effect on the considered alternatives’ evaluation outcomes, when used with the TOPSIS method. The vector NP-TOPSIS approach can therefore be applied to solve multi-criteria decision problems. Its application further allows the decision-makers and users to better select efficient solutions and, consequently, to make conclusive decisions.

CWBCM method to determine the importance of classification performance evaluation criteria in machine learning: Case studies of COVID-19, Diabetes, and Thyroid Disease

Problems with multiple conflicting criteria are usually modeled by the methods proposed in the field of Multi-Criteria Decision Making (MCDM). In MCDM, one of the most important topics is the weighting of criteria. On the other hand, classification is employed in numerous real-world issues, like disease diagnosis. Diverse algorithms have been developed for this purpose. It is important to evaluate the classification performance in every problem by evaluating algorithms. The evaluation of algorithms includes several conflicting criteria; Therefore, it can be represented as an MCDM problem. We aim to develop a new weighting method that can be used for the classification problem with more than two classes, involve the risk of threatening human life, and consider minor features for different diseases in weighting. At present, none of the existing weighting methods fulfill these requirements. This research presents a new method called “Criteria Weighting Based on Confusion Matrix (CWBCM)” and our innovation is that, for the first time, all these gaps are filled with this method. This method calculates the exact importance of criteria using the confusion matrix in machine learning. The proposed method has been implemented on six different datasets of three diseases: COVID-19, thyroid, and diabetes, and compared with two common methods, Shannon and AHP. Two methods, TOPSIS and EDAS, were also used to rank the classifiers. Finally, the results show that our method is superior to the other two weighting methods in all critical factors and has unique features that other methods do not have.

A study on the effects of objective weighting methods on TOPSIS-based parametric optimization of non-traditional machining processes

Developing advanced engineering materials with enhanced mechanical and metallurgical properties has caused non-traditional machining (NTM) processes to emerge as cost-effective and energy-efficient options. Improper settings of the input parameters of those processes may often lead to inferior quality and accuracy of the finished products. Multi-criteria decision-making (MCDM) methods appear as potent tools for multi-objective optimization of those processes. Determining criteria weights is a crucial step in any MCDM problem; subjective approaches for evaluating criteria weights may result in inconsistent judgments. In this paper, the effects of ten different objective weighting methods, i.e., equal weight, entropy weight, Criteria Importance Through Inter-criteria Correlation (CRITIC), Method based on Removal Effects of Criteria (MEREC), Logarithmic Percentage Change-driven Objective Weighting (LOPCOW), Symmetry Point of Criterion (SPC), Criteria Impact Loss (CILOS), Integrated Determination of Objective Criteria Weights (IDOCRIW), Principal Component Analysis (PCA) and Weighted Principal Component Analysis (WPCA) are studied on Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)-based optimization of two NTM processes. In the first example, the optimal parametric combination computed using equal weight, entropy, MEREC, LOPCOW, PCA, and WPCA is noticed to be the same. In contrast, a different set of optimal parameters is derived by applying CRITIC, SPC, CILOS, and IDOCRIW. In the second example, seven out of ten approaches obtain a unique set of parametric combinations, while CILOS, IDOCRIW, and PCA lead to a different set of intermixes. It can be concluded that the ranks of the experiment trials for both the examples are almost similar irrespective of the objective criteria weighting technique employed.

Quintic fuzzy sets: A new class of fuzzy sets for solving multi-criteria decision-making problems under uncertainty

This study proposes a new class of fuzzy sets called Quintic Fuzzy Set (QuFS), where the sum of the fifth power of the membership degree and non-membership degree is less than or equal to one. We introduce the complement operator and basic operations on QuFS and further develop various theorems based on these fundamental set operations. We also present the standard modal operators on QuFS and discuss its elementary properties. We then define a novel score and accuracy function for ranking QuFS, as well as the Euclidean and Hamming distances between two QuFSs. A supplier selection example is presented in detail to illustrate the viability and utility of the proposed QuF-TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method. We also present a multi-criteria decision-making (MCDM) problem on COVID-19 lab selection to perform a comparative analysis of QuFS with Fermatean Fuzzy Set (FFS) and Pythagorean Fuzzy Set (PFS). Furthermore, we demonstrate an existing real case study on selection of Health care waste treatment (HCWT) technique in India and perform a comparative analysis with TOPSIS, SAW (Simple Additive Weighting) and WASPAS (Weighted Aggregated Sum Product Assessment) MCDM methods in QuF framework. With the advent of QuFS, a decision-maker can now employ the fuzzy notion to manage complicated and uncertain human judgements. The comparative results indicate that the suggested QuF measures and QuF MCDM technique outperform other fuzzy concepts regarding effectiveness and validity. Due to the restrictive nature of the current fuzzy set theories, the decision-makers in some complex, uncertain real-life problems are not free to choose the degree of membership and non-membership of their choice. Compared to the Intuitionistic Fuzzy Set (IFS), PFS, and FFS, the QuFS developed in this study has a bigger space grade space. This feature of QuFS enables decision-makers to structure complex, uncertain circumstances with greater flexibility in terms of membership and non-membership degrees.

Spherical fuzzy sets based integrated DEMATEL, ANP, VIKOR approach and its application for renewable energy selection in Turkey

Renewable energy continues occupying the global agenda for the low-carbon transition. Identifying suitable sources for renewable energy involves different criteria and alternatives, which can be defined as a Multi-Criteria Decision-Making (MCDM) problem. MCDM methods can be enriched with Group Decision Making (GDM) to merge individual judgments into group opinions, as well as with fuzzy sets to better simulate human opinions. To handle uncertainties of DMs’ preferences, a recently developed fuzzy set extension, the Spherical Fuzzy Sets (SFSs), is combined in this study with different MCDM tools to establish a decision support tool for the energy source selection problem. This article proposes a novel MCDM approach that integrates SF-DEMATEL (Spherical Fuzzy Decision-Making Trial and Evaluation Laboratory), SF-ANP (Spherical Fuzzy Analytic Network Process), and SF-VIKOR (Spherical Fuzzy Vlse Kriterijumska Optimizacija Kompromisno Resenje) algorithms in a GDM environment and presents its application in a case study for selecting renewable energy sources in Turkey. Comparing wind, geothermal, solar, hydropower, and biogas, the proposed method highlighted both wind and solar energy as a compromise solution as the most suitable options for Turkey. It has been found that compared to similar fuzzy sets, SFS can better reflect the hesitation degree to address the lack of knowledge and errors in the membership function definitions. The robustness and plausibility of these findings are demonstrated with sensitivity and comparative analyses, suggesting this MCDM method can also be applied to similar problems in other settings.

A Trustworthy and Explainable Framework for Benchmarking Hybrid Deep Learning Models Based on Chest X-Ray Analysis in CAD Systems

Evaluating the trustworthiness of deep learning-based computer-aided diagnosis (CAD) systems is challenging. There is a need to optimize trust and performance in model selection. A wide range of models based on evaluation metrics can make it challenging to choose the best one, especially for complex multi-criteria decision-making problems. In the case of COVID-19 diagnosis, using both physicians’ evaluation and AI techniques to establish trust is essential. In this study, 1551 chest X-rays were analyzed using deep transfer learning (DTL) with six models and four SVM kernels. This resulted in 24 hybrid DTL–SVM models. Seven metrics were evaluated using fuzzy multiple-criteria decision-making (MCDM), which uses a dynamic decision matrix to select the best model. This matrix incorporates fuzzy-weighted zero-inconsistency (FWZIC) for weight coefficients and Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) for benchmarking. The Grad-CAM technique compared the best model with 16 images, ensuring explainability. Top-performing models were identified, including SqueezeNet-SVM linear, VGG19-SVM linear, and VGG19-SVM. Sensitivity analysis was used to quantify the impact of changing weighted criteria values. A physician expert validated fuzzy MCDM through Grad-CAM analysis, a new aspect of this study. The framework presented in this study was benchmarked against seven other studies and achieved a perfect score in four crucial areas. Trustworthiness is essential for CAD systems, and this study effectively addresses trust and performance challenges in AI model-based CAD systems. The study systematically evaluated the requirements for trustworthiness, including accountability, fairness, robustness, accuracy, and reproducibility, and the results supported this.