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Abstract: Advanced neuro-fuzzy modeling, namely an adaptive network-based fuzzy inference system (ANFIS), was employed to develop models for the prediction of suspended solids (SS) and chemical oxygen demand (COD) removal of a full-scale wastewater treatment plant treating process wastewaters from a paper mill. In order to improve the network performance, fuzzy subtractive clustering was used to identify model''s architecture and optimize fuzzy rule, meanwhile principal component analysis (PCA) was applied to reduce the input variable dimensionality. Input variables were reduced from six to four for COD and SS models, by considering PCA results and linear correlation matrices among input and output variables. The results indicate that reasonable forecasting and control performances have been achieved through the developed system. The minimum mean absolute percentage errors of 1.003% and 0.5161% for CODeff and SSeff could be achieved using ANFIS. The maximum correlation coefficient values for CODeff and SSeff were 0.9912 and 0.9882, respectively. The minimum mean square errors of 1.2883 and 0.0342, and the minimum RMSEs of 1.135 and 0.1849 for CODeff and SSeff could also be achieved. [Copyright &y& Elsevier]

We propose a new concept which is a generalization of fuzzy soft subset and fuzzy soft equal. Using such notions, we will be able to consider the distributive law of fuzzy soft sets. Using the distributive law of fuzzy soft sets, we point out that the distributive law of trapezoidal fuzzy soft sets as proposed by Xiao et al. (2012) is not true. The correction will further improve further extensions of the results of Xiao et al. (2012). We will also establish the generalized distributive law of trapezoidal fuzzy soft sets along with illustrative examples. [ABSTRACT FROM AUTHOR]

Missing data imputation is a critical task in the data pre-processing stage to ensure the quality, stability, and reliability of machine learning models. If missing values are imputed incorrectly, it can result in erroneous predictions and inconsistent model performance. Traditional imputation methods often struggle with complex data patterns having non-linearity and uncertainties. By integrating soft clustering principles, the proposed work provides a flexible framework for imputing missing data by taking into account the underlying inherent data pattern. To address the missing data challenges, this paper presents a novel imputation technique called Radial Basis Kernel Intuitionistic Fuzzy Ⅽ-Means Imputation (KIFCMI), which builds upon the standard Intuitionistic Fuzzy Ⅽ-Means (IFCM) technique. KIFCMI explores the application of centroid-based imputation using IFCM by incorporating the RBF kernel-induced metric in the data space as a replacement for the original Euclidean norm metric. By employing a kernel function, KIFCMI enables the clustering of data that lacks linear separability within the original space, enabling the formation of homogeneous clusters in a space of higher dimensionality. The effectiveness of the proposed imputation technique is validated on ten diverse real-world datasets obtained from the Public Library UCI with 10% and 20% missing data. The comparative analyses of the proposed technique KIFCMI, is carried out with three conventional techniques, namely fuzzy c-means imputation (FCMI), kernelized fuzzy c-means imputation (KFCMI), and intuitionistic fuzzy c-means imputation (IFCMI). The experimental results using two performance measures, namely RMSE and MAE, showcase the robustness and versatility of the proposed technique across other imputation outcomes. This research paper contributes to the evolving landscape of missing data imputation, offering insights into the practical applications of fuzzy clustering techniques. [ABSTRACT FROM AUTHOR]

The study of biotic nomenclature has resulted from gene expression profiling using integrated image analysis techniques. The study emphasized in this paper confers Modified Intuitionistic Fuzzy Clustering Method (MIFCM) for spot segmentation of microarray image. In order to achieve the basic condition of intuitionism, a generator using Intuitionistic Fuzzy set (IFS) is used. MIFCM approach considers degree of uncertainty, value of association and value of non-association to determine similarity between the microarray spot data points which further helps in clustering. For non-association value calculation, Sugeno's [47] and Yager's [30] [44] fuzzy complement generator [49] with intuitionism approach is proposed in this work. To achieve elementary level of intuitionism [49] , MIFCM is integrated with Hausdorff distance metrics [43]. The Hausdorff distance metrics is used to quantify the distance metrics betwixt microarray image pixel and cluster centers. The study discusses the constraints of the evolutionary Fuzzy C-Means (FCM) method [4] and adoption of new fuzzy complement generator which overcomes limitations to increase the clustering efficiency. Further, the paper presents detailed methodology of calculating the parameters required to convert crisp spot data of microarray image into fuzzy set which will be input to the next stage of kernel induced clustering using MIFCM technique. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to present a new multi-attribute decision-making (MADM) approach for solving the problems under the uncertain and complex environment. The key challenges during any MADM problem are how to quantify the objective uncertainty information in the data and how to aggregate such collective information. To answer this, in this paper, we utilize the concept of the bipolar fuzzy information to mark the information in terms of the positive and negative support. To aggregate this different information, we propose some power aggregation operators based on the Aczel-Alsina operators (AAO). The AAOs are the generalized t-norm based operations with an additional parameter to analyze the influence of the expert preferences. Based on these AAO and bipolar fuzzy information, we stated bipolar fuzzy AA power weighted averaging and geometric operators and investigate their features. Later, based on these operators, we establish a MADM algorithm to solve the decision-making problems. The applicability of the stated algorithm is demonstrated through a case study related to quantum computing. The comparative studies and advantages of the study are also analyzed with the various prevailing theories. [ABSTRACT FROM AUTHOR]

p , q -quasirung orthopair fuzzy set (p , q -QOFS) is an extension of the q -rung orthopair fuzzy set (q -ROFS) theory used to represent uncertainty and vagueness in decision-making processes. The paper aims to utilize robust sine-trigonometric operational laws to investigate the group decision-making process within the p , q -QOFSs framework. The p , q -QOFS possess a distinctive characteristic of handling uncertain information by utilizing a wider space for membership representation compared to q -ROFS. Consequently, the current paper has been categorized into three distinct phases. In the initial phase, novel operational laws will be presented for p , q -QOFSs. The fundamental concept behind these newly proposed operations is to integrate the properties of the sine function, which include being periodic and symmetric about the origin, into the decision-making process for objects. Then, based on these laws, several operators for aggregating information will be obtained, along with their necessary properties and relationships. Lastly, an algorithm will be presented for interpreting the problem of multi attribute group decision-making (MAGDM), utilizing the operators, and demonstrating it with an illustrative example. A comprehensive comparative analysis will be conducted with some of the existing methods to uncover their impacts. [ABSTRACT FROM AUTHOR]

• Construct QLBN for MAGDM problem considering the interference of beliefs. • Propose belief state and decision states in QLBN of three decesion-making stages. • Model causal reasoning of uncertainty and belief inteference among decision makers. • Aggregate quantum probabilities for the attributes and the alternatives in QLBN. • Calculate the interference values using belief entropy and Deng Entropy method. Multi-attribute group decision making (MAGDM) problem has become one of the most remarkable topics recently. MAGDM is made up of multiple decision makers (DMs) who perform opinions on a set of alternatives and then choose the appropriate one. In the classical decision-making process, the multiple DMs are usually regarded as independent and the opinions usually come from the preference of DMs when determining weights of attributes or giving evaluation of alternatives. However, MAGDM is a complicated cognitive process that involves the diverse and uncertainty cognition of DMs from different backgrounds and fields, and the opinions from DMs are likely to interfere with each other. This paper proposes an extension method based on quantum-like Bayesian network (QLBN) and belief entropy considering the interference of beliefs on the basis of our previous research. The purpose is to model subjectivity sourced from the interference of DMs' beliefs at different decision-making stages, including the aggregation of attributes probabilities and alternatives probabilities. In this paper, a QLBN for MAGDM problem is constructed firstly. The beliefs of DMs are in a superposition state in it, that is, the opinions of DMs are regarded as wave functions occurring in QLBN. Then the probabilities of attributes and the probabilities of alternatives in QLBN are aggregated across all DMs, and the alternatives are sorted. In the process of aggregation, the beliefs from different DMs will interfere with each other. Belief entropy, an index to calculate the uncertainty of probability is introduced to calculate the interference value. When the interference between DMs is considered only in a certain decision-making stage, the proposed method will degenerate into the existing QLBN methods; and when all DMs are regarded as independent, the QLBN will degenerate into a classical BN. Finally, a supplier selection problem is introduced to illustrate and validate our model. The comparison analyses show that the proposed approach can fully consider the interference between DMs and the ranking result are more reasonable and realistic. [ABSTRACT FROM AUTHOR]

• Proposed fuzzy small displacement torsor model for tolerance classification representation. • Established an assembly reliability index for evaluating assembly precision. • Developed constrained transformation method for efficient and high-accuracy calculation. • Proposed a novel fuzzy algorithm for assembly precision management. The assembly precision of a specified product is subject to epistemic uncertainty due to manufacturing and measurement errors. The efficient and accurate assembly precision management is essential for realizing smart production lines, which rely on the robust assembly precision analysis model and calculation method. Parametric models are extensively used for assembly precision analysis in industrial products, typically integrating worst-case and statistical methods for calculations. Nevertheless, the combined application of these methods presents inherent limitations. Therefore, a novel fuzzy algorithm for assembly precision management is proposed in this paper by using fuzzy sets to quantify epistemic uncertainty in assembly precision, which integrates the proposed fuzzy-based assembly precision analysis model and fuzzy-based calculation method. The proposed fuzzy small displacement torsor model is a fuzzy-based model for deviation representation and tolerance classification using decomposed fuzzy numbers, where an assembly reliability index is always established for the hierarchical evaluation and management of assembly precision. Subsequently, a comprehensive assembly precision analysis model is developed for precision prediction and contribution quantification by integrating the Jacobian model for deviation propagation. A new constrained transformation method is proposed as a fuzzy-based calculation method, offering efficient and highly accurate assembly precision computation. It accounts for torsor parameter constraints to ensure greater prediction accuracy than the worst-case method and improves computational efficiency compared to statistical methods. An assembly case of the centering pin mechanism is applied to verify the superiority of the proposed novel fuzzy algorithm compared with the Jacobian-Torsor model with worst-case or statistical methods. [ABSTRACT FROM AUTHOR]

Data normalization is essential in many fields, such as speech recognition, deep learning, machine learning, and optimization. Many researchers focus on developing various normalization techniques, such as min-max, score-based, maximum, vector, or sum, on processing data efficiently. However, classical normalization methods may need to be improved in Multi-Criteria Decision-Analysis (MCDA), where criteria are often non-monotonic. This paper proposes a new approach for identifying and normalizing nonmonotonic criteria in MCDA. The method combines a stochastic optimization technique - a genetic algorithm - with normalization based on triangular fuzzy numbers. This paper compares the proposed approach with classical normalization techniques, such as min-max, maximum, vector, or non-linear, using the classical MCDA method - the Technique of Order Preference Similarity to the Ideal Solution (TOPSIS). The study results showed that the proposed approach to normalizing non-monotonic criteria yields a better match between decision preferences and the actual reference model than traditional normalization methods. Optimization using the genetic algorithm helps identify the means of triangular fuzzy numbers, which generate more accurate results. Analysis of the R2 coefficient confirms a very good fit of the proposed model. Therefore, the new non-linear normalization approach in MCDA presented in this work has great potential in adjusting decision preferences to non-monotonic criteria. Future research should continue on the accuracy of this approach in identifying non-linear decision models and apply it to other MCDA methods and real-world decision problems. [ABSTRACT FROM AUTHOR]

In view of the limitations of triangular intuitionistic fuzzy numbers (TIFNs) in value selection and application, the purpose of this paper is to redefine and demonstrate the algorithm, expectation function and distance measure of TIFNs, and to put forward a new theory of triangular intuitionistic fuzzy sets (TIFSs). The new theory of TIFSs is then applied to the field of two-sided matching decision-making. To solve the two-sided matching problem based on TIFSs, the agent behavior factors of both sides are calculated by this theory. On this basis, a multi-objective matching model under TIFS preference is constructed. Furthermore, the optimal matching scheme is obtained by transforming and solving the model according to the expected score, the linear weighting and the algorithm of "being as good as possible". Finally, the practicability of the proposed two-sided matching method is verified by a transaction matching example. The novelty and key idea of the proposed method are as follows: (1) it combines the idea of closeness in TOPSIS method and the expected score in the new theory of TIFSs to measure the behavior factors of two-sided agents; (2) it builds a two-sided matching model considering the behavior factors under the preference of TIFSs; (3) according to the idea of "being as good as possible", a novel algorithm for solving the two-sided matching model under TIFS preference is proposed. The major conclusion and advantage of this paper is that the obtained BM scheme using the proposed method can reflect agent behavior factors and maximize agents' satisfaction as much as possible. [ABSTRACT FROM AUTHOR]

Clustering is a crucial technique used to identify the structure of data sets. It involves the task of splitting groups into different clusters based on suitable similarity measures. Fuzzy C-Means is a clustering technique that extends the fuzzy set theory. It is a widely used method among existing fuzzy clustering algorithms due to its easy implementation and straightforward approach. However, it still has some drawbacks, such as high sensitivity to outliers or noisy data, as well as to initialization conditions. Therefore, this paper proposes a modification to the Fuzzy C-Means algorithm using Fuzzy Chebyshev. The preprocessing of raw datasets includes the use of MinMax Scaler. Additionally, dimensional reduction techniques are applied to effectively address issues related to high-dimensional data. To determine the optimal number of clusters in the data set, the Elbow method is implemented. The final clustering is achieved by employing Fuzzy Chebyshev to replace the distance measurement component in the Fuzzy C-Means algorithm. A comparison between the proposed method and previous methods is performed. The effectiveness of the proposed method is illustrated through a numerical example involving genomic data of prostate cancer. Comparable results are presented to validate the feasibility of the proposed method. The results demonstrate that the proposed method aligns with those obtained from previous methods. [ABSTRACT FROM AUTHOR]

While academic metrics such as transcripts and GPA are commonly used to evaluate students' knowledge acquisition, there are limited comprehensive metrics to measure their preparedness for the challenges of post-graduation life. This research paper explores the impact of various factors on university students' readiness for change and transition, with a focus on their preparedness for careers. The methodology employed in this study involves designing a survey based on Paul J. Mayer's "The Balance Wheel" to capture students' sentiments on various life aspects, including satisfaction with the educational process and expectations of salary. The collected data from a KBTU student survey (n=47) were processed through machine learning models: Linear Regression, Support Vector Regression (SVR), and Random Forest Regression. Subsequently, an intelligent system was built using these models and fuzzy sets. The system is capable of evaluating graduates' readiness for their future careers and demonstrates a high predictive power. The findings of this research have practical implications for educational institutions. Such an intelligent system can serve as a valuable tool for universities to assess and enhance students' preparedness for post-graduation challenges. By recognizing the factors contributing to students' readiness for change, universities can refine curricula and processes to better prepare students for their career journeys. [ABSTRACT FROM AUTHOR]

Decision-making problem is a fundamental activity in human life every day. Regarding group decision-making, individuals have insufficient comprehension of the decision objects owing to the limited experience and knowledge and drawback the evaluation process. Therefore, the evaluation information is missing and the group cannot get the precise information for decision objects resulting in the generation of incomplete information systems. It is meaningful for individuals finding an approach to Leverage and tap into existing information. On the basis, the work presented in this paper focuses on group decision-making problems (GDM) with incomplete information. Under the framework of group decision-making, a GDM approach with an incomplete information system is presented combining the formal concept analysis and rough set theory. Firstly, we propose a concept called formal decision context and discuss the properties of the formal decision context, which could divide the incomplete information system into many cognitive units, and the definitions of cognitive units will be given. Then, the property and the relations of various cognitive units will be discussed. Additionally, the upper and lower approximation space under the formal decision context is founded considering the risk attitudes integrating fuzzy rough set and formal concept context. Considering the order relation of various cognitive units and decision objects, we introduce the dominance relation and the importance degree of each cognitive unit under the framework of formal decision context. Furthermore, a theoretical framework of the multi-criteria decision-making problem is presented and two models for the multi-criteria group decision-making problem are discussed combined with fuzzy rough set and formal decision context from two perspectives, including qualitative analysis and quantitative analysis. Finally, an illustrated example is applied to verify the validity and effectiveness of the proposed models. The contributions of this paper include two aspects. On the one hand, this paper provides a new perspective and paradigm considering MCGDM problems with the incomplete information system from the perspective of group consensus. On the other hand, this paper gives two approaches for group decision-making problems from sorting and set theory by the perspective of multi-granular rough set and group consensus. • A model of formal decision context with incomplete information to describe the cognitive situation. • An approach to MCDM problem combined rough set with formal decision context with incomplete information. • Two approaches to MCGDM problem from qualitative analysis and quantitative analysis. [ABSTRACT FROM AUTHOR]

In Turkey, the transportation industry's greenhouse gas (GHG) emissions increased by 147.1% between 1990 and 2019. Today, this transportation industry (i.e., freight and passenger) is among the significant contributors to greenhouse gas emissions in Turkey's megacities. Moreover, 65.43% of short-distance trips between home to work and home to school have been made by private automobiles in Istanbul and increasing concerns about environmental pollution have led practitioners to seek practical, robust, and effective solutions to reduce GHG emissions. Shared electric scooters have rapidly become popular for end-users and practitioners in megacities, depending on their valuable advantages. However, the rapid spread of micro-mobility, characterized by e-scooters, has also raised questions about this system's sustainability, suitability, and applicability. Thus, there are some critical and noteworthy gaps in this issue. This study investigates the factors affecting the suitable e-scooter selection for a sustainable urban transport system. Besides, it aims to develop a methodological framework for assessing the available e-scooter alternatives. For this purpose, a novel negotiation approach, a new form of the Delphi technique, was developed with the help of Fermatean fuzzy sets to identify the influential criteria. Also, the current paper presents a consensus-based MULTIMOORA (Multiple Objective Optimization on the basis of Ratio Analysis plus Full Multiplicative Form) decision-making model based on Fermatean fuzzy sets to address the appraisal problem concerning e-scooter selection. The current paper indicated that economic measures such as acquisition price and upkeep costs affect the e-scooter selection processes. In addition, an optimization model based on cross-entropy and dispersion measures is utilized to compute criteria weights. It highlighted that the costs of e-scooters are still high, and operators consider these criteria instead of the technical and operational features of the e-scooters. Finally, the validity check executed to test the robustness and trustworthiness of the model affirms the model's firmness and trustworthiness. [ABSTRACT FROM AUTHOR]

This paper proposes a new linguistic model called Linguistic q-Rung Orthopair fuzzy Z-number (LqROFZN), which combines the advantages of linguistic variables, Z-number and q-Rung Orthopair Fuzzy numbers. It can be used as a powerful tool for uncertain decision-making, which can effectively improve the accuracy and reliability of the decision-making results, and has a notable application prospect for the fields of information decision-making, risk assessment, diagnosis and so on. In this paper, firstly, the definition of LqROFZN and its operational rules are given, a new distance measure and the concept of entropy are given under LqROFZN, and the entropy of LqROFZN can assess the credibility situation of LqROFZN. Next, two aggregation operators under LqROFZN are given, namely the Linguistic q-Rung Orthopair fuzzy Z-number weighted aggregation (LqROFZWA) operator and the Linguistic q-Rung Orthopair fuzzy Z-number weighted Geometric aggregation (LqROFZWGA) operator. Finally, the MCDM method under LqROFZN is given and the credibility of the evaluation results is assessed using the entropy of LqROFZN. In a set of actual airline aircraft selection cases, the feasibility and advantages of the proposed method are verified through comparative analysis with other methods. [ABSTRACT FROM AUTHOR]

This paper discusses the use of portfolio approaches based on bandit algorithms to optimize multicriteria decision-making in recommender systems (accuracy and diversity). While previous research has primarily focused on single-item recommendations, this study extends the research to consider the recommendation of several items per iteration. Two methods, Multiple-play Gorthaur and Budgeted-Gorthaur, are proposed to solve the algorithm selection problem and their performances on real-world datasets are compared. Both methods provide a generalization of the Gorthaur method, which enables it to operate with any Multi-Armed Bandit (MAB) and Contextual Multi-Armed Bandit (CMAB) algorithm as meta-algorithm in a multi-item recommendation scenario. For Multiple-play Gorthaur, an empirical evaluation shows that the use of Thompson Sampling for algorithm selection (Gorthaur-TS) yields better results than the original EXP3 method (Gorthaur-EXP3) and the exclusive use of the optimal algorithm in the portfolio in contextual recommendation problems. Additionally, the paper includes a theoretical regret analysis based on the TS sketch proof applied for this variant of the method. Concerning Budgeted-Gorthaur, experiments show that it allows more flexibility to achieve a suitable trade-off between criteria and a broader coverage of the Pareto set of solutions, overcoming a natural limit of "a-priori" methods. Finally, this paper provides a detailed review, including pseudocodes and theoretical bounds, for all the fundamental MAB and CMAB algorithms used in this study. • Bandit literature lacks formal algorithm review, hindering clarity and comparability. • There is no silver bullet: no algorithm can be the best performer in every instance. • Recommender systems need to balance accuracy, diversity, multi-item recommendations. • Optimal algorithm balances criteria, matching decision maker's preferred trade-off. • Dynamic selection ensures safe performance when optimal algorithm is unknown. [ABSTRACT FROM AUTHOR]

Risks are uncertain events that can affect criteria such as project cost, quality, and completion time and ultimately lead to project failure. That is why the project risk management process, which is one of the most fundamental parts of project management, must be done properly. In this paper, a new multi-objective fuzzy model is proposed to respond appropriately to the primary and secondary project risks. The contributions, such as risk interdependency, considering the project with multi-mode activities, resource considerations, as well as attention to interval-valued fuzzy uncertainties are regarded simultaneously for the first time. The purpose of the proposed multi-objective mathematical model is to minimize cost, quality reduction, and project completion time. Then, a new two-stage uncertain solution approach is introduced in this paper. In this solution approach, using an equivalent method in the first step and then using an extended multi-choice goal programming method in the second step, for both lower and upper limits of the membership functions for interval-valued fuzzy numbers, the computational processes are performed. To show the application and effectiveness of the proposed model, a case study adapted from the literature is given. Finally, sensitivity analysis is conducted to analyze the behavior of the developed mixed-integer programming model. The analysis of obtained results indicates that the utilization of the proposed model leads to better and more appropriate solutions. • Presenting a new multi-objective programming model for project risk responses. • Proposing multi-mode activity and resource considerations in project risk modeling. • Introducing a new interval-valued fuzzy solution approach to handle uncertainty. • Focusing on primary and secondary risks along with project risk interdependency. • Implementing the proposed model in a case study for electricity industry projects. [ABSTRACT FROM AUTHOR]

The research uniquely focuses on advancing the field of fuzzy sets, specifically proposing a novel approach using Hexagonal Type-2 Fuzzy Variable (HT2FV), to handle higher degrees of uncertainty. Flooding, a recurrent and impactful phenomenon, necessitates a robust approach to effective disaster management. The study delves into the humanitarian supply chain dynamics during movement crises and flood catastrophes, introducing a novel methodology to harness the potential of HT2FV. Central to the paper is the innovative defuzzification concept of Critical Value (CV) reduction, strategically employed to eliminate fuzzy components within HT2FV, transforming it into crisp data. The research extends its novelty by proposing a comprehensive approach to distributing relief materials, employing a Multi-objective, Multi-level, Multi-modal (MOMLMM) approach, with a primary focus on boats for inundated areas. Significantly, the study aims to optimize the allocation of resources, minimize time and cost under uncertain environments, and enhance disaster relief operations. The paper is the first to use new hexagonal fuzzy numbers (HFNs) and focuses on how they can be used to sort vulnerable areas using the fuzzy Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods of the Multi-Criteria Decision-Making (MCDM) process. A case study of the 2022 Assam flood is looked at and solved using the Weighted Sum (WS), Neutrosophic Compromise (NC), and Goal Programming (GP) systematically on the LINGO solver to see if the suggested method can be used. Further, sensitivity analysis is employed to establish optimal credibility levels to validate the proposed methods. A real-life case study lends practicality, substantiating the approach's efficacy. At the same time, comprehensive comparative analysis compares and contrasts findings from different studies to synthesize existing knowledge and identify future scope, contributing significantly to the field of fuzzy sets. [ABSTRACT FROM AUTHOR]

• A phase duration calculation method is proposed based on multi-phase identification. • The components' fuzzy state probability vectors are acquired using the evidential reasoning rule. • A performance evaluation model of cyclic phased-mission systems is constructed by multi-valued decision diagrams. • A phase duration adjustment method based on the evaluation results is proposed. • The proposed method is verified by a performance evaluation case study on satellite turntable system. Phased-mission systems (PMS) often perform different missions that have multiple consecutive, non-overlapping phases. Many recent studies have focused on the reliability analysis for PMS. However, not much attention has been paid to the PMS performance evaluation and the phase cycle characteristic of PMS. In this paper, a performance evaluation method of non-repairable cyclic phased-mission systems (CPMS) is proposed. Considering the uncertainty caused by the change of phase duration and component performance degradation, the average duration of each phase and the fuzzy state probability vector of each component are obtained by the evidential reasoning rule (ER rule). Then, the multi-valued decision diagrams (MDD) manipulation rules suitable for cyclic phase conditions are proposed, and the component state composition path generation method based on cycle-end component states is developed. On the above basis, MDD models for CPMS (CPMS-MDD) in different states are established, and the system performance is evaluated by the continuous time Markov chains (CTMC). A phase duration adjustment strategy is further proposed based on the evaluation results. The effectiveness and correctness of the proposed method are verified by case studies on performance evaluation of satellite turntable system. Comparative study shows the concise and efficient of the proposed method. [ABSTRACT FROM AUTHOR]

In multi-attribute group decision-making (MAGDM), the social relationships among group members, professional backgrounds and psychological behaviors of decision makers are important factors for achieving high-quality group decisions. However, realizing the consideration of these factors in fuzzy and complex group decision-making scenarios is an important and urgent issue. In MAGDM problems, interval-valued hesitant fuzzy sets (IVHFSs) can better show the hesitant and fuzzy uncertainty information because they are an extension of fuzzy sets. This paper focuses on the score function of IVHFSs and develops a generalized TODIM evaluation method utilizing the novel score functions of IVHFEs and trust networks. The developed method effectively realizes the application of these factors in fuzzy and complex group decision making scenarios. In this contribution, a new deviation function for IVHFSs is created in this paper. It takes into account two types of deviation that are common in IVHFSs: the ambiguity of interval width and the hesitation and uncertainty of multiple intervals. In the sequel, a novel score function for IVHFSs is developed with help of the novel deviation function and the traditional score function. Concerning the perspective of group consistency, a model for determining expert weights is constructed using quality parameters, which combine the novel score function with the trust network. A subjective and objective comprehensive weighting model is made to get attribute weights based on how certain decision information is and the experts' subjective experience. This is done because the more uncertain something is, the higher the risk. Eventually, we develop a generalized TODIM technique for MAGDM based on the novel score function and trust network in IVHFS environment. The developed approach is demonstrated with a preventive engineering decision-making problem. Sensitivity and comparative analyses are implemented to demonstrate the superiority, stability, and validity of the proposed method in this paper. According to the findings of this study, we conclude that the proposed methodology offers a comprehensive and systematic approach to evaluate MAGDM in the context of IVHFS with trust networks. [ABSTRACT FROM AUTHOR]

The selection of new energy vehicle power battery (NEVPB) recycling service outlet will promote the rapid development of new energy vehicle industry. In order to cope the green and low-carbon development path of NEVPB recycling under information uncertainty and interaction. This paper intends to construct a multidimensional consensus fusion framework of self-confidence Fermatean fuzzy trust network. Firstly, individuals express their opinions based on Fermatean fuzzy sets with self-confidence (FFS-SC). Subsequently, a novel trust propagation and aggregation is built to obtain complete trust relations, and weights of individuals are determined by trust network, self-confidence, and relative deviation. Meanwhile, the trust network- driven consensus feedback mechanism is developed to collect evaluation information. Furthermore, the correlation coefficient to eliminate the homogeneity influence of indicators. In addition, the decision results are derived by Multi-Attributive Border Approximation area Comparison (MABAC) method. Finally, an applied case with five NEVPB recycling service outlets selection is presented to verify the feasibility of the established framework, and the effectiveness is further demonstrated through sensitivity analysis and comparative analysis. The case results show that the indicator with demonstration of recycling service outlet and market supervision departments strengthen supervision indicators have great impact on NEVPB recycling service outlets selection. Furthermore, this paper has reference significance for standardizing the management policy and technology of power battery recycling and realizing the green and low-carbon environmental protection of the whole life cycle of new energy vehicles. [ABSTRACT FROM AUTHOR]

This paper proposes a rectified complex spherical fuzzy set (rCTSFS) model that enables the phase term of a complex number to function truthfully to its inherent meaning of representing directions, phases, or color hues. In addition, this paper proposes the score and accuracy functions for rectified complex spherical fuzzy numbers (rCTSFn), which allows the three types of membership degrees of an rCTSFn to fulfill human judgment/intuition. The proposed rCTSFS model proves to be a productive extension of the complex spherical fuzzy set (CSFS), complex fuzzy set (CFS), and spherical fuzzy set (SFS) models. On the other hand, Dombi t -norms prove more flexible and comprehensive than some of the other families of triangular norms, such as the algebraic t -norms and the Einstein t -norms, due to the presence of a parameter γ. The parameter γ determines the amount of aggressiveness at estimating the maximum and the minimum of a population based on a sample obtained. Therefore, this paper proposes two Dombi-Choquet integral operators, namely, the rectified complex t -spherical fuzzy arithmetic Dombi-Choquet integral (r C T S F A γ , w λ ) operator and the rectified complex t -spherical fuzzy geometric Dombi-Choquet integral (r C T S F G γ , w λ ) operator. A multi-criteria decision making (abbr. MCDM) algorithm utilizing the two Dombi-Choquet integral operators is innovated. The proposed Dombi-Choquet MCDM algorithm for the rCTSFS model is applied to an MCDM problem related to diabetic retinopathy detection on five real-life fundus images of different severity levels taken from the Messidor2 dataset. Our newly proposed algorithm proves to be the only algorithm that yields the correct diagnostic results that match the hard truth. On the other hand, none of the 50 algorithms observed among recent works in literature can produce the correct diagnostic results, even after lending the fuzzification procedure innovated in this work to them. [ABSTRACT FROM AUTHOR]

This paper abstracts the complex heterogeneous multi-attribute group decision-making (CHMAGDM) characterized by two-layer decision-makers (DMs), individual attribute sets, complex relationships among attributes and heterogeneous evaluation information. DMs are composed by internal decision-makers (IDMs) and external decision-makers (EDMs). The evaluation information is represented by linguistic variables (LVs), intervals and real numbers. To handle such CHMAGDM, this paper puts forward an integrated method of prospect theory, DEMATEL (decision-making trial and evaluation laboratory) and QUALIFLEX (qualitative flexible). Firstly, a novel reference point determining approach is proposed based on three special indicators. A linguistic variable inverse prospect value function is designed and introduced to the transformation process from LVs to clouds to reduce the impacts of DMs' psychological behaviors on decision-making. Secondly, a cloud-based DEMATEL approach is proposed to determine the attribute weights, where LVs are employed to judge the relationships among attributes. A new linguistic scale function is initiated and introduced to another transformation process from clouds to LVs. A representative indicator of cloud is designed for facilitating the normalization of direct relation matrix. Moreover, a linear programming model is built to calculate the attribute weights. Thirdly, an extended QUALIFLEX approach is developed to obtain the optimal ranking and EDM weights, where adoption coefficient is provided by IDMs. Another linear programming model is constructed to calculate the optimal collective concordance/discordance index of each permutation. The optimal ranking is generated by the maximum collective concordance/discordance index. Finally, a photovoltaic power station site selection example validates the proposed method. The advantages are demonstrated with sensitivity and comparison analyses. [ABSTRACT FROM AUTHOR]

Fuzzy set theory aims to solve the problem of mining more valuable human reasoning knowledge from quantitative databases, and to narrow the gap between computer and human understanding. Fuzzy Frequent Itemset (FFI) mining, which is very important in fuzzy association rule mining, converts quantitative values into language, and finds fuzzy frequency itemset according to the defined membership function. In the traditional fuzzy frequent pattern mining method, only the language item with the largest scalar base is considered, and the uncertainty of the membership function is not considered. At the same time, it is mainly considered for the fixed data set. This paper proposes a Fuzzy Frequent Pattern mining algorithm based on the Type-2 Fuzzy Set (T2FS) theory of the data stream. Under the T2FS theory, the data stream is dynamically divided based on the sliding window method, and the ambiguity is quickly found from the numerical data stream. In order to reduce the search space and improve over-mining, this paper designs a dynamic compressed lists structure and trees method. Under different minimum support degrees and sliding window sizes, many experiments have been carried out, and the experiments have verified the efficiency and effectiveness of the designed method in terms of running time and memory usage. The results can also contribute to exchange the information and preferences among the people who cooperate in decision-making. [ABSTRACT FROM AUTHOR]

The multiple-attribute decision-making (MADM) problem is resolved through the q -rung complex diophantine neutrosophic normal set (q -rung CDNNS). An important way to express uncertain information is using q -rung orthopair fuzzy sets (q -ROFs). Yager introduced q -ROFs as a generalization of intuitionistic fuzzy sets in which the sum of membership and non-membership degrees is one. In addition, they have superiority over intuitionistic fuzzy sets and Pythagorean fuzzy sets. Complex diophantine fuzzy sets are generalizations of neutrosophic and diophantine fuzzy sets, respectively. Several aggregating operations (AOs) are discussed here, as well as their respective interpretations. The paper discusses q -rung CDNN weighted averaging (q -rung CDNNWA), q -rung CDNN weighted geometric (q -rung CDNNWG), q -rung generalized CDNN weighted averaging (q -rung GCDNNWA) and q -rung generalized CDNN weighted geometric (q -rung GCDNNWG). We will review several of these sets with important properties in greater detail using algebraic operations. Additionally, we develop an algorithm for solving MADM problems using these operators. Several real-world examples illustrate how enhanced score values can be applied. Sensor robots are said to rely heavily on computer science and machine tool technology. Four factors are to evaluate when determining a sensor robotics system's quality: resolution, sensitivity, error, and environment. It is possible to compare expert opinions with the criteria and determine the best alternative. Therefore, the value of q significantly impacts the model's results. To prove that the models considered are valid and useful, we will compare the current and proposed models. Thus, q has a significant impact on the results of the model. [ABSTRACT FROM AUTHOR]

In this study, an observer-based model predictive control (MPC) algorithm is addressed for an uncertain discrete-time nonlinear networked control system (NCS) subject to hybrid malicious attacks by using interval type-2 Takagi–Sugeno (IT2 T–S) fuzzy theory. Hybrid malicious attacks, including two typical attacks, i.e., denial-of-service (DoS) attacks and false data injection (FDI) attacks, are considered in the communication networks. Under DoS attacks, the control signals will be interfered, which cause the degradation of signal-to-interference-plus-noise ratio, then lead to packets loss. Under FDI attacks, the false signals are injected and output signals are modified so that the system performance is deteriorated. For the NCS subject to hybrid attacks, a secure observer that can resist FDI attacks is devised and a fuzzy MPC algorithm that can solve the controller gains is proposed. Besides, by updating the bound of augmented estimation error, the recursive feasibility can be guaranteed. Finally, illustrative examples are given to show the effectiveness of proposed scheme. • The IT2 T–S fuzzy MPC scheme for NCS subject to uncertainties and hybrid attacks is investigated in this paper. • The uncertainties for the NCS appear not only in the membership functions but in both state and input matrices. • The hybrid attacks (DoS attack and FDI attack) in the communication channels of the NCS are considered. • The probability of packets loss depending on SINR is given and a secure observer is designed to estimate system states and FDI attacks. • By optimizing the performance objective function, an on-line fuzzy MPC algorithm is presented. [ABSTRACT FROM AUTHOR]

It is common practice in the MCDA to use several multi-criteria decision methods and then compares obtained rankings with one or two different rank correlation coefficients. The problem is that different rank correlation coefficient gives different values for the same pair of rankings, and the number of studies which tries to investigate it is small. Studying the similarity of rankings is a very important challenge in multi-criteria decision support, and the coefficients themselves seem to be the most practical ways of evaluating rankings. This paper compares chosen rank correlation coefficients to show how much different they are. Spearman's, Weighted Spearman's, Kendall Tau and Rank similarity correlation coefficient are compared statistically. The paper confirms that the coefficients are closely related, and their dependence is graphically represented, which initiates research towards allows for their better selection in the future. In conclusions, directions of further development are indicated. [ABSTRACT FROM AUTHOR]

One of the expression forms of uncertain information are interval-valued fuzzy information systems (IFISs). Whereas, psychological experiments show that psychological behaviors of decision maker (DM) affect the decision results under uncertain information. Consequently, the main research objectives of this paper are two-fold: 1. To study how to portray the influence of psychological behaviors on decision-making under IFISs, so that the decision-making process is more realistic. 2. To investigate how to efficiently solve decision-making problems in the context of IFISs. Three-way decision (3WD) theory and fuzzy rough sets (FRSs) are effective tools for solving uncertain information. For that reason, this paper develops a 3WD model based on prospect theory (PT) under IFISs, which can provide the best decision action for objects from a viewpoint of optimization. First, an attribute-oriented interval fuzzy set is introduced, which establish a bridge between the state sets in 3WD and the reference points in PT. Furthermore, conditional probability of an object is reasonably estimated by interval-valued fuzzy rough sets (IVFRSs). Meanwhile, an attribute-oriented relative value model is proposed, which can get the prospect values of an object under each action. Second, an intelligent 3WD model is developed from a viewpoint of information granularity. Finally, through the search of the existing literature, relevant research data is obtained, and then case research method, qualitative and quantitative combination method, control variable method are adopted in turn to design the case study, comparative and experimental analyses. In short, the developed model not only expands the development of related theories, 3WD, PT, FRSs, but also offers new methods for solving the decision-making problems under IFISs, which has important practical guidance significance. • An intelligent three-way decision model is developed from a viewpoint of information granularity. • An attribute-oriented interval fuzzy set is introduced. • Conditional probability of an object is reasonably estimated with the help of interval-valued fuzzy rough sets. • An attribute-oriented relative value model is proposed. [ABSTRACT FROM AUTHOR]

Best-worst method (BWM) is an efficient multi-attribute decision-making (MADM) method. This paper puts forward two decision-making methods with intuitionistic fuzzy (IF) BWM (IF-BWM). Firstly, a new consistency definition of IF-BWM is presented. To comprehensive reflect the consistency level of original IF preference comparisons, an acceptable input-and-output-based consistency ratio (CR) of IF-BWM preference comparisons is defined to measure the consistency level of IF-BWM preference comparisons. A goal linear programming model is built to improve the consistency level of input-based CR from the original IF-BWM preference comparisons. To induce an optimal multiplicative normalized IF weight vector (IFWV), a programming model is set up. Accordingly, a novel individual IF-BWM is proposed. Using the deviation between IF values, an analytic expression of determining experts' weights is formulated. By minimizing the weighted deviation between individual multiplicative normalized IFWVs and group multiplicative normalized IFWV, a programming model is built to determine the optimal group multiplicative normalized IFWV. Subsequently, a novel group IF-BWM is put forward. Two real-life examples are furnished to reveal the validity of proposed individual IF-BWM and group IF-BWM in practice. In view of theoretical aspect, this paper fosters the theory of IF-BWM by firstly proposing an input-based CR, output-based CR, an acceptable input-and-output-based CR and group IF-BWM. The model of improving CR of IF-BWM preference comparisons is initially discussed. This paper has a certain guiding significance for the following research on IF-BWM and provides a novel perspective for an MADM problem with positive and negative preference information. [ABSTRACT FROM AUTHOR]

• The centroid distance of PFNs is proposed and its properties are discussed. • Propose a score function based on the centroid distance and discuss its properties. • Applications of Pythagorean fuzzy clustering, ranking and MCDM are developed. • Some advantages of the proposed methods are showed through comparative analysis. By using Pythagorean fuzzy set (PFS), people can quantitatively describe and process information with fuzziness, and then make reasonable and effective judgments or decisions. In this process, distance measure often serves as a useful and important tool. The purpose of this paper is to explore some information processing methods and techniques in Pythagorean fuzzy environment. Firstly, the research progress of PFS is reviewed, and the main research directions and some hot issues in relevant research fields are discussed. Secondly, by analyzing the information of hesitation degree of Pythagorean fuzzy number (PFN), definitions of hesitation factor and centroid distance measure based on the representation of centroid coordinates of the hesitation regions are proposed, and properties of hesitation factor and centroid distance measure are discussed. Finally, the novel clustering algorithm, ranking method and multi criteria decision making (MCDM) method are developed in Pythagorean fuzzy environment, which are based on the new centroid distance measure. The effectiveness of the proposed algorithm and methods are verified through numerical examples and comparative analysis. The research results indicate that the centroid distance measure proposed in this paper can effectively characterize the distance between PFNs, thus making the clustering algorithm of PFNs, the ranking method of PFNs, and the Pythagorean fuzzy MCDM method have obvious superiorities and advantages. [ABSTRACT FROM AUTHOR]

Medical image segmentation is a challenging task owing to its aliasing artifacts, existence of mixed pixels, interference of noise and blurring effect, etc. The brain and the spinal cord together constitute the Central Nervous System (CNS), with the brain being the most complex component. Brain segmentation is crucial for surgical planning, disease detection, and therapeutic interventions. A unique entropy based soft clustering approach (EMT2FCM) for the brain MRI imaging on both real and simulated datasets is proposed in this paper. This paper presents a refined version of the type-2 Fuzzy C-Means (FCM) technique (EMT2FCM) for isolating diverse tissues in Magnetic Resonance (MR) brain images, achieved through an enhanced entropy-based membership function. Difficulty in edge detection occurs due to the vagueness caused by mixed pixels. To overcome the problem with mixed pixels a new membership function proposal has been given. EMT2FCM, i.e., fuzzy membership function with Shannon's entropy-based variation, is able to handle uncertainty and vagueness in images offered by mixed pixels, by implementing new distance criteria modification for the calculation of optimum cluster. The approach has been validated using datasets from BRAINWEB (simulated) and IBSR (real-life). Following the deployment of our new algorithm, we assessed its performance using six observation criteria. The results demonstrated significant improvements in clustering performance, as evidenced by enhanced Mean Squared Error (MSE), Dice Index, and Jaccard Index, Accuracy, Sensitivity and Partition Indices validation measures. The evaluation of EMT2FCM in comparison to other state-of-the-art methods is established to reduce segmentation errors significantly. [Display omitted] [ABSTRACT FROM AUTHOR]

• This paper aims to solve multiple criteria sorting problems involving multiple DMs. • A preference disaggregation approach with uncertain and contradictory preferences. • Assignment examples and pairwise comparisons for reference alternatives are considered. • A case study of financial investment decisions for government-funded projects. Preference disaggregation analysis is effective for inferring a preference model of decision makers from decision examples. Although multiple criteria sorting problems are often handled within the context of group decision-making, it has not been well studied how to estimate a collective sorting model for a group with uncertain and inconsistent preferences through preference disaggregation. To this end, this paper proposes a threshold-based value-driven preference disaggregation method to solve multiple criteria sorting problems involving multiple decision-makers. We allow decision-makers to reduce the cognitive effort of preference expressions by providing possible classes of reference alternatives or pairwise comparisons between them through uncertain expressions. In addition, we develop a two-stage inconsistency identification and elimination procedure that includes dealing with contradictory preference information provided by a single decision maker and managing disagreement among a group of decision makers. A collective preference model consisting of an additive value function and value thresholds is estimated by linear programming. The proposed method is demonstrated by a practical example of financial investment decisions for government-funded projects. The results show that dealing with uncertain and inconsistent preferences can improve the accuracy of preference disaggregation. [ABSTRACT FROM AUTHOR]

Human decision-making is an essential direction of current research. Fuzzy sets and relations have been used to model human behavior, reasoning, and decision-making over the years. Since social science research shows that omitting or zeroing out negative information does not fully describe human behavior and decision-making, the concept of balanced sets and relations was developed in response to this problem. Balanced sets and relations are mathematical concepts that support both positive and negative data analysis. Balanced sets of equations are considered to find relationships between different sets. In this article, the idea of balanced systems of equations is presented. The paper discusses the existence and how to determine their set of solutions. A method for solving balanced systems of equations with balanced MAX and MIN operations is given. [ABSTRACT FROM AUTHOR]

Concept hierarchies, as part of knowledge representation methods, play an important role in supporting the exchange and sharing of information. We developed and automated a concept hierarchies construction process which includes several artificial intelligence techniques. When automating their construction from an existing, more or less structured, body of knowledge, the evaluation of the resulting concept hierarchy is an important step. We propose an approach for concept hierarchy construction (CHC) from short sentences, that makes use of methods like Sentence Embedding, Clustering, and Automatic Labeling to create a hierarchical representation consisting of three layers. Our major focus in this paper is not on the algorithms used but on their evaluation using manual clustering by experts and fuzzy sets. [ABSTRACT FROM AUTHOR]

The probabilistic hesitant fuzzy sets (P-HFSs) allow experts to express their preferences regarding different membership degrees with probabilistic information. Fuzzy entropy is an important concept to measure the uncertainty of probabilistic hesitant fuzzy information. In this paper, we propose a novel fuzzy entropy named as the exponential probabilistic hesitant fuzzy entropy for the P-HFEs. This novel fuzzy entropy not only observes the basic property of fuzzy entropy, but also has the same characteristics and change tends with the existing fuzzy entropy proposed and studied by other scholars. Then, based on the cardinal reconciliation method and TODIM(Tomada de decisao interativa multicriterio) method, we propose a multi-criteria decision-making (MCDM) problem, where the attribute weight is determined by the exponential probabilistic hesitant fuzzy entropy of the integration results. Finally, a application case in green building is given for the sake of illustrating the efficiency of the MCDM problem. Numerical and theoretical results show that a MCDM problem based on the proposed novel fuzzy entropy and the TODIM method have a wide range of application. [ABSTRACT FROM AUTHOR]

• This paper extends the EVAMIX (EVAluation of MIXed Data) method. • These extensions are fuzzy extension, group decision and expert prioritization. • Four criteria and three alternatives are determined for gas transportation industry. • Ship selection is conducted as an empirical study. • The ranking result reflects the recent oversupply of LNG carriers. This paper extends the EVAMIX (EVAluation of MIXed Data) as an exemplary multi-criteria decision-making method in three perspectives. First, the problem is investigated in a fuzzy environment. Secondly, multiple decision-makers involve in decision-making process. It allows the moderator to benefit the opinions of multiple experts. Third, experts are assigned a coefficient considering their professional career represented in years. In the conventional approach, the experts have assumed identical, but expert prioritization deals with the instability. The extensions applied in this study are currently available in the literature, and it is used for the first time in the EVAMIX method. This method can be applied to decision-making problems in any research field. A study is carried out to combine the pre-determined types of ships with reliable quantitative and qualitative criteria and create data for new investors and shipowners in the selection of ships using a novel mathematical approach. As a result of the study, preferences are modelled for candidate ships, and database and value options are presented to decision-makers, ship owners, and investors. The qualitative and quantitative data discussed in this selection process to support the decision-making process and can be designed appropriately to be used in similar selection problems. The most suitable vessel to be selected from the candidate's vessels is carried out based on the existing criteria being evaluated; therefore, it is a reference for similar methodologies. [ABSTRACT FROM AUTHOR]

This paper exhibits a novel approach for solving fully intuitionistic fuzzy multi-objective fractional transportation problem (FIF-MOFTP). Because of the change of market policies, we expect that the transportation cost, the shipped quantity, the source, and the destination parameters are not generally exact. In this paper, a theorem which demonstrate that FIF-MOFTP is ever solvable was presented. In our approach, the problem is converted into a linear one based on some transformations. Then the linearized model is reduced to a crisp multi-objective transportation problem utilizing the accuracy function for each objective. Moreover, various theorems that set up the relation among the FIF-MOFTP and its equivalent crisp model using linear, hyperbolic, and parabolic membership functions are also proofed. To approve the proposed approach, a numerical example is incorporated. Deductions and future exploration of this paper are depicted at end. [ABSTRACT FROM AUTHOR]