Compared to Fermatean fuzzy sets, Pythagorean fuzzy sets, and intuitionistic fuzzy sets, (p, q)-rung orthopair fuzzy sets ((p, q)-ROFSs) can display membership grades over a wider range, allowing them to present more confusing circumstances. This article elaborates the use of (p, q)-ROFS in engineering design for material selection. Material selection is a crucial part of engineering because it satisfies all of the object’s functional requirements. The design process’s crucial and time-consuming phase of material selection. The output, profitability, and reputation of a manufacturer can suffer from the choice of the incorrect material(s). An essential tool in the engineering design process for handling the complexity of material selection is multi-attribute decision-making (MADM). However, the outcomes of using the current MADM approaches are frequently inconsistent. To solve these issues, a novel aggregation method based on the truthness and falsity indices of (p, q)-ROFS is suggested for material selection in engineering design. We present (p, q)-rung orthopair fuzzy Hamacher interactive aggregation operators (AOs) that take advantage of (p, q)-ROFS and smooth approximation with interactive Hamacher operations. Based on the indicated AOs, in engineering design, a trustworthy MADM method is advised for material selection (MS). The main contributions of this article are as follows: (1) The aggregation operators for (p, q)-rung orthopair fuzzy numbers and their attributes have been studied using Hamacher norms. (2) MADM is established under (p, q)-rung orthopair fuzzy sets. A step-by-step explanation of the proposed method is given using an algorithm. (3) The developed method is then applied as a case study in the selection of materials for cryogenic storage tanks. (4) The results have been contrasted with the rankings obtained by several currently employed techniques. The authenticity analysis and comparison analysis are also intended to talk about the reliability and sanity of the best choice.
In this paper, we propose a novel multi-attribute group decision making (MAGDM) approach under the p, q-quasirung orthopair fuzzy number (p, q-QOFN) environment. For this, we propose new multiplication operation and scalar power operation for p, q-QOFNs based on Yager’s norm. Then, by using the proposed multiplication operation and scalar power operation of p, q-QOFNs and the concept of prioritized geometric aggregation operator (AO), we propose the p, q-quasirung orthopair fuzzy Yager prioritized weighted geometric (p, q-QOFYPWG) AO for aggregating p, q-QOFNs. We also prove the different properties of the proposed p, q-QOFYPWG AO of p, q-QOFNs. However, based on the proposed p, q-QOFYPWG AO, we propose a new MAGDM approach in the context of p, q-QOFNs environment. Afterwards, we utilize the proposed MAGDM approach to solve the different MAGDM problems, and compare the preference orders (POs) obtained from the proposed MAGDM approach to POs obtained from other existing MAGDM approaches. The proposed MAGDM approach can overcome the shortcomings of the existing MAGDM approaches, where they cannot distinguish the POs of the alternatives in some cases. The proposed MAGDM approach provides a very useful approach to deal with MAGDM problems in the p, q-QOFNs environment.
The correlation coefficient is a powerful tool to measure the relationship between two variables and is very useful in decision-making. In this paper, we propose a new multiattribute decision-making (MADM) method for q-rung orthopair fuzzy number (q-ROFN) environment. For this, we propose a novel correlation coefficient for q-rung orthopair fuzzy sets (q-ROFSs), which measures the strength of the relationship between two q-ROFSs. We also present the various properties of the proposed correlation coefficient of q-ROFSs. Moreover, we also develop the weighted correlation coefficient of q-ROFSs. Afterward, we propose a new MADM method under the q-ROFNs environment based on the proposed weighted correlation coefficient of q-ROFSs and the “Technique for Order Preference by Similarity to Ideal Solution” (TOPSIS) method. The proposed MADM method can overcome the shortcomings of the existing MADM methods of the q-ROFNs environment, where they cannot distinguish the ranking orders (ROs) of the alternatives. The proposed MADM method provides a very useful method to deal with MADM problems in the q-ROFNs environment.
This paper introduces an enhanced fuzzy k-nearest neighbor (FKNN) approach called the feature-weighted Minkowski distance and local means-based fuzzy k-nearest neighbor (FWM-LMFKNN). This method improves classification accuracy by incorporating feature weights, Minkowski distance, and class representative local mean vectors. The feature weighting process is developed based on feature relevance and complementarity. We improve the distance calculations between instances by utilizing feature information-based weighting and Minkowski distance, resulting in a more precise set of nearest neighbors. Furthermore, the FWM-LMFKNN classifier considers the local structure of class subsets by using local mean vectors instead of individual neighbors, which improves its classification performance. Empirical results using twenty different real-world data sets demonstrate that the proposed method achieves statistically significantly higher classification performance than traditional KNN, FKNN, and six other related state-of-the-art methods.
Probabilistic linguistic term sets (PLTSs), a form of fuzzy language, are capable of effectively expressing the evaluation information of decision-makers (DMs) in emergency decision-making (EDM) for disasters. Thus, an EDM method based on PLTSs and regret theory is proposed, addressing the uncertainty of decision-making information and the incomplete rationality of DMs in disaster scenarios. First, a novel distance measure method for PLTSs is established, integrating Euclidean distance, Jensen–Shannon (JS) divergence and Jousselme distance. Next, expert weights are determined based on the trust in each expert and the similarity of viewpoints. During consensus reaching, a feedback adjustment coefficient is introduced to maintain the integrity of the original evaluation information provided by the experts. Furthermore, a combined weighting method is developed, incorporating both objective and subjective attribute weights to derive comprehensive attribute weights. Taking into account the incomplete rationality of DMs, an EDM method is formulated using PLTSs and regret theory to prioritize alternatives. Finally, the effectiveness of the proposed method is validated through a case study using the selection of a transportation plan for relief supplies during the Yushu earthquake as an example, along with sensitivity analysis and a comparison with other existing approaches.
In the realm of expressing fuzzy and vague information, T-spherical fuzzy sets (TSPFSs) emerge as a powerful extension of both picture fuzzy sets (PFSs) and spherical fuzzy sets (SFSs), offering decision-makers a broader spectrum of descriptive capabilities. Within the domain of multi-attribute group decision-making (MAGDM), the significance of T-spherical fuzzy aggregation operators (AOs) under T-spherical fuzzy conditions cannot be overstated. Hence, our manuscript contributes by introducing a collection of ground-breaking T-spherical fuzzy AOs. This paper establishes a set of innovative T-spherical fuzzy operational laws grounded in Dombi t-norm and Dombi t-conorm (DTNCN) principles. Utilizing the strengths of power aggregation operators, which effectively capture the implications of unfavorable information, and Heronian mean (HM) operators, which adeptly assess the collective association among the evaluated arguments. Some aggregation operators are examined, namely T-spherical fuzzy Dombi power Heronian mean (TSPFDPHM) operator, T-spherical fuzzy Dombi weighted power Heronian mean (TSPFDWPHM) operator, T-spherical fuzzy Dombi geometric power Heronian mean (TSPFDGPHM) operator, and T-spherical fuzzy Dombi weighted geometric power Heronian mean (TSPFDWGPHM) operator. Additionally, we present a host of properties exhibited by these proposed AOs, along with specific cases that allow for adjustable parameters. Subsequently, we develop a comprehensive algorithm for MAGDM based on the proposed AOs within the T-spherical fuzzy environment. In conclusion, we apply the devised algorithm to a real-world scenario involving selecting the best road construction company for a post-flood road rehabilitation project in Pakistan. Through comparative analysis with existing methodologies, we demonstrate the validity and superiority of our developed scheme, thereby reinforcing its practical applicability and effectiveness.
Interval-valued fuzzy sets are the generalization of classical fuzzy sets. The assumption behind the theoretical interpretation of interval-valued fuzzy sets is that each element has exactly one real-valued truth membership degree from an interval. Information and knowledge measures play a major part in the interval-valued fuzzy set theory. This manuscript’s main objective is to investigate the information and knowledge measures in an interval-valued fuzzy context. A knowledge measure for interval-valued fuzzy sets is proposed axiomatically in this manuscript. The effectiveness and consistency of the proposed knowledge measure are demonstrated by numerical examples for structured linguistic comparison, ambiguity, and criteria weights computation in the interval-valued fuzzy context. An accuracy measure in interval-valued fuzzy-context is developed using the proposed knowledge measure. Apart from that, a similarity and a dissimilarity measure in an interval-valued fuzzy context are proposed. The suggested accuracy, similarity, and dissimilarity measures are used to solve cluster analysis and pattern detection issues. Additionally, a case study on the damage caused by floods and heavy rainfall in India between 2012 and 2021 is discussed, and the data obtained from this study are used to create clusters using the suggested accuracy measure. Furthermore, the accuracy, similarity, and dissimilarity measures that have been proposed, are used to address the pattern detection problems.
Picture fuzzy set (PFS) concepts are modified versions of fuzzy sets. Picture fuzzy sets cover all aspects of portraying human opinion accurately. In this paper, we create Muirhead mean (MM) operators employing arithmetic operations modelled by Hamacher t-norm (TN) and t-conorm (TCN) using picture fuzzy information. These operators are known as picture fuzzy. Hamacher MM (PFHMM) and picture fuzzy Hamacher weighted MM (PFHWMM). Combining Hamacher t-norm and t-conorm arithmetic with the MM operator allows for flexible aggregation and consideration of attribute interrelationships. Also, MM is a generalization of commonly used aggregation operators, including arithmetic mean (AM), geometric mean (GM), Bonferroni mean (BM), and Maclaurin symmetric mean (MSM). The paper discusses some desirable properties and exceptional cases of proposed operators. The study also examines the Multiple Attribute Decision Making (MADM) technique using the suggested PFHWMM operator under the system of PFS information. A MADM problem is about allocating healthcare resources during a pandemic to test how well the suggested operators and methods work. To demonstrate the superiority of the currently proposed methods, we conducted a comprehensive comparative analysis to contrast the results of these approaches with the prevailing theories in the literature.
One of the most commonly used reliability analysis methods is failure mode and effects analysis, which is very effective at finding, assessing, and addressing potential failure modes in a variety of commercial applications. Its wide-ranging viewpoint facilitates the investigation of potential failures, causes, and effects in designs, products, and processes. On the other hand, traditional failure mode and effects analysis is often criticized for its shortcomings in identifying the weights of the criteria, identifying the failure modes’ relative risk, and managing ambiguity in the risk assessment process. To overcome these complications, this article considers the analytic hierarchy process and the VIKOR method with picture fuzzy rough numbers. Primarily, a picture fuzzy rough number is offered to represent an expert’s expertise, compile group risk assessments, and address subjectivity and uncertainty in risk assessment. Then, an extended analytic hierarchy process based on picture fuzzy rough numbers is offered to regulate the criterion’s weights. An extended VIKOR method based on picture fuzzy rough number is used to rate the failure scenarios based on risk priority. A case study of the check valve in real life is used to validate the effectiveness of the suggested failure mechanism and effect analysis. The effectiveness of the suggested picture fuzzy rough multi-criteria group decision-making method is demonstrated by comparative studies, which also highlight its significant advantages in managing subjectivity and ambiguity during the evaluation of failure modes.
Pythagorean fuzzy set (PyFS) is an effective model to describe the vagueness and uncertainty of decision-makers. Several novel averaging aggregation operators (AOs) have been formulated by using the PyF environment. The main focus of this article is to explore the unique mathematical model of Aczel-Alsina operational laws (A-AOls) for PyF information. To comprehensively identify the theory of power Bonferroni mean (PBM) operators which is the generalized formation of power average (PA) and Bonferroni mean (BM) operators that tend to reduce the adverse consequences of imprecise predictions and can perform the connections between attributed values. To acquire benefits from PA and BM operators, we utilize (A-AOls) and power Bonferroni AOs (PBAOs) to propose some new AOs such as PyFA-APBM and PyFA-A weighted PBM (PyFA-AWPBM) operators and also elaborate their persuasive particular characteristics. The proposed PyFAAWPBM operators are specifically relevant to improve the accuracy and adaptability of the information integration process by incorporating the AA operational rules Moreover, we provide a methodology for solving multi-attribute decision-making problems (MADM) by using the PyF framework based on the newly developed AOs. Furthermore, a numerical example is provided to demonstrate the efficiency and reliability of the developed AOs. Finally, a comparative analysis is carried out to exhibit the reliability and validity of the suggested strategy.
Strategic planning is a crucial activity for the owners and managers of business organisations, and it is an effective process that incorporates many distinct decision-making circumstances. Although there are numerous researches done to aid decision-makers, there are only a few studies that may provide the desirable generality, flexibility, and compatibility in adapting risk preferences. This study intends to propose a generalized multicriteria group decision-making (MCGDM) methodology by means of generalized parameter and Archimedean t-norms and t-conorms under linguistic q -rung orthopair fuzzy (Lq-ROF) theory for managing uncertainties in strategy formulations. For this purpose, a wide range of generalized aggregation operators, viz., Lq-ROF Archimedean weighted averaging, Lq-ROF Archimedean weighted geometric, Lq-ROF Archimedean generalized weighted averaging, and Lq-ROF Archimedean generalized weighted geometric operators are investigated. The contribution of this research lies in providing a robust and flexible methodology that integrates generalized parameters and Archimedean operators within the Lq-ROF framework, thereby offering a valuable tool for decision-makers navigating the complexities of strategy formulation in the presence of uncertainties. Additionally, some novel operational laws based on Archimedean t-norms and t-conorms are defined for Lq-ROF numbers. Further, several prominent characteristics of the developed operators are investigated. A strategic MCGDM model with Lq-ROF context is put forward and is applied to a financial strategy-making problem for a multinational organisation. The sensitivity analysis undertaken shows that the developed method possesses favourable flexibility and effectiveness. The potentiality and superiority are explored by comparing the obtained results with several existing studies.
Topological indices (TIs) are numerical structures that are associated with a graph to identify its topology. TIs are highly popular in the literature with a wide range of applications from chemistry to economics. However, TIs have limitations in representating complex relations within the graphs creating some uncertainities. Fuzzy graph (FG) and intuitionistic fuzzy graph (IFG) are introduced to overcome these uncertainities. While a FG a describes degree of membership of an object in a graph, IFG delineate information on membership or nonmembership under uncertainity. This study aims to introduce novel TIs such as the general second Zagreb index, the Sombor index of the third version, and the Sombor index of the fourth version in the IFG framework in order to improve practicality of FG and IFG applications. Some properties of the proposed indices and their upper bounds are provided as well. Proposed TIs are applied to an internet routing network as a case study. Results of the study show that adding more internet routers in the network can increase internet speed and the strength of the entire system. Finally, comparative studies for the Sombor index of the third version and the Sombor index of the fourth version are also revealed.
In a dynamic world of technological advances, the Internet of Things (IoT) is a transformational and widespread force that has revolutionized the way we communicate with our surroundings and regulate our environments. It offers several advantages but also introduces inherent risks. In this study, we provide a comprehensive analysis of the risks associated with IoT and employ the effectiveness of a Linear Diophantine Fuzzy Set to rank the risk factors. Because of the significant uncertainties frequently present in IoT contexts, the use of a fuzzy framework is invaluable in discerning and addressing these risks. The primary contribution is to employ the Measurement of Alternatives and Ranking according to the Compromise Solution (MARCOS) method and linear diophantine fuzzy sets to propose a multi-criteria group decision-making method (MCGDM) for ranking attributes to facilitate risk prioritization, enabling consumers to determine the crucial hazards in their IoT systems. Furthermore, we implement a comparative study and a sensitivity analysis to demonstrate the robustness of our proposed methodology. The insights obtained from our research not only improve the awareness of IoT hazards but also enable organizations and individuals to make informed decisions when navigating IoT fields. By proactively addressing these risks, we endorse the development and secure deployment of IoT technology.
Linguistic q-rung orthopair fuzzy number (Lq-ROFN) is a valuable tool for expressing the uncertainty of qualitative information that has received a lot of attention over the last 5 years. In this article, we propose the correlation coefficient to measure the strength of the relationship between two linguistic q-rung orthopair fuzzy sets (Lq-ROFSs). We also provide the various properties of the proposed correlation coefficient of Lq-ROFSs. Moreover, we also propose the weighted correlation coefficient of Lq-ROFSs. Afterward, using the proposed weighted correlation coefficient of Lq-ROFSs and the “technique for order of preference by similarity to ideal solution” (TOPSIS) method, we develop a novel multiattribute group decision-making (MAGDM) method under the Lq-ROFNs environment. We also solve the different MAGDM problems using the proposed MAGDM method and compare the preference order (PO) obtained by the proposed MAGDM method with the POs obtained by the existing MAGDM methods. The comparison analysis shows that the drawbacks of the existing MAGDM methods can be successfully overcome by the proposed MAGDM method, where existing MAGDM methods cannot distinguish the POs of alternatives. In the Lq-ROFNs environment, the proposed MAGDM method provides a useful decision-making method for solving MAGDM problems.
The Best Worst Method (BWM), a reduced version of the AHP, is a recent multi-criteria decision-making tool based on pairwise comparisons with reference to the best and worst criteria. Consistency Ratio (CR) measurement for the rating quality and prioritizations is still a controversial topic. Firstly, the computation for the current CR of BWM must rely on a software optimization solver to find the optimal values, and the solver may not always guarantee the exact optimal solutions, especially if the computational cost settings are not large enough for higher number of criteria. Secondly, much effort to evaluate optimization algorithms is needed to find the best solutions with the least computational resources due to diverse solvers possibly leading to different results with different performances. Thirdly, optimization programming code is not trivial to be implemented for general BWM users. To address these issues, this paper presents the closed-form solutions, Max of Edge Error Matrix (MEEM) (Eq. (44) of Theorem 4) and Minmax Edge Error Determinant (MEED) (Algorithm 1), to replace the BWM optimization models to directly calculate the CR values. Two simulations have been performed with a basic laptop using a single process. One simulation of twenty thousand random pairs of vectors took 26.34 h to perform to verify that the approximate results are higher than or very close to the exact closed-form values of both methods when high computational cost is allocated for the solver to increase the precision. Another simulation of one million random pairs of vectors only took 1.27 h to perform to verify that the MEED and MEEM methods always produce the same results for the number of criteria up to nine. The computational time for the exact results is dramatically reduced when the solver is not needed. The advantages of the proposed solutions include the following: the software to solve the optimization model to obtain CR is unnecessary, and the proposed calculation is extremely efficient to obtain the exact accuracy. The two-step optimization model can preserve the fixed Minmax Edge Error to find the weights which add up to one, which is the condition to determine if the model reaches exact optimal solutions. As the CR optimization model produces multiple versions of weights, which are recommended not to be used, the new method does not need to compute the unnecessary weight values to get the Minmax Edge Error. With the provision of equations leading to closed forms, users can understand the properties of CR in much clearer perspectives. Due to the computational efficiency and explainability, the proposed closed forms can replace the CR optimization model to compute CR efficiently and accurately for all diverse applications using BWM.
The concept of a neutrosophic set is an extension of a fuzzy set that uses indeterminacy. Similarly, an intuitionistic set has an extension, which is known as a single-valued neutrosophic set. The extension of intuitionistic fuzzy graphs and fuzzy graphs is single-valued neutrosophic fuzzy graphs (SVNF-graphs), which is the new component of graph theory. These versions of graph theory play an important role in many real-world problems, like medical diagnoses, law, engineering, finance, and industry. SVNF-graphs play an important role in linguistics, genetics, networking, sociology, computer technology, economics, and communication. The topological graph parameter gives a real number to the associated graph. There are numerous topological graph parameters proposed in the literature. In topological graph parameters, some uncertainty exists. Rosenfeld, Atanssov, and Smarandache introduced the concepts of a fuzzy graph, intuitionistic fuzzy graph (IFG), and SVNF-graph to overcome these uncertainties. SVNF-graph, IFG, and FG have vital roles in solving world-life problems. In this research work, we proposed a pythonic environment for the single-value neutrosophic fuzzy topological graph parameters. We introduced for the very first time some SVNF-graph parameters, like the Sombor graph parameter: the third and fourth versions of the SVNF-Sombor graph parameters for the SVNF-graph framework. Also, we have proved some characteristics and bounds of these topological graph parameters. We have discussed the social media application for the SVNF-Sombor graph parameter and its third and fourth versions. Under consideration application, We have shown that deleting a person (vertex) in the network can increase or decrease the chances of sending friend requests to other people of artificial intelligence.
In recent years, there has been a growing interest in multi-label data classification, with a particular emphasis on multi-label feature selection. While various information-theoretic methods have been devised to determine feature correlations, a majority of them rely on sequential and greedy search strategies for feature subset selection. Concurrently, within the realm of multi-criteria decision-making (MCDM), fuzzy-based methods have gained traction due to their versatile capabilities. In this study, contrary to sequential search, the multi-label feature selection problem is formulated as an MCDM problem with features as alternatives by exploiting mutual information between features and labels. Further, the compromise ranking of alternatives from distance to ideal solution (CRADIS) method is extended to Pythagorean fuzzy sets (PFSs) to solve this MCDM problem and rank the features. To validate the efficacy of the proposed method, a comparative analysis is conducted against six existing methods across twelve benchmark datasets, assessing performance through six multi-label learning evaluation metrics. Furthermore, the proposed approach’s efficiency is proved by the demonstration of statistical significance and stability.
Granular neural networks (GNNs) are a type of advanced prediction models that produce information granules, offer more abstract and adaptable results. In this study, we address three significant issues in time series prediction within a federated learning (FL) scenario: the management of distributed data, the aggregation of GNNs, and the optimization of granularity levels. Traditional centralized models are insufficient for managing distributed data while ensuring privacy and reducing communication costs, and existing studies on GNNs have not explored their aggregation under a federated framework, which is essential for enhancing model robustness and stability. Additionally, determining the optimal level of granularity for GNNs remains a challenge, impacting the model's predictive accuracy and computational efficiency. To address these issues, we propose a novel federated learning framework that enhances the performance of GNNs for time series prediction. Our approach involves a comprehensive FL framework that enables the collaborative training of local GNNs, refining their granular weights through global aggregation, ensuring better privacy management, and reducing communication overhead. By focusing on the aggregation of parameters within the federated scenario, we enhance the robustness and stability of GNNs which are crucial for effective time series prediction. Furthermore, we determine the optimal levels of information granularity by employing multi-objective optimization techniques, specifically using Pareto fronts to balance the trade-offs between different objectives. Experiments on predicting air quality index for 35 stations in Beijing (China) show the effectiveness of our method.
Cosmetics can help improve our mood, beautify our looks, and raise our personality in addition to our physical health. The objective of cosmetic brands is to create new, affordable, and simple beauty goods for all consumers in order to impress a large number of individuals. The purpose of this study is to identify the cosmetic brand that, when applied to the skin can provide the desired effect. Presently, it is commonly thought of as a common multi-attribute group decision-making (MAGDM) problem. To thoroughly examine the cosmetic brands, this analysis employs the Criterion Impact Loss (CILOS) with Weighted Aggregated Sum Product Assessment (WASPAS). This study highlights that (1) product factor; (2) pricing factor; (3) distribution channel factor; and (4) consumer communication aspect are four essential attributes that affect individuals’ readiness, a brand’s development, and enhance consumers’ purchase intentions. The weights of the four described attributes are calculated using the CILOS method then ten selected cosmetic brands are ranked using the WASPAS method. The obtained results show that L’Oréal and Coty are the best cosmetic brands to meet individual beauty demands. Finally, we discuss about conclusions, the impact of the study, its limitations, and the possibility of more research.
The linguistic Pythagorean fuzzy sets (LPFSs) are productive and advantageous when decision makers (DMs) express evaluation information in decision making problems (DMPs). Due to the variability of parameters, the Aczel–Alsina t-norm and t-conorm have great applications in DMP under fuzzy sets environment. The traditional TODIM method can consider DMs’ psychological behaviors in DMPs which is a powerful tool. So, this article proposes a new multiple attribute group decision-making (MAGDM) approach based on the novel versions of TODIM method about linguistic Pythagorean fuzzy Aczel–Alsina operators. First, we introduce the operations based on Aczel–Alsina t-norm and t-conorm about linguistic Pythagorean fuzzy numbers (LPFNs). Second, we give the linguistic Pythagorean fuzzy Aczel–Alsina weighted averaging operator and linguistic Pythagorean fuzzy Aczel–Alsina weighted geometric operator, and relevant properties of the introduced operators are listed. Then, we establish a new multiple attribute group decision-making (MAGDM) approach based on ExpTODIM in LPFSs, and the built method can solve the DMPs with weight information completely unknown or completely known, the weight information is completely unknown which can be gotten by gray correlation coefficient. Finally, we solve a DMP about green building using the established approach and compare with the methodologies in existence to illustrate the advantages of purposed approach.
