Some cosine similarity measures and distance measures between q -rung orthopair fuzzy sets

Cosine similarity and distance measures for p , q - quasirung orthopair fuzzy sets: Applications in investment decision-making

Similarity measures and distance measures are used in a variety of domains, such as data clustering, image processing, retrieval of information, and recognizing patterns, in order to measure the degree of similarity or divergence between elements or datasets. p , q - quasirung orthopair fuzzy ( p , q - QOF) sets are a novel improvement in fuzzy set theory that aims to properly manage data uncertainties. Unfortunately, there is a lack of research on similarity and distance measure between p , q - QOF sets. In this paper, we investigate different cosine similarity and distance measures between to p , q - quasirung orthopair fuzzy sets ( p , q - ROFSs). Firstly, the cosine similarity measure and the Euclidean distance measure for p , q - QOFSs are defined, followed by an exploration of their respective properties. Given that the cosine measure does not satisfy the similarity measure axiom, a method is presented for constructing alternative similarity measures for p , q - QOFSs. The structure is based on the suggested cosine similarity and Euclidean distance measures, which ensure adherence to the similarity measure axiom. Furthermore, we develop a cosine distance measure for p , q - QOFSs that connects similarity and distance measurements. We then apply this technique to decision-making, taking into account both geometric and algebraic perspectives. Finally, we present a practical example that demonstrates the proposed justification and efficacy of the proposed method, and we conclude with a comparison to existing approaches.

Trade-off between Pore-Throat Structure and Mineral Composition in Modulating the Stability of Soil Organic Carbon

The preservation of soil organic carbon (OC) is an effective way to decelerate the emission of CO2 emission. However, the coregulation of pore structure and mineral composition in OC stabilization remains elusive. We employed the in situ nondestructive oxidation of OC by low-temperature ashing (LTA) combined with near edge X-ray absorption fine structure (NEXAFS), high-resolution microtomography (μ-CT), field emission electron probe microanalysis (FE-EPMA) with C-free embedding, and novel Cosine similarity measurement to investigate the C retention in different aggregate fractions of contrasting soils. Pore structure and minerals contributed equally (ca. 50%) to OC accumulation in macroaggregates, while chemical protection played a leading role in C retention with 53.4%-59.2% of residual C associated with minerals in microaggregates. Phyllosilicates were discovered to be more prominent than Fe (hydr)oxides in C stabilization. The proportion of phyllosilicates-associated C (52.0%-61.9%) was higher than that bound with Fe (hydr)oxides (45.6%-55.3%) in all aggregate fractions tested. This study disentangled quantitatively for the first time a trade-off between physical and chemical protection of OC varying with aggregate size and the different contributions of minerals to OC preservation. Incorporating pore structure and mineral composition into C modeling would optimize the C models and improve the soil C content prediction.

A novel IFN-CSM-CoCoSo approach for multiple-attribute group decision-making with intuitionistic fuzzy sets: An application in assessing corporate social responsibility performance

With the rapid growth of the economy, enterprises have encountered a series of problems while pursuing economic benefits, such as food safety and environmental pollution issues, resource shortages and energy consumption issues, which affect the sustainable development of enterprises. Establishing a corporate performance evaluation system from the perspective of social responsibility, based on stakeholder theory and the importance of overall goals reflected in the weight of social responsibility indicators, is a very effective measure to achieve corporate social responsibility (CSR) goals through CSR motivation and stakeholders. The performance evaluation of CSR from the perspective of environmental accounting is a MAGDM. Recently, the CoCoSo technique and cosine similarity measure (CSM) technique was utilized to conduct the MAGDM. The intuitionistic fuzzy sets (IFSs) are utilized as a technique for conducting uncertain information during the performance evaluation of CSR from the perspective of environmental accounting. In this study, the intuitionistic fuzzy CoCoSo based on the CSM (IFN-CSM-CoCoSo) technique is built for MAGDM with IFSs. Finally, a numerical example for performance evaluation of CSR from the perspective of environmental accounting is conducted to verify the IFN-CSM-CoCoSo technique.

An innovative approach to passport quality assessment based on the possibility q-rung ortho-pair fuzzy hypersoft set

This research article aims to evaluate the quality of passports issued by different countries. Passport quality assessment is critical in ensuring secure and efficient international travel. By leveraging this novel structure, we address the limitations of existing methods and provide a comprehensive and accurate evaluation of passport quality. Our proposed PQROFHS (possibility q-rung orthopair fuzzy hypersoft set) based structure integrates various attributes related to passport quality, considering the inherent uncertainties and imprecisions associated with each attribute. Through extensive experimentation, we demonstrate the superior performance of our approach, achieving higher accuracy, reliability, and consistency than traditional methods. The flexibility of the PQROFHS framework allows for a nuanced representation of uncertainty, enabling informed decision-making in real-world scenarios. Implementing the presented approach can enhance global travel security, streamline immigration processes, and facilitate seamless international travel experiences. An explanatory example of a real-world problem is shown to demonstrate the suggested method.

φ-OTDR signal compression scheme based on the compressed sensing theory

In this paper, based on the compressed sensing theory and the orthogonal matching pursuit algorithm, we have designed a data compression scheme, taking the Space-Temporal graph, time domain curve, and its time-frequency spectrum of phase-sensitive optical time-domain reflectometer as the target signals. The compression rates of the three signals were 40%, 35%, and 20%, while the average reconstruction times were 0.74 s, 0.49 s, and 0.32 s. The reconstructed samples effectively retained the characteristic blocks, response pulses, and energy distribution that symbolize the presence of vibrations. The average correlation coefficients of the three kinds of reconstructed signals with the original samples were 0.88, 0.85, and 0.86, respectively, and then a series of quantitative metrics were designed to evaluate the reconstructing efficiency. We have utilized the neural network trained by the original data to identify the reconstructed samples with an accuracy of over 70%, indicating that the reconstructed samples accurately present the vibration characteristics.

Employing q ˜ -rung picture fuzzy Frank accumulation operators for decision-making strategy

Accumulation of q ˜ -rung picture fuzzy information plays an essential part in decision-making situations. q ˜ -rung picture fuzzy sets can handle the uncertain information more precisely and flexibly because of the presence of parameter q ˜ . Also the Frank t-norm and t-conorm operations perform suitably for the data accumulation with the operational parameter. In this paper, we introduce q ˜ -Rung picture fuzzy Frank weighted averaging operator and q ˜ -rung picture fuzzy Frank weighted geometric operator by extending q ˜ -rung orthopair fuzzy Frank arithmetic and geometric aggregation operators respectively. We establish an algorithm to address the tedious decision-making problems using these operators. Eventually, we discuss a multiple attribute decision-making problem to demonstrate the utility and efficacy of the proposed method. A comparison of existing methods is made to reveal the supremacy and benefits of our proposed method.

Vector Similarity Measures of Dual Hesitant Fuzzy Linguistic Term Sets and Their Applications

The dual hesitant fuzzy linguistic term set (DHFLTS) is defined by two functions that express the grade of membership and the grade of non-membership using a set of linguistic terms. In the present work, we first quote an example to point out that the existing complement operation of DHFLTS is on the wrong track. Meanwhile, we redefine this operation to fill the holes in the existing ones. Next, the notion of information energy under a dual hesitant fuzzy linguistic background is provided in order to build the criteria weight determination model. To further facilitate the theory of DHFLTS, we propose two vector similarity measures, i.e., Jaccard and Dice similarity measures, and their weighted forms for DHFLTS. In addition, we pioneer some generalized similarity measures of DHFLTSs and indicate that the Dice similarity measures are particular instances of the generalized similarity measures for some parameter values. Afterward, the similarity measures-based model with unknown weight information under the background of dual hesitant fuzzy linguistic environment is constructed. Lastly, an illustrated example is included to validate the method’s application, along with sensitivity analysis and comparative analysis, demonstrating the practicality and validity of its results.

Multi-homed abnormal behavior detection algorithm based on fuzzy particle swarm cluster in user and entity behavior analytics

User and entity behavior analytics (UEBA) is an anomaly detection technique that identifies potential threat events in the enterprise's internal threat analysis and external intrusion detection. One limitation of existing methods in UEBA is that many algorithms use deterministic algorithms only for one category labeling and only compare with other samples within this category. In order to improve the efficiency of potential threat identification, we propose a model to detect multi-homed abnormal behavior based on fuzzy particle swarm clustering. Using the behavior frequency-inverse entities frequency (BF-IEF) technology, the method of measuring the similarity of entity and user behavior is optimized. To improve the iterative speed of the fuzzy clustering algorithm, the particle swarm is introduced into the search process of the category centroid. The entity's nearest neighbor relative anomaly factor (NNRAF) in multiple fuzzy categories is calculated according to the category membership matrix, and it is combined with boxplot to detect outliers. Our model solves the problem that the sample in UEBA is evaluated only in one certain class, and the characteristics of the particle swarm optimization algorithm can avoid clustering results falling into local optimal. The results show that compared with the traditional UEBA approach, the abnormal behavior detection ability of the new method is significantly improved, which can improve the ability of information systems to resist unknown threats in practical applications. In the experiment, the accuracy rate, accuracy rate, recall rate, and F1 score of the new method reach 0.92, 0.96, 0.90, and 0.93 respectively, which is significantly better than the traditional abnormal detections.

A New Approach to the Viable Ranking of Zero-Carbon Construction Materials with Generalized Fuzzy Information

This paper aims to put forward an integrated decision approach, with generalized fuzzy information for the viable selection of zero- and low-carbon materials for construction. In countries such as India, the construction sector accounts for high pollution levels and high carbon emissions. To restore sustainability and eco-friendliness, the adoption of low-carbon materials for construction is essential and, owing to the multiple attributes associated with the selection, the problem is viewed as a multi-criteria decision-making problem. Earlier studies on material selection have faced certain issues, such as the following: (i) the modeling of uncertainty is an ordeal task; (ii) the flexibility given to experts during preference elicitation is lacking; (iii) the interactions among the criteria are not well captured; and (iv) a consideration of the criteria type is crucial for ranking. To alleviate these issues, the primary objective of this paper was to develop an integrated framework, with decision approaches for material selection in the construction sector that promote sustainability. To this end, generalized fuzzy information (GFI) was adopted as the preference style as it is both flexible and has the ability to model uncertainty from the following three dimensions: membership, non-membership, and hesitancy grades. Furthermore, the CRITIC approach was extended to the GFI context for calculating criteria weights objectively, by effectively capturing criteria interactions. Furthermore, the COPRAS technique was put forward with the GFI rating for ranking zero- and low-carbon construction materials, based on diverse attributes. The usefulness of the framework was demonstrated via a case example from India and the results showed that the design cost, the financial risk, safety, water pollution, and land contamination were the top five criteria, with blended cement, mud bricks, and bamboo as the top three material alternatives for zero- and low-carbon construction. Finally, a sensitivity analysis and a comparison with other methods revealed the theoretical positives of this framework’s robustness and consistency–but it also revealed some limitations of the proposed framework.

Information Measures Based on T-Spherical Fuzzy Sets and Their Applications in Decision Making and Pattern Recognition

The T-spherical fuzzy set (TSFS) is a modification of the fuzzy set (FS), intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PyFS), q-rung orthopair fuzzy set (q-ROFS), and picture fuzzy set (PFS), with three characteristic functions: the membership degree (MD) denoted by S, the nonmembership degree (NMD) denoted by D, and the abstinence degree (AD) denoted by I. It can be used to solve problems of uncertain information with no restrictions. The distance measure (DM) is a tool that sums up the difference between points, while the similarity measure (SM) is a method applied to calculate the similarity between objects within an interval of [0,1]. The current work aims to introduce novel DMs and SMs in the environment of TSFSs to show the limitations of the previously defined DMs and SMs. The suggested DMs and SMs provide more room for all three degrees to be selected without restriction. We investigated the effectiveness of the proposed DMs and SMs by applying a pattern-recognition technique, and we determined their applicability for multicriteria decision making (MCDM) using numerical examples. The newly proposed DMs and SMs are briefly compared to existing DMs and SMs, and appropriate conclusions are drawn.

Evaluate the challenges of sustainable supply chain 4.0 implementation under the circular economy concept using new decision making approach

Industry 4.0 has the potential of growing industrialization and, on the other hand, disrupting the sustainability of prevailing manufacturing supply chains through inducing great challenges such as higher resource consumption that, in turn, results in global warming and climate change. As a result, researchers working in the area of sustainable supply chain 4.0 need to make deep evaluations on the challenges arising for manufacturing supply chains contemplating the improvement of their sustainability levels and having a digital transformation toward Industry 4.0. To fill this gap, the current paper designs an innovative framework on the basis of the Stepwise Weight Assessment Ratio Analysis (SWARA) technique and the Complex Proportional Assessment (COPRAS) approach to evaluate the challenges that may arise for supply chain 4.0 in the q-Rung Orthopair Fuzzy Sets (q-ROFSs) setting. The proposed method uses an extended SWARA process to determine the criteria importance degrees considering the experts’ preferences. The performance of the proposed method was assessed by conducting an empirical case study under the q-ROFSs condition. Further, a sensitivity analysis was executed to check whether the proposed method is stable enough to be relied on parameter values. Finally, the results obtained were compared to those of currently used methods to verify the obtained results’ reliability. As revealed by the comparative results, the framework proposed in this article was of higher consistency and strength compared to other prevailing approaches.

The cross-entropy and improved distance measures for complex q-rung orthopair hesitant fuzzy sets and their applications in multi-criteria decision-making

The complex q-rung orthopair fuzzy set (Cq-ROFS) is the extension of complex Pythagorean fuzzy set (CPFS) in which the sum of the q-power of the real part (imaginary part) of the support for and the q-power of the real part (imaginary part) of the support against is limited by one; however, it is difficult to express the hesitant information. In this study, the conception of complex q-rung orthopair hesitant fuzzy set (Cq-ROHFS) by combining the Cq-ROFS and hesitant fuzzy set (HFS) is proposed, and its properties are discussed, obviously, Cq-ROHFS can reflect the uncertainties in structure and in detailed evaluations. Further, some distance measures (DMs) and cross-entropy measures (CEMs) are developed based on complex multiple fuzzy sets. Moreover, these proposed measures are utilized to solve a multi-criteria decision-making problem based on TOPSIS (technique for order preference by similarity to ideal solution) method. Then, the advantages and superiority of the proposed measures are explained by the experimental results and comparisons with some existing methods.

A method to multi-attribute decision making problems by using heronian mean operators based on linear diophantine uncertain linguistic settings

In the real decision process, an important problem is how to express the attribute value more efficiently and accurately. In the real world, because of the complexity of decision-making problems and the fuzziness of decision-making environments, it is not enough to express attribute values of alternatives by exact values. For this managing with such sorts of issues, the principle of Linear Diophantine uncertain linguistic set is a valuable and capable technique to manage awkward and inconsistent information in everyday life problems. In this manuscript, we propose the original idea of Linear Diophantine uncertain linguistic set and elaborated their essential laws. Additionally, to determine the association among any numbers of attributes, we elaborated the Linear Diophantine uncertain linguistic arithmetic Heronian mean operator, Linear Diophantine uncertain linguistic weighted arithmetic Heronian mean operator, Linear Diophantine uncertain linguistic geometric Heronian mean operator, Linear Diophantine uncertain linguistic weighted geometric Heronian mean operator, and their properties are also discovered. By using these operators, we utilize the multi-attribute decision-making procedure by using elaborated operators. To determine the consistency and validity of the elaborated operators, we illustrate some examples by using explored operators. Finally, the superiority and comparative analysis of the elaborated operators with some existing operators are also determined and justified with the help of a graphical point of view.

DDMF: A Method for Mining Relatively Important Nodes Based on Distance Distribution and Multi-Index Fusion

In research on complex networks, mining relatively important nodes is a challenging and practical work. However, little research has been done on mining relatively important nodes in complex networks, and the existing relatively important node mining algorithms cannot take into account the indicators of both precision and applicability. Aiming at the scarcity of relatively important node mining algorithms and the limitations of existing algorithms, this paper proposes a relatively important node mining method based on distance distribution and multi-index fusion (DDMF). First, the distance distribution of each node is generated according to the shortest path between nodes in the network; then, the cosine similarity, Euclidean distance and relative entropy are fused, and the entropy weight method is used to calculate the weights of different indexes; Finally, by calculating the relative importance score of nodes in the network, the relatively important nodes are mined. Through verification and analysis on real network datasets in different fields, the results show that the DDMF method outperforms other relatively important node mining algorithms in precision, recall, and AUC value.

Performance Evaluation of Solar Energy Cells Using the Interval-Valued T-Spherical Fuzzy Bonferroni Mean Operators

To find the correspondence between every number of attributes, the Bonferroni mean (BM) operator is most widely used and proven to be a flexible approach. To express uncertain information, the frame of the interval-valued T-spherical fuzzy set (IVTSFS) is a recent development in fuzzy settings which discusses four aspects of uncertain information using closed sub-intervals of [0,1] and hence reduces the information loss greatly. In this research study, we introduced the principle of BM operators with IVTSFS to develop the principle of the inter-valued T-spherical fuzzy (IVTSF) BM (IVTSFBM) operator, the IVTSF-weighted BM (IVTSFWBM) operator, the IVTSF geometric BM (IVTSFGBM) operator, and the IVTSF-weighted geometric BM (IVTSFWGBM) operator. To see the significance of the proposed BM operators, we applied these BM operators to evaluate the performance of solar cells that play an important role in the field of energy storage. To do so, we developed a multi-attribute group decision-making (MAGDM) procedure based on IVTSF information and applied it to the problem of solar cells to evaluate their performance under uncertainty, where four aspects of opinion about solar cells were taken into consideration. We studied the results obtained using BM operators with some previous operators to see the significance of the proposed IVTSF BM operators.

New distances for dual hesitant fuzzy sets and their application in clustering algorithm

Compared to hesitant fuzzy sets and intuitionistic fuzzy sets, dual hesitant fuzzy sets can model problems in the real world more comprehensively. Dual hesitant fuzzy sets explicitly show a set of membership degrees and a set of non-membership degrees, which also imply a set of important data: hesitant degrees.The traditional definition of distance between dual hesitant fuzzy sets only considers membership degree and non-membership degree, but hesitant degree should also be taken into account. To this end, using these three important data sets (membership degree, non-membership degree and hesitant degree), we first propose a variety of new distance measurements (the generalized normalized distance, generalized normalized Hausdorff distance and generalized normalized hybrid distance) for dual hesitant fuzzy sets in this paper, based on which the corresponding similarity measurements can be obtained. In these distance definitions, membership degree, non-membership-degree and hesitant degree are of equal importance. Second, we propose a clustering algorithm by using these distances in dual hesitant fuzzy information system. Finally, a numerical example is used to illustrate the performance and effectiveness of the clustering algorithm. Accordingly, the results of clustering in dual hesitant fuzzy information system are compared using the distance measurements mentioned in the paper, which verifies the utility and advantage of our proposed distances. Our work provides a new way to improve the performance of clustering algorithms in dual hesitant fuzzy information systems.

Density aggregation operators for interval-valued q-rung orthopair fuzzy numbers and their application in multiple attribute decision making

The symmetry between fuzzy evaluations and crisp numbers provides an effective solution to multiple attribute decision making (MADM) problems under fuzzy environments. Considering the effect of information distribution on decision making, a novel approach to MADM problems under the interval-valued q-rung orthopair fuzzy (Iq-ROF) environments is put forward. Firstly, the clustering method of interval-valued q-rung orthopair fuzzy numbers (Iq-ROFNs) is defined. Secondly, Iq-ROF density weighted arithmetic (Iq-ROFDWA) intermediate operator and Iq-ROF density weighted geometric average (Iq-ROFDWGA) intermediate operator are developed based on the density weighted intermediate operators for crisp numbers. Thirdly, combining the density weighted intermediate operators with the Iq-ROF weighted aggregation operators, Iq-ROF density aggregation operators including Iq-ROF density weighted arithmetic (Iq-ROFDWAA) aggregation operator and Iq-ROF density weighted geometric (Iq-ROFDWGG) aggregation operator are proposed. Finally, effectiveness of the proposed method is verified through a numerical example.

Internet of things challenges of sustainable supply chain management in the manufacturing sector using an integrated q-Rung Orthopair Fuzzy-CRITIC-VIKOR method

Purpose

The “Internet of Things (IoT)” is a platform for involving smart devices via the Internet at a worldwide scale. It supports the “supply chain (SC)” and “information and communication technology (ICT)” infrastructure to be well integrated into an organization and externally with customers and suppliers. The “sustainable supply chain (SSC)” is currently unavoidable if a company seeks to satisfy the aggressive change in its customers' requirements. Numerous studies have confirmed that manufacturing firms have to accelerate the shift of their focus toward sustainability and the implementation of novel technologies, such as IoT, to accomplish their organizational goals most effectively. Although the literature consists of many theoretical approaches to IoT and numerous studies that have extremely concentrated upon the IoT technology and its potential applications, it lacks research with a focus on the challenges that arise when applying IoT to the “sustainable supply chain management (SSCM)”.

Design/methodology/approach

The present study proposes an integrated framework using the “Criteria Importance Through Intercriteria Correlation (CRITIC)” and “VlseKriterijumska optimizcija I kaompromisno resenje in Serbian (VIKOR)” models and employs to evaluate the IoT challenges to implement the SSCM. For estimating the criteria weights, the CRITIC tool is utilized. The organization's prioritization is obtained by the VIKOR procedure, which delivers simple mathematical procedures with precise and consistent outcomes.

Findings

To exhibit the practicality of the introduced model, a case study is taken to evaluate the IoT challenges to implement the SSCM within the “q-Rung Orthopair Fuzzy Sets (q-ROFSs)” environment. Moreover, the authors exhibit a sensitivity investigation over given parameter values, examining the stability of developed approach. Finally, the authors draw attention to a comparison between developed q-ROF-CRITIC-VIKOR decision-making approach with an existing q-ROF-TOPSIS method to show its superiority and potency.

Originality/value

The outcome of the study lies in observing the top benefits of individual businesses, and their entire SSCs can be found by implementing IoT. This paper investigates the most important challenges that individual firms and entire SSCs might while applying IoT. It provides a deep insight regarding the effects of IoT upon SSCM and the issues every firm need to contemplate when it is to apply IoT solutions.

Multi-attribute group decision-making method based on time-series q-rung orthopair fuzzy sets

The q-rung orthopair fuzzy set is a powerful and useful tool to deal with uncertainty, but in actual decision-making process, decision-makers are usually required to analyze the actual problem dynamically. Therefore in this paper, we consider the time-series q-rung orthopair fuzzy decision making. First, we introduce the new cosine similarity measure of q-ROFS which combines the cosine similarity measure and the Euclidean distance measure. Then, we combine the advantages of projection method and grey correlation degree, establishing the nonlinear programming model to calculate the weights of attributes. Furthermore, we use the exponential decay model to get the weights formulas of q-ROFS at different times. Then we replace the distance function with grey relational projection and extend TOPSIS method. Based on these, we propose a new MAGDM approach to deal with time-series q-rung orthopair fuzzy problem not only from the point of view of geometry but also from the point of view of algebra. Finally, we give a practical example to illustrate effectiveness and feasibility of the new method.

Improved cosine and cotangent function-based similarity measures for q-rung orthopair fuzzy sets and TOPSIS method

Despite the importance of cosine and cotangent function- based similarity measures, the literature has not provided a satisfactory formulation for the case of q-rung orthopair fuzzy set (qROFS). This paper criticizes the existing attempts in terms of respect of the basic axioms of a similarity measure and strict inclusion relation. In addition, the maximum operator-based similarity measures are criticized. Then, new improved, axiomatically supported cosine and cotangent function-based similarity measures for qROFSs are proposed. Additional properties of the new similarity measures are discussed to guarantee their good performance. Two algorithmic procedures of TOPSIS method that based on fixed and relative ideal solutions are discussed. The numerical examples are provided to support the findings

Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of [0, 1] that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from [0, 1] intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

Evaluation of government strategies against COVID-19 pandemic using q-rung orthopair fuzzy TOPSIS method

The COVID-19 outbreak, which emerged in China and continues to spread rapidly all over the world, has brought with it increasing numbers of cases and deaths. Governments have suffered serious damage and losses not only in the field of health but also in many other fields. This has directed governments to adopt and implement various strategies in their communities. However, only a few countries succeed partially from the strategies implemented while other countries have failed. In this context, it is necessary to identify the most important strategy that should be implemented by governments. A decision problem based on the decisions of many experts, with some contradictory and multiple criteria, should be taken into account in order to evaluate the multiple strategies implemented by various governments. In this study, this decision process is considered as a multi-criteria decision making (MCDM) problem that also takes into account uncertainty. For this purpose, q-rung orthopair fuzzy sets (q-ROFSs) are used to allow decision-makers to their assessments in a wider space and to better deal with ambiguous information. Accordingly, two different Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) approaches are recommended under the q-ROFS environment and applied to determine the most appropriate strategy. The results of the proposed approaches determine the A1 — Mandatory quarantine and strict isolation strategy as the best strategy. Comparisons with other q-rung orthopair fuzzy MCDM methods and intuitionistic fuzzy TOPSIS method are also presented for the validation of the proposed methods. Besides, sensitivity analyses are conducted to check the robustness of the proposed approaches and to observe the effect of the change in the q parameter.

Three-Way Decisions Based on Q-Rung Orthopair Fuzzy 2-Tuple Linguistic Sets with Generalized Maclaurin Symmetric Mean Operators

As a typical model of three-way decisions (3WD), decision-theoretic rough sets (DTRS), have gained attention from scholars in decision-making problems. The q-rung orthopair fuzzy 2-tuple linguistic variable (QROF2-TLV) is a mixture of two different notions, q-rung orthopair fuzzy sets (QROFS) and 2-tuple linguistic variables (2-TLV), and is an extensive and proficient technique for coping with awkward and complicated information in realistic decision-making. In this paper, we first propose a DTRS model for 3WD based on QROF2-TLV that gives a new method for evaluating loss functions (LF) of DTRS. We further present the q-rung orthopair fuzzy 2-tuple linguistic generalized Maclaurin symmetric mean (QROF2-TLGMSM) and weighted QROF2-TLGMSM operators and then provide the LFs of DTRS based on QROF2-TLV with the values aggregated by the QROF2-TLGMSM operator. Thus, we propose the q-rung orthopair fuzzy 2-tuple linguistic variable DTRS (QROF2-TLV-DTRS) model. Subsequently, a technique for concluding another DTRS model, which can give the related semantic translation of the decision consequences of every other option, is presented. The model is applied to expound the proposed technique in detail, and the impacts of various conditional probabilities on decision outcomes are discussed. A comparative analysis of the proposed approach is also conducted to examine the proficiency of the proposed method.

An Extension TOPSIS Method Based on the Decision Maker’s Risk Attitude and the Adjusted Probabilistic Fuzzy Set

The paper studies an extension TOPSIS method with the adjusted probabilistic linguistic fuzzy set in which the decision maker’s behavior tendency is considered. Firstly, we propose a concept of probabilistic linguistic q-rung orthopair set (PLQROS) based on the probability linguistic fuzzy set (PLFS) and linguistic q-rung orthopair set (LQROS). The operational laws are introduced based on the transformed probabilistic linguistic q-rung orthopair sets (PLQROSs) which have the same probability. Through this adjustment method, the irrationality of the existing methods in the aggregation process is avoided. Furthermore, we propose a comparison rule of PLQROS and the aggregated operators. The distance measure of PLQROSs is also defined, which can deal with the symmetric information in multi-attribute decision making problems. Considering that the decision maker’s behavior has a very important impact on decision-making results, we propose a behavioral TOPSIS decision making method for PLQROS. Finally, we apply the practical problem of investment decision to demonstrate the validity of the extension TOPSIS method, and the merits of the behavior decision method is testified by comparing with the classic TOPSIS method. The sensitivity analysis results of decision-maker’s behavior are also given.

Multi-criteria decision-making methods based on q-rung picture fuzzy information

 The q-rung picture fuzzy sets serve the fuzzy set theory as a competent, broader and accomplished extension of q-rung orthopair fuzzy sets and picture fuzzy sets which exhibit excellent performance in modeling the obscure data beyond the limits of existing approaches owing to the parameter q and three real valued membership functions. The accomplished strategy of VIKOR method is established on the major concepts of regret measure and group utility measure to specify the compromise solution. Further, TOPSIS method is another well established multi-criteria decision-making strategy that finds out the best solution with reference to the distances from ideal solutions. In this research study, we propose the innovative and modified versions of VIKOR and TOPSIS techniques using the numerous advantages of q-rung picture fuzzy information for obtaining the compromise results and rankings of alternatives in decision-making problems with the help of two different point-scales of linguistic variables. The procedure for the entropy weighting information is adopted to compute the normal weights of attributes. The q-rung picture fuzzy VIKOR (q-RPF VIKOR) method utilizes ascending order to rank the alternatives on the basis of maximum group utility and minimum individual regret of opponent. Moreover, a compromise solution is established by scrutinizing the acceptable advantage and the stability of decision. In the case of TOPSIS technique, the distances of alternatives to ideal solutions are determined by employing the Euclidean distance between q-rung picture fuzzy numbers. The TOPSIS method provides the ranking of alternatives by considering the descending order of closeness coefficients. For explanation, the presented methodologies are practiced to select the right housing society and the suitable industrial robot. The comparative results of the proposed techniques with four existing approaches are also presented to validate their accuracy and effectiveness.

Multi-attributive border approximation area comparison (MABAC) method based on normal q-rung orthopair fuzzy environment

The normal intuitionistic fuzzy number (NIFN), which membership function and non-membership function are expressed by normal fuzzy numbers (NFNs), can better describe the normal distribution phenomenon in the real world, but it cannot deal with the situation where the sum of membership function and non-membership function is greater than 1. In order to make up for this defect, based on the idea of q-rung orthopair fuzzy numbers (q-ROFNs), we put forward the concept of normal q-rung orthopair fuzzy numbers (q-RONFNs), and its remarkable characteristic is that the sum of the qth power of membership function and the qth power of non-membership function is less than or equal to 1, so it can increase the width of expressing uncertain information for decision makers (DMs). In this paper, firstly, we give the basic definition and operational laws of q-RONFNs, propose two related operators to aggregate evaluation information from DMs, and develop an extended indifference threshold-based attribute ratio analysis (ITARA) method to calculate attribute weights. Then considering the multi-attributive border approximation area comparison (MABAC) method has strong stability, we combine MABAC with q-RONFNs, put forward the q-RONFNs-MABAC method, and give the concrete decision steps. Finally, we apply the q-RONFNs-MABAC method to solve two examples, and prove the effectiveness and practicability of our proposed method through comparative analysis.

Generalized complex q-rung orthopair fuzzy Einstein averaging aggregation operators and their application in multi-attribute decision making

The recently proposed q-rung orthopair fuzzy set, which is characterized by a membership degree and a non-membership degree, is effective for handling uncertainty and vagueness. This paper proposes the concept of complex q-rung orthopair fuzzy sets (Cq-ROFS) and their operational laws. A multi-attribute decision making (MADM) method with complex q-rung orthopair fuzzy information is investigated. To aggregate complex q-rung orthopair fuzzy numbers, we extend the Einstein operations to Cq-ROFSs and propose a family of complex q-rung orthopair fuzzy Einstein averaging operators, such as the complex q-rung orthopair fuzzy Einstein weighted averaging operator, the complex q-rung orthopair fuzzy Einstein ordered weighted averaging operator, the generalized complex q-rung orthopair fuzzy Einstein weighted averaging operator, and the generalized complex q-rung orthopair fuzzy Einstein ordered weighted averaging operator. Desirable properties and special cases of the introduced operators are discussed. Further, we develop a novel MADM approach based on the proposed operators in a complex q-rung orthopair fuzzy context. Numerical examples are provided to demonstrate the effectiveness and superiority of the proposed method through a detailed comparison with existing methods.

The Linguistic Picture Fuzzy Set and Its Application in Multi-Criteria Decision-Making: An Illustration to the TOPSIS and TODIM Methods Based on Entropy Weight

The paper considers the multi-criteria decision-making problem based on linguistic picture fuzzy information. Firstly, we propose the concept of linguistic picture fuzzy set(LPFS), where the positive-membership, the neutral-membership and the negative-membership are represented by linguistic variables, and its operation rules are also discussed. The linguistic picture fuzzy weighted averaging (LPFWA) operator and linguistic picture fuzzy weighted geometric (LPFWG) operator are developed based on the proposed operation rules. Secondly, we propose the generalized weighted distance measure, the generalized weighted Hausdorff distance measure, and the generalized hybrid weighted distance measure between LPFSs and discuss their properties. Thirdly, we extend the technique for order of preference by similarity to the ideal solution (TOPSIS) method and the TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method to the proposed distance measure, and the linguistic picture fuzzy entropy method is proposed to calculate the weights of the criteria. Finally, an illustrative example is given to verify the feasibility and effectiveness of the proposed methods, the comparative analysis with other existing methods and sensitivity analysis of the proposed methods are also discussed.

MICKEY 2.0.85: A Secure and Lighter MICKEY 2.0 Cipher Variant with Improved Power Consumption for Smaller Devices in the IoT

Lightweight stream ciphers have attracted significant attention in the last two decades due to their security implementations in small devices with limited hardware. With low-power computation abilities, these devices consume less power, thus reducing costs. New directions in ultra-lightweight cryptosystem design include optimizing lightweight cryptosystems to work with a low number of gate equivalents (GEs); without affecting security, these designs consume less power via scaled-down versions of the Mutual Irregular Clocking KEYstream generator—version 2-(MICKEY 2.0) cipher. This study aims to obtain a scaled-down version of the MICKEY 2.0 cipher by modifying its internal state design via reducing shift registers and modifying the controlling bit positions to assure the ciphers’ pseudo-randomness. We measured these changes using the National Institutes of Standards and Testing (NIST) test suites, investigating the speed and power consumption of the proposed scaled-down version named MICKEY 2.0.85. The (85) refers to the new modified bit-lengths of each MICKEY 2.0 register. The results show that it is faster, requires less power, and needs fewer GEs. The proposed variant will enhance the security of applications, such asRadio-frequency identification (RFID) technology, sensor networks, and in Internet of things (IoT) in general. It also will enhance research on the optimization of existing lightweight cryptosystems.

Q-rung Orthopair Normal Fuzzy Aggregation Operators and Their Application in Multi-Attribute Decision-Making

Q-rung orthopair fuzzy set (q-ROFS) is a powerful tool to describe uncertain information in the process of subjective decision-making, but not express vast objective phenomenons that obey normal distribution. For this situation, by combining the q-ROFS with the normal fuzzy number, we proposed a new concept of q-rung orthopair normal fuzzy (q-RONF) set. Firstly, we defined the conception, the operational laws, score function, and accuracy function of q-RONF set. Secondly, we presented some new aggregation operators to aggregate the q-RONF information, including the q-RONF weighted operators, the q-RONF ordered weighted operators, the q-RONF hybrid operator, and the generalized form of these operators. Furthermore, we discussed some desirable properties of the above operators, such as monotonicity, commutativity, and idempotency. Meanwhile, we applied the proposed operators to the multi-attribute decision-making (MADM) problem and established a novel MADM method. Finally, the proposed MADM method was applied in a numerical example on enterprise partner selection, the numerical result showed the proposed method can effectively handle the objective phenomena with obeying normal distribution and complicated fuzzy information, and has high practicality. The results of comparative and sensitive analysis indicated that our proposed method based on q-RONF aggregation operators over existing methods have stronger information aggregation ability, and are more suitable and flexible for MADM problems.