Intuitionistic Fuzzy Sets in Multi-Criteria Group Decision Making Problems Using the Characteristic Objects Method

Applied research on the design of protective clothing based on the Kano-QFD-PUGH method

In order to improve the user experience of protective clothing for healthcare workers and reduce the design blindness and subjectivity of developers, we propose a research methodology that combines the Kano model, QFD quality function deployment, and PUGH decision-making scheme to develop conceptual solutions for medical protective clothing design. Firstly, we use the Kano model to identify the user requirements of healthcare workers and construct a hierarchy of functional requirements for protective clothing. Secondly, we use the QFD method to weigh the protective clothing design elements, convert user requirements into design elements, establish a relationship matrix between user requirements and design elements, and generate four conceptual design solutions based on the results. Finally, we use the PUGH decision-making method to filter and select the best concept solution for protective clothing design, and validate the design evaluation. Our results show that the protective clothing solutions designed using the combined Kano-QFD-PUGH system approach have a higher level of satisfaction compared to traditional protective clothing design. This method accurately explores the mapping relationship between user requirements and design functional elements and can be used as a general reliability design method. It helps to improve the development efficiency of designers and the decision-making role for design concept solution preference. Overall, our research methodology provides a comprehensive approach to developing medical protective clothing, which can be useful for designers and decision-makers in the healthcare industry.

Innovative player evaluation: Dual-possibility Pythagorean fuzzy hypersoft sets for accurate international football rankings

This study introduces an advanced approach for ranking international football players, addressing the inherent uncertainties in performance evaluations. By integrating dual possibility theory and Pythagorean fuzzy sets, the model accommodates varying degrees of ambiguity and imprecision in player attributes. Additionally, the use of hypersoft set theory enriches the analysis by capturing the multifaceted nature of player evaluations. The proposed aggregation operators refine the synthesis of diverse information sources, leading to a comprehensive and nuanced assessment. This research significantly enhances player evaluation methodologies, providing a more adaptable framework for a fair assessment of international football talent. A practical example illustrates the application of dual-possibility Pythagorean fuzzy hypersoft sets (DP-PFHSS). A numerical technique is proposed for solving multi-criteria decision-making (MCDM) challenges with known dual possibility information using the proposed aggregation operators. This decision-making algorithm effectively determines a football player's worth, contributing to the overall ranking and evaluation process. The approach aids in scouting and recruitment by facilitating talent identification and informed player signings. Graphical analysis, comparing existing and proposed methods using average and geometric operators, demonstrates the superiority of the proposed approach in the players evaluation, indicating thatF 1 is in the top ranking.

On t-intuitionistic fuzzy graphs: a comprehensive analysis and application in poverty reduction

This paper explains the idea of t-intuitionistic fuzzy graphs as a powerful way to analyze and display relationships that are difficult to understand. The article also illustrates the ability of t-intuitionistic fuzzy graphs to establish complex relationships with multiple factors or dimensions of a physical situation under consideration. Moreover, the fundamental set operations of t-intuitionistic fuzzy graphs are proposed. The notions of homomorphism and isomorphism of t-intuitionistic fuzzy graphs are also introduced. Furthermore, the paper highlights a practical application of the proposed technique in the context of poverty reduction within a specific society. By employing t-intuitionistic fuzzy graphs, the research demonstrates the potential to address the multifaceted nature of poverty, considering various contributing factors and their interdependencies. This application showcases the versatility and effectiveness of t-intuitionistic fuzzy graphs as a tool for decision-making and policy planning in complex societal issues.

A Geometric-Based LSGDM Method for Tourism Project Decision Optimization with Trust–Distrust Relationships

In this paper, we discuss the decision optimization of tourism projects in Hebei Province, China. To improve the process of analyzing tourism projects, we introduce a model that includes multiple decision makers as subjects based on a standard four-dimensional evaluation system. In order to improve the effectiveness of decision-making results, we will increase the number of decision makers to 40. A novel large-scale group decision-making (LSGDM) algorithm that incorporates the trust–distrust asymmetric relationships between decision makers is proposed. This model contains three main innovations: firstly, in the evaluation of decision makers’ social network relations, the trust–distrust value is introduced as a new carrier, and a weighted directed network and data integration operator are constructed based on the evaluation between decision makers; secondly, an extended Girvan-Newman (GN) algorithm is constructed to cluster the decision makers from this weighted network; thirdly, the interval-valued intuitionistic fuzzy number (IVIFN) is used to evaluate the alternatives, studying the IVIFN’s geometric significance by placing in a rectangular coordinate system. Finally, a new LSGDM model is proposed. Using the development of a cultural tourism project in a township as an example, the effectiveness of the proposed model is illustrated. By comparing the results of our method to those of a LSGDM algorithm that does not incorporate trust relationships, we assess the performance of the new model.

Objective Criticism and Negative Conclusions on Using the Fuzzy SWARA Method in Multi-Criteria Decision Making

The quality of output or decision-making depends on high-quality input data, their adequate evaluation, the application of adequate approaches, and accurate calculation. In this paper, an objective criticism of applying the fuzzy SWARA (step-wise weight assessment ratio analysis) method based on the Chang TFN (triangular fuzzy number) scale is performed. Through research, it has been noticed that a large number of studies use this approach and, as an epilogue, there are wrong decisions based on inconsistent values in relation to the initial assessment of decision-makers (DMs). Seven representative studies (logistics, construction industry, financial performance management, and supply chain) with different parameter structures and decision matrix sizes have been singled out. The main hypothesis has been set, which implies that the application of this approach leads to wrong decisions because the weight values of the criteria are incorrect. A comparative analysis with the improved fuzzy SWARA (IMF SWARA) method has been created and a number of negative conclusions has been reached on using the fuzzy SWARA method and the Chang scale: Primarily, that using such an approach is impossible for two or more criteria to have equal value, that allocating TFN (1,1,1) leads to criteria values that are inconsistent with expert evaluation, that the last-ranked criteria in the fuzzy SWARA method have no influential value on the ranking of alternatives, that there is a great gap between the most significant and last-ranked criteria, and that the most significant criterion has a huge impact on the evaluation of alternative solutions and decision making. As a general conclusion, it is given that this approach is not adequate for application in problems of multi-criteria decision making because it produces inadequate management of processes and activities in various spheres.

A Novel Integration of IF-DEMATEL and TOPSIS for the Classifier Selection Problem in Assistive Technology Adoption for People with Dementia

The classifier selection problem in Assistive Technology Adoption refers to selecting the classification algorithms that have the best performance in predicting the adoption of technology, and is often addressed through measuring different single performance indicators. Satisfactory classifier selection can help in reducing time and costs involved in the technology adoption process. As there are multiple criteria from different domains and several candidate classification algorithms, the classifier selection process is now a problem that can be addressed using Multiple-Criteria Decision-Making (MCDM) methods. This paper proposes a novel approach to address the classifier selection problem by integrating Intuitionistic Fuzzy Sets (IFS), Decision Making Trial and Evaluation Laboratory (DEMATEL), and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The step-by-step procedure behind this application is as follows. First, IF-DEMATEL was used for estimating the criteria and sub-criteria weights considering uncertainty. This method was also employed to evaluate the interrelations among classifier selection criteria. Finally, a modified TOPSIS was applied to generate an overall suitability index per classifier so that the most effective ones can be selected. The proposed approach was validated using a real-world case study concerning the adoption of a mobile-based reminding solution by People with Dementia (PwD). The outputs allow public health managers to accurately identify whether PwD can adopt an assistive technology which results in (i) reduced cost overruns due to wrong classification, (ii) improved quality of life of adopters, and (iii) rapid deployment of intervention alternatives for non-adopters.

Archimedean t-Norm and t-Conorm-Based Aggregation Operators of HFNs, with the Approach of Improving Education

The aim of this paper is to develop the calculus of hesitant fuzzy numbers (HFNs), have been recently proposed as the newest extension of hesitant fuzzy sets. At first, based on the willingness of decision maker to each part of HFNs, a new method has been proposed to compare them. Then, several t -norm and t -conorm-based aggregation operators of HFNs, i.e., algebraic t -norm and t -conorm, Einstein t -norm and t -conorm, Hamacher t -norm and t -conorm, Frank t -norm and t -conorm have been defined, and some of their mathematical properties are also discussed. As the special cases of the above t -norm and t -conorm-based aggregation operators of HFNs, Archimedean t -norm and t -conorm-based HFN weighted averaging operator, Archimedean t -norm and t -conorm-based HFN weighted geometric operator, Archimedean t -norm and t -conorm-based HFN ordered weighted averaging operator, and Archimedean t -norm and t -conorm-based HFN ordered weighted geometric operator have been proposed. The new problem of improving the process of educational activities under the Covid-19 epidemic conditions, for instance, has been defined as a multi-attribute group decision-making (MAGDM) problem, in which students are its options, courses are its criteria, and teachers are members of the decision-making team. Then, the scores of final exams and teachers’ assessments merged together as HFNs, and a new method has been proposed based on the before mentioned operators to solve the resulting MAGDM problem. A numerical example, the results of which are also analyzed, is responsible for explaining what is proposed in this article. Finally, subsequent studies in this area are briefly stated.

New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis

The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods.

Policies for Rapid Mitigation of the Crisis’ Effects on Agricultural Supply Chains: A Multi-Criteria Decision Support System with Monte Carlo Simulation

This paper proposes an integrated approach towards rapid decision-making in the agricultural sector aimed at improvement of its resilience. Methodologically, we seek to devise a framework that is able to take the uncertainty regarding policy preferences into account. Empirically, we focus on the effects of COVID-19 on agriculture. First, we propose a multi-criteria decision-making framework following the Pugh matrix approach for group decision-making. The Monte Carlo simulation is used to check the effects of the perturbations in the criteria weights. Then, we identify the factors behind agricultural resilience and organize them into the three groups (food security, agricultural viability, decent jobs). The expert survey is carried out to elicit the ratings in regard to the expected effects of the policy measures with respect to dimensions of agricultural resilience. The case of Lithuania is considered in the empirical analysis. The existing and newly proposed agricultural policy measures are taken into account. The measures related to alleviation of the financial burden (e.g., credit payment deferral) appear to be the most effective in accordance with the expert ratings.

Identification of Shipyard Priorities in a Multi-Criteria Decision-Making Environment through a Transdisciplinary Energy Management Framework: A Real Case Study for a Turkish Shipyard

Ship building, as an energy-intensive sector, produces significant amounts of air emissions, including greenhouse gases. Most research in greenhouse gas reductions from shipping concentrates on the reduction in emissions during the operational phase. However, as emissions during ship operation are reduced, the construction and dismantling phases of ships are becoming increasingly important in the assessment of the life-cycle impact of ships. In this study, priorities for a Turkish shipyard to become energy efficient were identified by means of a semi-structured questionnaire and an interview. This was undertaken using Fuzzy Multi-Criteria Decision-Making methods, including the Fuzzy Analytical Hierarchy Process and Fuzzy Order of Preference by Similarity to Ideal Solution, which are part of a proposed systematic and transdisciplinary Energy Management Framework and System. By applying Multi-Criteria Decision-Making methods, this framework supports the shipyard’s decision makers to make rational and optimized decisions regarding energy sectors within their activities. Applying the framework has significant potential to help achieve good product quality while reducing costs and environmental impacts, and can thereby enhance the sustainability of shipping. Moreover, the framework can boost both business and socio-economic perspectives for the shipyard, and improve its reputation and competitiveness, in alignment with achieving the Nationally Determined Contributions of States under the Paris Agreement.

Reducing Cognitive Effort in Scoring Negotiation Space Using the Fuzzy Clustering Model

Negotiation scoring systems are fundamental tools used in negotiation support to facilitate parties searching for negotiation agreement and analyzing its efficiency and fairness. Such a scoring system is obtained in prenegotiation by implementing selected multiple criteria decision-aiding methods to elicit the negotiator’s preferences precisely and ensure that the support is reliable. However, the methods classically used in the preference elicitation require much cognitive effort from the negotiators, and hence, do not prevent them from using heuristics and making simple errors that result in inaccurate scoring systems. This paper aims to develop an alternative tool that allows scoring the negotiation offers by implementing a sorting approach and the reference set of limiting profiles defined individually by the negotiators in the form of complete packages. These limiting profiles are evaluated holistically and verbally by the negotiator. Then the fuzzy decision model is built that uses the notion of increasing the preference granularity by introducing a series of limiting sub-profiles for corresponding sub-categories of offers. This process is performed automatically by the support algorithm and does not require any additional preferential information from the negotiator. A new method of generating reference fuzzy scores to allow a detailed assignment of any negotiation offer from feasible negotiation space to clusters and sub-clusters is proposed. Finally, the efficient frontier and Nash’s fair division are used to identify the recommended packages for negotiation in the bargaining phase. This new approach allows negotiators to obtain economically efficient, fair, balanced, and reciprocated agreements while minimizing information needs and effort.

Symmetric and Asymmetric Data in Solution Models

This Special Issue covers symmetric and asymmetric data that occur in real-life problems. We invited authors to submit their theoretical or experimental research to present engineering and economic problem solution models that deal with symmetry or asymmetry of different data types. The Special Issue gained interest in the research community and received many submissions. After rigorous scientific evaluation by editors and reviewers, seventeen papers were accepted and published. The authors proposed different solution models, mainly covering uncertain data in multi-criteria decision-making problems as complex tools to balance the symmetry between goals, risks, and constraints to cope with the complicated problems in engineering or management. Therefore, we invite researchers interested in the topics to read the papers provided in the Special Issue.

A LSGDM method based on social network and IVIFN’s geometric characteristics for evaluating the collaborative innovation problem1

During the development of regional economy, introducing collaborative innovation is an important policy. Constructing a scientific and effective measurement for evaluating the collaborative innovation degree is essential to determine an optimum collaborative innovation plan. As this problem is complex and has a long-lasting impact, this paper will propose a novel large scale group decision making (LSGDM) method both considering decision makers’ social network and their evaluation quality. Firstly, the decision makers will be detected based on their social connections and aggregated into different subgroups by an optimization algorithm. Secondly, decision makers are weighted according to their important degree and decision information, where the information is carried by interval valued intuitionistic fuzzy number (IVIFN). During the information processing, IVIFN is put in rectangular coordinate system considering its geometric meaning. And some related novel concept are given based on the barycenter of rectangle region determined by IVIFN. Meanwhile, the criteria’s weights are calculated by the accurate degree and deviation degree. A classical example is used to illustrate the effect of weighting methods. In summary, a large scale group decision making method based on the geometry characteristics of IVIFN (GIVIFN-LSGDM) is proposed. The scientific and practicability of GIVIFN-LSGDM method is illustrated through evaluating four different projects based on the constructed criteria system. Comparisons with the other methods are discussed, followed by conclusions and further research.

Evaluation of Online Teaching Quality: An Extended Linguistic MAGDM Framework Based on Risk Preferences and Unknown Weight Information

Evaluation of online teaching quality has become an important issue because many universities are turning to online classes due to the Corona Virus Disease 2019 (COVID-19) pandemic. In this paper, online teaching quality evaluation is considered as a linguistic multi-attribute group decision-making (MAGDM) problem. Generally, the evaluation sematic information can be symmetrically or asymmetrically distributed in linguistic term sets. Thus, an extended linguistic MAGDM framework is proposed for evaluating online teaching quality. As the main contribution, the proposed method takes into account the risk preferences of assessment experts (AEs) and unknown weight information of attributes and sub-attributes. To be specific, the Delphi method is employed to establish a multi-level evaluation indicator system (EIS) of online teaching quality. Then, by introducing the group generalized linguistic term set (GLTS) with two risk preference parameters, a two-stage optimization model is developed to calculate the weights of attributes and sub-attributes objectively. Subsequently, the linguistic MAGDM framework was divided into two stages. The first stage maximizes the group comprehensive rating values of teachers on different attributes to obtain partial ranking results for teachers on each attribute. The latter stage maximizes the group comprehensive rating values of teachers to evaluate the overall quality. Finally, a case study is provided to illustrate how to apply the framework to evaluate online teaching quality.

A Fuzzy Inference System for Players Evaluation in Multi-Player Sports: The Football Study Case

Decision support systems often involve taking into account many factors that influence the choice of existing options. Besides, given the expert’s uncertainty on how to express the relationships between the collected data, it is not easy to define how to choose optimal solutions. Such problems also arise in sport, where coaches or players have many variants to choose from when conducting training or selecting the composition of players for competitions. In this paper, an objective fuzzy inference system based on fuzzy logic to evaluate players in team sports is proposed on the example of football. Based on the Characteristic Objects Method (COMET), a multi-criteria model has been developed to evaluate players on the positions of forwards based on their match statistics. The study has shown that this method can be used effectively in assessing players based on their performance. The COMET method was chosen because of its unique properties. It is one of the few methods that allow identifying the model without giving weightings of decision criteria. Symmetrical and asymmetrical fuzzy triangular numbers were used in model identification. Using the calculated derivatives in the point, it turned out that the criteria weights change in the problem state space. This prevents the use of other multi-criteria decision analysis (MCDA) methods. However, we compare the obtained model with the Technique of Order Preference Similarity (TOPSIS) method in order to better show the advantage of the proposed approach. The results from the objectified COMET model were compared with subjective rankings such as Golden Ball and player value.

TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators

The theory of complex spherical fuzzy sets (CSFSs) is a mixture of two theories, i.e., complex fuzzy sets (CFSs) and spherical fuzzy sets (SFSs), to cope with uncertain and unreliable information in realistic decision-making situations. CSFSs contain three grades in the form of polar coordinates, e.g., truth, abstinence, and falsity, belonging to a unit disc in a complex plane, with a condition that the sum of squares of the real part of the truth, abstinence, and falsity grades is not exceeded by a unit interval. In this paper, we first consider some properties and their operational laws of CSFSs. Additionally, based on CSFSs, the complex spherical fuzzy Bonferroni mean (CSFBM) and complex spherical fuzzy weighted Bonferroni mean (CSFWBM) operators are proposed. The special cases of the proposed operators are also discussed. A multi-attribute decision making (MADM) problem was chosen to be resolved based on the proposed CSFBM and CSFWBM operators. We then propose the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method based on CSFSs (CSFS-TOPSIS). An application example is given to delineate the proposed methods and a close examination is undertaken. The advantages and comparative analysis of the proposed approaches are also presented.