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Heterogeneous multi-criteria group decision making (MCGDM) is a hot topic in the decision analysis field. This paper proposes a fairness-concern-based LINMAP (Linear Programming Technique for Multidimensional Analysis of Preference) method for heterogeneous MCGDM with hesitant fuzzy linguistic (HFL) truth degrees. Heterogeneous evaluation information includes crisp numbers, interval numbers, intuitionistic fuzzy values (IFVs), trapezoidal fuzzy numbers (TrFNs) and hesitant fuzzy sets (HFSs). This paper introduces the fairness concern to calculate the HFL consistency and the HFL inconsistency indices. Based on the framework of LINMAP, a bi-objective HFL programming model is built to derive the criteria weights, the positive ideal fairness vector (PIFV) and the negative ideal fairness vector (NIFV) for each decision maker (DM) simultaneously. Based on the TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution), a multi-objective programming model is built to obtain DMs' weights. The alternatives ranking is derived by comprehensive collective relative closeness degrees. Finally, a real example is applied to verify effectiveness and superiority of this heterogeneous MCGDM method. The proposed heterogeneous MCGDM method provides a very useful approach for MCGDM with heterogeneous information. [ABSTRACT FROM AUTHOR]

Regarding the defects of Ruspini partition-based clustering in revealing the intrinsic correlation between classes, this paper proposes a series of generalized multiplicative fuzzy possibilistic product partition clustering algorithms. First, based on the existing concept of generalized multiplicative intuitionistic fuzzy sets, this paper introduces a new concept of generalized multiplicative fuzzy sets and further defines the corresponding multiplicative fuzzy partition. Then, based on the concept of multiplicative fuzzy partition, a novel generalized multiplicative fuzzy possibilistic product partition C-means (GMFPCM) clustering algorithm is presented, and its local convergence is strictly proved using Zangwill's theorem. Meanwhile, a robust Gaussian-base radial kernel based on the M-estimator is introduced into the GMFPCM algorithm to improve its robustness against noise and outliers in numerical data. Additionally, a multiplicative fuzzy possibilistic local information factor is constructed and embedded into the GMFPCM algorithm to strengthen its ability to suppress noise in images. Finally, the comparison with existing fuzzy possibilistic clustering algorithms in the literature confirms the competitiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper proposes a new intuitionistic fuzzy best-worst method (IFBWM) for group decision making (GDM) with intuitionistic fuzzy (IF) preference relations (IFPRs). IF values (IFVs) are used to express reference comparisons of criteria. Based on the additive consistency of IFPRs, this paper proposes the definition of additive consistency of IF reference comparisons (IFRCs). Based on the deviation minimization, a linear goal programming model is established to calculate the optimal IF priority weights. By the additive consistency, the consistency index in the closed form is computed by the score function of IFVs. A new approach is devised to enhance the additive consistency of IFRCs. Thus, an IFBWM with the additive consistency of IFRCs is proposed. For GDM with IFPRs, the best criterion and the worst criterion are identified for each decision maker by constructing the score matrix of the IFPR. The individual ranking order of the criteria is obtained by using the proposed IFBWM. Then, the collective ranking order of the criteria is obtained via building a 0–1 integer programming model. Therefore, a GDM method based on the developed IFBWM with IFPRs is proposed. Four examples are analyzed to demonstrate the effectiveness and the advantages of the proposed IFBWM for GDM. [ABSTRACT FROM AUTHOR]

• Research about the intuitionistic fuzzy set theory is analyzed systematically with quantitative analysis. • The evolution of hot topics and knowledge diffusion path are investigated. • The self-citations phenomenon is deeply discussed when performing main path analysis. • The application of the intuitionistic fuzzy set in the domain of decision making is becoming more and more dominant. Since the intuitionistic fuzzy set theory was proposed, it has received widespread attention. To get a deeper understand of this field, this paper analyzes a total of 2913 papers downloaded from the Web of Science (WoS) from 1984 to 2019 from different perspectives. On the one hand, this research identifies important themes and their interrelationships, showing the thematic evolution of this field vividly. On the other hand, this research digs out the knowledge diffusion paths of this domain with the help of global and key-route main paths. From the perspective of the thematic evolution, five thematic area are detected including Intuitionistic fuzzy relation , IVIFS-Similarity , MCDM/MADM-GDM , Aggregation operator and Extensions of IFS. Among them, MCDM/MADM-GDM has evolved from an emerging theme to a motor theme being the most important topic and GDM integrating themes MADM 、 MCDM and Aggregation operator shows continuous growth. From the perspective of knowledge diffusion paths, research topic has gradually translated from theorical construction to practical application, and several factors such as self-citation, indirect citation, hierarchy and references that may influence the result of the main path are discussed. In general, this research systematically provides scholars with the development process in this domain, which is conductive to them to fully grasp the state-of-the-art research. [ABSTRACT FROM AUTHOR]

Multiattribute group decision-making (MAGDM) is a decision analysis method used to address decision-making problems that have multiple attributes and multiple decision alternatives. It is generally believed that multigranulation rough sets (MGRSs) are a twofold scheme to solve MAGDM problems. Thus, in this paper, we aim to generalize MGRSs and decision-theoretic rough sets (DTRSs) to intuitionistic fuzzy β -covering (IF β C) information systems and propose a novel MAGDM method to handle decision-making problems, which not only deepens the cognition of the three-way decision (3WD) model but also expands its application in decision-making problems. The paper first introduces a novel conditional probability using the ideal positive degree of intuitionistic fuzzy numbers (IFNs) and then investigates its properties. Second, in the IF β C environment, we utilize the proposed conditional probabilities to construct two types of multigranulation decision-theoretic rough set (MGDTRS) models, an optimistic strategy and a pessimistic strategy, discuss their theoretical properties and explore the relationship between the two strategies. Third, a novel MAGDM method for multi-intuitionistic β -neighborhoods is established in accordance with the proposed MGDTRS model. We also establish an algorithm for the proposed MAGDM method. Fourth, we apply the proposed method to address several MAGDM problems. By conducting comparative analysis with existing methods, we demonstrate the effectiveness of the proposed method and discuss the advantages and limitations of the proposed method. Furthermore, we conduct extensive parameter experimentation analysis on the proposed method from different perspectives. The experimental results demonstrate the stability and effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]

This paper aims to develop a new axiomatic design-based mathematical programming method for heterogeneous multi-criteria group decision making (HMCGDM) problems with linguistic fuzzy truth degrees (LFTDs). The main contributions of this paper are summarized in five aspects: (1) The information content definitions for six types of fuzzy numbers are initially provided according to axiomatic design. (2) Considering the authority of experts on different criteria and group consensus, a bi-objective programming model is constructed to derive experts' weights by maximizing individual deviation and minimizing group discordance. (3) Each alternative is assessed on the basis of its information content to a fuzzy positive ideal solution. Information content is firstly used to define the linguistic fuzzy consistency and inconsistency indices. (4) A bi-objective linguistic fuzzy mathematic programming model is built to determine the criteria weights, which considers consistency and inconsistency indices simultaneously. This model can be dexterously transformed into a crisp linear programming model for resolution by the linguistic scale function. (5) The group information content of each alternative to fuzzy positive ideal solution is calculated to determine the ranking order of alternatives. Finally, an example of blockchain service provider selection is given to validate the proposed method. [ABSTRACT FROM AUTHOR]

• Establish formulas to compute spread and indeterminacy indices of fuzzy judgments. • Develop a novel trapezoidal fuzzy extension of Saaty's consistency. • Propose a new framework to normalize trapezoidal fuzzy utility vectors. • Build a linear program to acquire trapezoidal fuzzy utility vectors from TFRPMs. • Find an analytical solution for optimal fuzzy utility vectors of consistent TFRPMs. Fuzzy extensions of Saaty's consistency play an important role in developing fuzzy analytic hierarchy process based decision-making methods. This paper proposes formulas to calculate ratio-based increasing and decreasing spread indices and to obtain ratio-based indeterminacy indices of modal and support intervals for fuzzy judgments of trapezoidal fuzzy reciprocal preference matrices (TFRPMs). A transitivity equation with parametric fuzzy elements is introduced and combined with the existence of parameter values to define consistency of TFRPMs. To cope with the challenge of identifying the existence, computational formulas are developed to directly obtain values of parameters from the fuzzy judgments in a TFRPM, and an equivalent consistency concept is proposed for TFRPMs. Properties of consistent TFRPMs are presented and a logarithmic deviation based formula is provided to compute consistency indices of TFRPMs. A new framework of normalized vectors with trapezoidal fuzzy elements is introduced. A logarithmic goal programming model is established and transformed into a linear program for acquiring normalized trapezoidal fuzzy utility vectors from TFRPMs. An analytical solution is found for optimized trapezoidal fuzzy utility vectors of consistent TFRPMs. The developed models are validated by three numerical illustrations possessing comparative studies. [ABSTRACT FROM AUTHOR]

Consensus reaching process (CRP) is very important for multi-criteria group decision making (MCGDM). Recently, social network driven CRP methods have been deeply investigated. However, these methods rarely considered knowledge levels of DMs. In fact, knowledge levels of DMs can decide the correctness of final decision result which play an important role in CRP. Therefore, this paper proposes knowledge degree to measure knowledge level of DM and develops a new social network driven CRP method for probabilistic linguistic MCGDM problems. Based on the similarity degree and knowledge degree, similarity degree-based social network (SDSN) and trust relationship-based social network (TRSN) are constructed successively. According to the constructed SDSN and TRSN, the proposed CRP method consists of two stages. In the first stage, pair-wise DMs in complementary social network adjust their evaluations. In the second stage, the evaluations of DMs who contribute less to group consensus are modified. To ensure that the group consensus index (GCI) is non-decreasing in the above two stages, the constructed programming models not only improve similarity degrees between DMs-to-adjust and reference DMs but also consider similarity degrees between DMs-to-adjust and other DMs. Finally, an investment selection example and comparison analyses demonstrate the applicability and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

As information continues to expand and uncertainty intensifies, traditional three-way decision methods in multi-criteria environments often appear inadequate when dealing with ranking problems. Most traditional three-way decision methods usually rely on subjective concepts or require decision-makers to specify probability parameters when constructing scheme descriptions, which leads to high subjectivity of the methods. Based on this background, this paper proposes an optimization-based three-way decision model for multi-criteria ranking strategy considering intuitionistic fuzzy concept, with the aim of mitigating the excessive subjectivity observed in most of the three-way decision methods. Firstly, a scheme-oriented intuitionistic fuzzy concept is defined to represent the decision-maker's fuzzy perception and selection of the scheme. Then, using the scheme-oriented intuitionistic fuzzy concept and the classic description of candidate schemes obtained through intuitionistic fuzzy c -means clustering algorithm, this paper provides a new method for estimating the conditional probability of the schemes that is not limited by parameter settings. Secondly, combining the scheme-oriented intuitionistic fuzzy concept and intuitionistic fuzzy information table, a new risk loss function is proposed, which is suitable for decision problems under intuitionistic fuzzy environment. Then, based on three-way decision model formulated using an optimization-based approach, an objective new ranking strategy is constructed. In addition, numerical analysis, comparative analysis, and parameter analysis are used to validate the rationality and feasibility of the presented ranking strategy. Finally, through quantitative analysis of multiple datasets and qualitative analysis of several ranking models, the operability of the new ranking strategy is verified. [ABSTRACT FROM AUTHOR]

Formation control of multi-agent systems has a wide range of applications, but it has not been paid much attention in Takagi–Sugeno (T-S) fuzzy systems. In this paper, an event-triggered sampling strategy is designed for the formation control of T-S fuzzy systems, which allows the fuzzy controller and the fuzzy model not to share the same membership functions. The control strategy reduces the transmission frequency of sampling states by setting event conditions for information transmission. By means of Lyapunov stability theory, a set of formation conditions based on LMI is established. Less conservative and more efficient conditions are also obtained based on the properties of membership functions. Numerical examples show the validity of the proposed formation conditions, and the conservatism of the two criteria is compared. [ABSTRACT FROM AUTHOR]

The comprehensive logistics distribution center location selection (CLDCLS) problem is a multiattribute group decision-making (MAGDM) problem in which multiple commodity preference weights are considered. To better describe the preference information and expert evaluation information, this paper utilizes 2-dimensional linguistic (2DL) information to express the preference information of various commodities and the expert evaluation, which can represent not only the evaluation information of experts but also the reliability of the evaluation information. Additionally, for solving the CLDCLS problem, this paper puts forward improved operational rules a score function, a distance formula and a correlation coefficient measure. Based on the 2DL information and the improved operational rules, we propose a 2-dimensional linguistic similarity-degree-based clustering analysis method, the 2-dimensional linguistic partitioned Maclaurin symmetric mean (2DLPMSM) operator, and the 2-dimensional linguistic weighted partitioned Maclaurin symmetric mean (2DLWPMSM) operator. The corresponding properties and special cases are demonstrated. By using these proposed methods, this paper constructs a MAGDM solution framework for the CLDCLS problem. A practical case of the CLDCLS problem is presented to demonstrate the effectiveness, rationality, robustness and superior performance of the proposed method. [ABSTRACT FROM AUTHOR]

Recently, some researchers have explored three-way decision models in the fuzzy multi-criteria environments from the perspective of criterion fuzzy concept. The main characteristics of these models include the subjective preference of decision-maker for criteria and the evaluation value information system provided by decision-maker. However, the criterion fuzzy concept only considers the decision-maker's membership preference to each criterion, and ignores the decision-maker's non-membership preference to each criterion. In view of this, this paper further proposes a new criterion fuzzy concept, namely the intuitionistic fuzzy concept, to express decision-maker's preference for each criterion. At the same time, we build an intuitionistic fuzzy concept-oriented three-way decision model to solve the ranking and classification problem in the intuitionistic fuzzy multi-criteria environments with decision-maker's preference. Firstly, based on the defined intuitionistic fuzzy concept, we construct a new intuitionistic fuzzy loss function model. Meanwhile, using intuitionistic fuzzy similarity, we propose a new conditional probability calculation method to express the correlation degree between the intuitionistic fuzzy concept and alternative's evaluation values. Secondly, we introduce three decision-making perspectives from the membership degree and non-membership degree of expected loss to obtain the final three-way classification scheme. Moreover, by combining the thresholds of the positive and negative perspectives, we obtain the comprehensive thresholds of the comprehensive perspective, which can be used to rank all alternatives. Finally, a supplier selection problem is used to verify the feasibility and superiority of the model, and six data sets are used to verify the applicability of the model. [ABSTRACT FROM AUTHOR]

• The problem is formulated in a general setting investigating pairwise comparisons matrices. • Innovative concepts of consistency, intensity and coherence of FPCMs are introduced. • New algorithm for calculating the priority vector is proposed. • Two illustrating examples of the proposed algorithm are presented and discussed. Applying the Analytic Hierarchy Process (AHP) in a decision making (DM) problem, fuzzy elements are appropriate whenever the decision maker is uncertain about the value of his/her evaluation of the relative importance of the elements in question, i.e., criteria and/or alternatives. The method, often called the fuzzy AHP, is also used when aggregating crisp pairwise comparisons of a group of decision makers in the group DM problem. In this paper, the DM problem is formulated in a general setting using pairwise comparisons matrices with elements from an Abelian linearly ordered group (alo-group). Such an approach enables extensions of traditional multiplicative, additive, or fuzzy approaches. Here, we propose some desirable properties (consistency, coherency, and intensity) of priority vectors, and derive sufficient conditions for the existence of priority vectors with those properties. In general, the most popular methods for deriving the priority vector – the Eigenvector Method and the Geometric Mean Method – do not always provide priority vectors having these desirable properties. Here, we formulate a new solution algorithm for deriving the priority vector based on a specific optimization problem satisfying the desirable properties under appropriate assumptions. Two illustrating examples of the algorithm are presented and discussed. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed nonlinear programming methodology, the Euclidean distance between interval-valued intuitionistic fuzzy values (IVIFVs), and the proposed score function of IVIFVs. Firstly, a new score function of IVIFVs is proposed to overcome the shortcomings of the existing score functions of IVIFVs. Then, we construct the score matrix based on the proposed score function of IVIFVs and the decision matrix given by the decision maker. Then, a nonlinear programming model is proposed based on the Euclidean distance between IVIFVs and the interval-valued intuitionistic fuzzy weights of the attributes provided by the decision maker. Then, we solve the proposed nonlinear programming model to obtain the optimal weights of the attributes. Then, the weighted score of each alternative is calculated based on the obtained score matrix and the obtained optimal weights of the attributes. Finally, the alternatives are ranked according to the obtained weighted scores of the alternatives. The MADM method proposed in this paper can conquer the shortcomings of the existing MADM methods in the environments of IVIFVs. [ABSTRACT FROM AUTHOR]

Multiobjective optimization problems (MOPs) are the optimization problem with multiple conflicting objectives. Generally, an optimization algorithm can find a large number of optimal solutions for MOPs, which easily overwhelm decision makers (DMs) and make it difficult for decision-making. Preference-based evolutionary multiobjective optimization (EMO) aims to find the partial optima in the regions preferred by the DM. Although it narrows the scope of the optimal solutions, it usually still returns a population of optimal solutions (typically 100 or larger in EMO) with a small distance between adjacent optima. Top-K, which is a well-established research subject in many fields to find the best K solutions, may be a direction to reduce the number of optimal solutions. In this paper, first, we introduce the top-K notion into preference-based EMO and propose the top-K model to obtain the best K individuals of multiobjective optimization problems (MOPs). Then, with the top-K model, we propose NSGA-II-TopK and SPEA2-TopK to search for the top-K preferred solutions for preference-based continuous and combinatorial MOPs, respectively. Finally, the proposed algorithms with several representative preference-based EMO algorithms are compared in different preference situations for MOPs. Experimental results show the proposed algorithms have strong performances against the compared algorithms. [ABSTRACT FROM AUTHOR]

Consensus building is crucial in multi-criteria group decision making (MCGDM) because a consensual decision outcome is beneficial for implementing the result. However, expert credibility and its dynamic variation are rarely considered in the consensus reaching process (CRP) for MCGDM problems. In reality, experts are not completely reliable, and their credibility changes dynamically during the CRP. Therefore, this paper proposes a novel CRP method based on dynamic expert credibility for GDM under Dempster-Shafer theory (DST). First, expert credibility is defined by measuring the extrinsic discrepancy and intrinsic ambiguity of decision information to quantify experts' abilities to provide high-quality evaluations. Then, a novel consensus measure is proposed based on the inverse-square law to check whether the current consensus level satisfies the designated threshold. If not, a new feedback mechanism considering dynamic expert credibility is activated to promote group consensus. Furthermore, the attribute weights are comprehensively determined from both objective and subjective perspectives. Finally, an illustrative example and comparative analysis are presented to validate the proposed method. [ABSTRACT FROM AUTHOR]

[Display omitted] • Generalized preference information is used to reduce subjective randomness. • Imputation of missing values occurs systematically under different scenarios. • Weights of experts and criteria are systematically determined. • Waste treatment options are ranked rationally. • Practicality is validated by using a case study from Tamil Nadu. A generalized orthopair fuzzy set can express uncertain information easier than most other processes, which gives us more space for decision-making. In recent times, the selection of healthcare waste treatment (HCWT) technology can be considered as multi-criteria decision-making (MCDM) problem due to the involvement of multiple conflicting criteria. To reduce the unhealthy impact on the ecosystem and promote sustainable disposal, researchers have investigated MCDM problems to select apt HCWTs. In a bid to the minimize negative environmental impact of healthcare waste, researchers adopted MCDM, and faced challenges such as: (i) handling uncertainty/subjective randomness; (ii) imputation of missing values; and (iii) consideration to experts' attitude and interdependencies during MCDM process. To remedy these, this paper has attempted to establish a novel decision model with generalized orthopair fuzzy information (GOFI). Initially, missing values are systematically imputed. Experts' preferences were fused to obtain an aggregated matrix by considering the interdependencies among experts. Also, criteria weights were computed utilizing attitude-based entropy measures, and HCWTs were ranked using the GOFI-evaluation based on distance from average solution (GOFI-EDAS) approach. Lastly, the methodology's superiority was validated using an illustrative example, followed by a comparison with extant models. The results confirm that the developed framework is more efficient than and consistent with earlier methods under uncertainty. [ABSTRACT FROM AUTHOR]

Multi-attribute decision making (MADM) plays an important role in decision analysis. Based on a new fuzzy rough set theory (FRS), this paper presents a multi-attribute prediction analysis model in fuzzy information systems (FISs). In this prediction model, the proposed FRS is based on an attribute-oriented fuzzy similarity relation; the cosine deviation of a candidate to optimistic decision and pessimistic decision is proposed to construct a trend function, for further predicting the development trend of the candidate. It deals with MADM problems from the perspective of multi-attribute predictive analysis, and is a valuable continuation of fuzzy decision making research. To evaluate the validity and feasibility of the proposed prediction model, experiments with real data sets and comparative experimental analysis are conducted. The experimental results prove that the prediction performance of the proposed model is well-pleasing in terms of both prediction accuracy and AUC results. [ABSTRACT FROM AUTHOR]

The good development of health care is conducive to improve the value and prospects of society. However, health sectors of Ghana are facing a challenge in providing medical services with expected quality for an ever-increasing number of patients in response to competitive pressures. In such circumstances, the proper evaluation of hospital health-care delivery quality becomes critical. Thus, to achieve this goal, this paper proposes an integrated medical triangular fuzzy MULTIMOORA approach (IMTFMA). We firstly construct the appropriate evaluation criteria system based on the analysis of Ghana's medical services. Then, to properly evaluate the weight of the criteria in a comprehensive manner, we determine the weight of criteria from subjective and objective perspectives. Meantime, we handle the fuzzy evaluation of experts for the criterion importance with the enhanced alpha-level sets method. According to the triangular fuzzy rating for hospitals provided by respondents, we further develop a novel evaluation method based on MULTIMOORA with the axiomatic design for accurately evaluating health-care delivery quality. The research is conducted on 8 selected hospitals, including 4 public and 4 private hospitals in the Greater Accra Region of Ghana, with 24 criteria. 15 experts with rich experience in related fields and 480 respondents assessed the above 8 selected hospitals by questionnaires. According to the outcome of the empirical analysis, even though public hospitals benefit subsidy from the government, they perform abysmally low, whereas private hospitals which are self-sponsored rather perform extremely better than expectation. [ABSTRACT FROM AUTHOR]

As the generalization of fuzzy covering, fuzzy β covering can effectively deal with uncertain information in hybrid data. Swarm intelligence algorithm has unique advantages in feature selection. This paper proposes a novel cooperative swarm intelligence feature selection method for hybrid data based on fuzzy β covering and fuzzy self-information. First, the parameterized fuzzy β neighborhood and fuzzy decision in a fuzzy β covering decision information system are defined, and the lower and upper fuzzy approximations are further studied. Fuzzy rough set model exclusively focuses on the information derived from the lower fuzzy approximation within a decision. In actual circumstances, the uncertainty of fuzzy information is linked to not only the lower fuzzy approximation but also the upper fuzzy approximation. Then, by incorporating the lower and upper fuzzy approximations of a decision, fuzzy self-information and relative fuzzy self-information are introduced as two evaluation indicators of feature selection. Next, a forward feature selection algorithm based on heuristic search strategy is designed by means of these two evaluation indicators. Moreover, in order to effectively explore feature subsets to a greater extent, a cooperative swarm intelligent feature selection algorithm based on random search strategy is also designed by combining particle swarm optimization algorithm and cuckoo search algorithm. Finally, an array of experiments is executed to compare two designed algorithms with five other existing feature selection algorithms. Experimental results show that these two designed algorithms achieve a high feature selection rate while improving the classification accuracy of the raw data. [ABSTRACT FROM AUTHOR]

• Criteria system construction for selecting GRID suppliers. • Introduction of novel fuzzy sets (SVZs, SVZPRs) combining Z-numbers and CST. • Improved efficiency of S-BWM through SVZPR extension. • Development of TOPSIS with SVZs combining TOPSIS and CST. • Enhancement of decision reliability through PageRank integration in SMCDM. Firms need a reliable decision-making framework to select suppliers who are Green, Resilient, and embrace Inclusive Development (GRID). However, GRID supplier selection is challenged by events that are uncertain and often dependent. Such events affect supplier rankings in a fuzzy decision environment. This paper builds a GRID-based criteria system and applies an enhanced Best Worst Method (BWM) and Technique for Order Preferencing using the Similarity to the Ideal Solution (TOPSIS), with Scenario-Varying Z-numbers (SVZs) and reversed PageRank. The decision criteria are extracted from the literature and confirmed by expert judgement. The SVZs and SVZ Preference Relations (SVZPRs) are developed by combining the Concept of Stratification Theory (CST) with Z-numbers, to reflect the impact of Dependent Uncertain Events (DUEs). Reverse PageRank is then used to find the occurrence probability of the scenarios due to DUEs. BWM is applied in an SVZPR environment to obtain the weights of the decision criteria. TOPSIS, incorporating SVZs, is used to rank the suppliers. An example is used to highlight the enhanced BWM-TOPSIS, to find the priority ranking of the GRID weights. Comparative and sensitivity analyses are conducted to validate the proposed method. [ABSTRACT FROM AUTHOR]

• Complete consistent matrix corresponding to an IFPR is constructed. • Necessary and sufficient conditions for IFPRs to be multiplicatively consistent are proposed. • Ratio-based deviation matrix that takes an accurate measurement of deviation of every element in an IFPR is constructed. • Every indeterminacy degree of an IFPR is never changed in the revising process. In this paper, we propose a method for improving the multiplicative inconsistency of an intuitionistic fuzzy preference relation (IFPR) without computing any model to derive an underlying priority weight's vector with respect to alternatives. For this, a necessary and sufficient condition for the IFPR to be multiplicative consistent is proposed and proved. Based on it, a ratio-based deviation identifying matrix that takes an accurate measurement of deviation of every element in the IFPR is constructed. We prove that the greater the value of the deviation matrix is, the more inconsistent is its corresponding element in the IFPR and based on it, a convergent iterative algorithm of improving the multiplicative consistency is presented. The algorithm uses the fact that all the indeterminacy degrees of the IFPR are never changed in the revising process of multiplicative inconsistency and as a result, the most inconsistent elements are uniquely determined by suitable elements in the IFPR, respectively. The proposed method makes a great difference from the previous methods that derived the underlying priority weight's vector with respect to alternatives based on the given IFPR for improving consistency. A numerical example is provided to show the feasibility and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

We develop an agent-based artificial general intelligent system that can be implemented in compact and power-efficient electronic hardware. The hardware under development is called the Street Engine, which is a hardware-based cognitive architecture for implementing agent-based artificial intelligence. In this paper, we introduce an agent-based system to replicate simple cognitive behaviours. In the processes of this system, numerical data are converted into fuzzy symbolic representations of the surrounding environment, and reasoning rules are included in a modified Fuzzy Inference System to support the cognitive decision-making. We use a case study example, the homing behaviour of the honey bee, to demonstrate constructing production rules and implementing the cognitive and reasoning capabilities of agents. The low level cognitive behaviour is converted into a rule-based fuzzy system, and hardware-based experiments have been conducted to verify the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

In the period of internationalization, choice of a country for doing business is a challenging problem. In existing works, this problem is considered for the cases of crisp, statistical, or fuzzy information. However, real international business problems are characterized by fuzziness and partial reliability of information. In this paper we propose a multi-attribute decision making approach to country selection under Z-number-valued information. The approach relies on the methods (which were published by the authors earlier) of consistency-driven Z-number-valued matrix and determination of its eigenvector. A real-world application on country selection with nine real countries is used to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

The optimal selection, ranking and classification of objects are important aspects in the multi-criteria decision-making (MCDM) problem. In this paper, we try to propose a three-way MCDM method with fuzzy complementary preference relation based on additive consistency to select the optimal object, rank objects and classify objects at the same time, which will help decision-makers better make decisions. Firstly, we give the fuzzy complementary judgment matrix based on additive consistency. Then, based on this matrix, we construct the concept of ξ -similarity class, and define a new relative loss function. Subsequently, we describe the detailed decision-making processes of the newly proposed three-way MCDM method. Further, through the trainer selection problem, we verify the feasibility of the method. Comparative analyses show that our method has stronger decision-making function than some existing methods. Experimental analyses show that our method is stable in ranking the considered objects and selecting the optimal object. Moreover, the proposed method can not only provide reasonable ranking decision suggestion for decision-makers, but also can meet the decision-makers' preference in the classification decision. [ABSTRACT FROM AUTHOR]

The determination of both thresholds in decision-theoretic rough sets is an important problem of study that has aroused widespread attention in recent years. Although many related methods have been proposed, they may need a substantial amount of computation in model solving even not capture the thresholds in some cases. In this paper, we introduce linguistic intuitionistic fuzzy numbers (LIFNs) into loss functions due to LIFNs integrating the advantages of linguistic terms and intuitionistic fuzzy numbers, and propose a single optimization model-based, threshold-determined method to derive three-way decision. First, we define a novel measure for ranking LIFNs, verify its properties, analyze the relationships between loss functions with LIFNs and establish linguistic intuitionistic fuzzy decision-theoretic rough sets with a novel measure for LIFNs. Second, we investigate linguistic intuitionistic fuzzy, three-way decision methods from three perspectives, especially from the third perspective. We construct a single optimization model for capturing the thresholds that can overcome the shortcomings of the methods from two other perspectives, and the uniqueness of the optimal solution of this model is proven with the aid of the Karush-Kuhn-Tucker (KKT) condition. Third, a single model-based perspective method and its corresponding algorithm are designed to determine the thresholds for linguistic intuitionistic fuzzy information. Last, an illustrative example and simulated experiments are conducted to show the validity of our method. [ABSTRACT FROM AUTHOR]

Consistency has a crucial influence on the rationality of preference information and even the final decision result. This paper presents two new definitions of additive consistency for hesitant fuzzy preference relations (HFPRs): completely additive consistency (CAC) and weakly additive consistency (WAC). To verify the CAC or WAC of HFPRs, some linear programming models and 0–1 mixed programming models are developed. The methods consider all the information given by the decision maker without changing the length of hesitant fuzzy elements (HFEs). Accordingly, a method of modifying an inconsistent HFPR into an additively consistent HFPR is proposed. The deviation between the original complementary matrix and the modified one is minimal. Then, several linear programming models are developed to obtain priority weights from an HFPR. From these, an integrated algorithm is designed to illustrate the process of consistency test, inconsistency modification and weights derivation for HFPRs. The proposed methods are also extended to deal with WAC and CAC of incomplete HFPRs. Finally, three numerical examples and comparative analysis are presented to illustrate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Deep learning-based recommendations have demonstrated impressive performance in improving recommendation accuracy. However, such approaches mainly utilize implicit feedback to predict user preferences and neglect the adverse impact of explicit preference noise, which affects the robustness and reliability of model training. To consider the reliability of both rating input and output, we propose a novel joint deep neural recommendation framework that incorporates rating reliability derived solely from ratings to provide reliable recommendations for active users. Firstly, we introduce a noise detection method based on intuitionistic fuzzy sets to identify incorrect ratings from the perspective of fuzzy preferences and label them to generate a binary rating reliability matrix. Subsequently, we propose a joint deep neural framework that integrates rating reliability to simultaneously capture the high-order features of users and items, yielding predictions with their corresponding reliability probabilities. Finally, to achieve a balance between accuracy and reliability for recommendations, we design a reliability threshold selection strategy based on K-means clustering to find an appropriate threshold. Experimental results on three widely used datasets show that our model achieves an average improvement of 9.4% and 8.0% in the metrics Recall and NDCG, respectively, compared with the closest competitor. This paper provides new insights for integrating rating reliability into a deep neural network to enhance the performance of recommender systems. [ABSTRACT FROM AUTHOR]

• A PF-WPA-CRITIC-MARCOS framework is reported to select the preferential sustainable food supplier for resilient cities. • A hierarchical model of criteria for sustainable food supplier selection is constructed. • The deviation between input data and the interactive criteria is considered in selecting sustainable food suppliers. • A numerical case of the food supply chain is illustrated to test the proposed model. Sustainable food supplier selection (SFSS) can be handled as an uncertain decision-making issue. The Pythagorean fuzzy set (PFS), a type of non-standard fuzzy set, offers an expanded description space for articulating fuzzy and uncertain data. Accordingly, this paper proposes a Pythagorean fuzzy synthetic decision method-based selection framework for solving the SFSS problem within a subjective context. Then, the weighted distance measures for the PFS are introduced to derive the importance degrees of the experts, which can provide a more objective decision result. Then, an information fusion method with a PFS-weighted power average (WPA) operator is introduced to form a group decision matrix competent to accommodate the deviation effect. Next, an extended PF-measurement of alternatives and ranking according to compromise solution (MARCOS) method integrating PF-criteria importance through inter-criteria correlation (CRITIC) is presented to calculate the priority of each supplier, which can capture the inter-correlations between criteria. Finally, a numerical example of SFSS is implemented to show the application of the proposed synthetic decision approach. Subsequently, the sensitivity analysis of distance parameters and comparison analysis among different SFSS approaches were conducted to test the rationality and advantages of the proposed framework for resolving the SFSS problem. The results show that the reported method can provide a practical way to resolve the SFSS problems with uncertain data. [ABSTRACT FROM AUTHOR]

A variety of fuzzy sets, especially Pythagorean fuzzy sets (PFSs), are commonly utilized to describe the ambiguity of information in three-way decision (3WD) models. PFSs can handle fuzzy information well but ignore the description of stochastic information. To address this issue, in this paper, we attempt to construct a novel three-way multiattribute decision model by combining 3WD with constrained Pythagorean fuzzy sets (CPFSs) which can measure the reliability of PFSs. Firstly, we introduce the concept of constrained Pythagorean fuzzy information systems (CPFISs). Comprehensive positive and negative similarities of objects are given in a CPFIS by introducing normalization, score function, comparison rules, and positive and negative ideal solutions. Secondly, by comprehensive positive and negative similarities, novel formulas for calculating comprehensive relative utility function values are obtained and an objective method for estimating conditional probabilities is presented in the absence of decision attributes. Based on the above knowledge, we establish a similarity-based three-way multiattribute decision model in a CPFIS. Furthermore, we conduct a case analysis of appendicitis to realize the application of our proposed model and several comparative analyses to demonstrate the effectiveness and superiority of our model. Finally, the good performance of the new model is verified through experimental analyses. [ABSTRACT FROM AUTHOR]

Being a pair of dual concepts, the normalized distance and similarity measures are important tools for decision-making and pattern recognition under the intuitionistic fuzzy set framework. In this paper, we first construct some counterexamples to illustrate that two existing similarity measures do not meet the axiomatic definition of intuitionistic fuzzy similarity measures. We then show that (1) these two measures cannot effectively distinguish some intuitionistic fuzzy values (IFVs); (2) except for the endpoints, there exist infinitely many pairs of IFVs, where the maximum distance "1" can be achieved under these two distances, leading to counter-intuitive results. To overcome these drawbacks, we introduce the concept of strict intuitionistic fuzzy distance measure (SIFDisM) and strict intuitionistic fuzzy similarity measure (SIFSimM), and propose an improved intuitionistic fuzzy distance measure based on Jensen-Shannon divergence. Moreover, we prove that (1) it is a SIFDisM; (2) its dual similarity measure is a SIFSimM; (3) its induced entropy is an intuitionistic fuzzy entropy. Comparative analysis and numerical examples demonstrate that our proposed distance measure is superior to the existing ones. In particular, our proposed distance measure can better distinguish and rank intuitionistic fuzzy sets. [ABSTRACT FROM AUTHOR]

This paper introduces comprehensive and theoretically-driven approach to decision making under bimodal uncertainty in form of Z-numbers. The proposed decision making approach relies on synergy of consistency-driven preferences construction method, eigenvector determination method of Z-number valued matrixes proposed by author and his colleagues and modified WSM model. Consistency-driven preferences construction method is used to obtain a consistent Z-valued pair-wise comparison matrix (PCM) given inconsistent one. Indeed, initial Z-number-valued degrees of pairwise comparison of criteria importance provided by a decision maker are often inconsistent. Next, an eigenvector of the consistent Z-valued PCM is computed to derive criteria importance weights. To arrive at normalized Z-values of criteria, a normalization technique is proposed. Overall evaluations of alternatives are computed as a weighted sum of normalized criteria values. Finally, overall values are compared by using ranking of Z-numbers. The suggested decision method is rank reversal free. Correctness and feasibility of suggested method is illustrated by example. [ABSTRACT FROM AUTHOR]

• A new hybrid group decision making model for QFD under uncertainty is proposed. • Interval type-2 fuzzy sets are used to handle various uncertainties in experts' assessments. • Entropy weighting method is adopted to objectively compute customer requirement weights. • An extended TODIM model is developed to determine the ranking of engineering characteristics. • The advantages of the new model are illustrated with an empirical case study. Quality function deployment (QFD) is a team-based product development technique for determining critical engineering characteristics based on customer requirements to realize higher customer satisfaction. Given its simplicity and visibility, the QFD has been broadly utilized in a variety of industries for product or service planning. However, traditional QFD method assumes that the behavior of domain experts is completely rational, and is only suitable for product development problems with a small number of experts. In this paper, we aim to develop a new large group QFD approach based on an extended TODIM (Portuguese acronym for interactive multi-criteria decision making) method under interval type-2 fuzzy context. The interval type-2 fuzzy sets are utilized to describe the imprecise and uncertain correlation assessment information between customer requirements and engineering characteristics. The normal TODIM is modified and used to derive the priority of engineering characteristics considering the psychological factors of experts. Also, an entropy weighting method was adopted to derive the weights of customer requirements objectively. Finally, we provide an electric vehicle product development case and perform a comparison analysis with previous methods to reveal the effectiveness and practicability of the proposed large group QFD approach. [ABSTRACT FROM AUTHOR]

Decision-theoretic rough sets (DTRSs) as a classic model of three-way decisions have been widely applied in the field of risk decision-making. Considering situations where experts hesitate among several evaluation values, hesitant fuzzy sets, as a new generalization of fuzzy sets, can describe uncertain information flexibly in the decision-making process. In this paper, we propose a decision-theoretic fuzzy rough set (DTFRS) model in hesitant fuzzy information systems and discuss its application in multi-attribute decision-making (MADM). More specifically, we first define a novel fuzzy binary relation between two objects by using the hesitant fuzzy distance function. Then, we study the calculations of the fuzzy similarity class and the conditional probability. At the same time, based on the connection between the loss functions and the attribute values, we develop a data-driven calculation method of the relative loss functions. With these discussions, we construct a DTFRS model in hesitant fuzzy information systems and explore the related decision-making mechanism. Furthermore, a three-way decision method based on the proposed DTFRS model is established to handle MADM problems in the context of a hesitant fuzzy environment. The established method not only takes the decision risk into consideration, but also instructs us how to choose the action for each alternative and gives its corresponding semantic explanation. An illustrative example of the stock investment problem is presented to verify the efficacy of our method. Finally, we take a sensitivity analysis and a comparison analysis to show the established method's performance and characteristics. [ABSTRACT FROM AUTHOR]

By combining ideas from three-way decision and Pedrycz shadowed sets, this paper investigates two possible solutions to the problem of constructing a shadowed set from an Atanassov intuitionistic fuzzy set. The first solution treats the pair of membership and nonmembership functions as two evaluations and directly applies the two-evaluation based model of three-way decision. The second solution transforms the pair of membership and nonmembership functions into an evaluation and applies a single-evaluation based model of three-way decision. To address a fundamental issue of the determination of a pair of thresholds on evaluations, we present a general optimization based formulation and use Chebyshev distance to calculate the required thresholds. The results are useful for three-way decision with fuzzy sets, Atanassov intuitionistic fuzzy sets, and shadowed sets. [ABSTRACT FROM AUTHOR]

Recent multi-criteria group decision making methods focus their analysis on the experts preferences. They do not take into account the reasons why each expert has provided a specific set of preferences. In this paper, a method that introduces novel measures capable of explaining the reasons behind experts decisions is presented. A novel concept, the arguments are presented. They represent the experts have for maintaining a certain position in the debate. Several measures related to the arguments are proposed. These new argumentation measures, along with consensus measures, help us to get a clear idea about how and why a specific resolution has been reached. They help us to determine which is the most influential expert, that is, the expert whose contributions to the debate have inspired the rest. Also, the proposed method allows us to determine which are the arguments that most of the experts have followed. A clear overview about how the debate is evolving in terms of arguments is also provided. The novel presented analysis indicate how the experts change their opinions in every round and what was the reason for it, which changes have occurred between rounds and they also provide global analysis results. [ABSTRACT FROM AUTHOR]

Dempster-Shafer evidence theory (D-S) is an effective instrument for merging the collected pieces of basic probability assignment (BPA), and it exhibits superiority in achieving robustness of soft computing and decision making in an uncertain and imprecise environment. However, the determination of BPA is still uncertain, and merely applying evidence theory can sometimes lead to counterintuitive results when lines of evidence conflict. In this paper, a novel BPA generation method for binary problems called as the base algorithm is designed based on the kernel density estimation to construct the probability density function models, using the pairwise learning method to establish binary classification pairs. By means of the new BPA generation method, a new decision-making algorithm based on D-S evidence theory, fuzzy preference relation and nondominance criterion is effectively designed. The strength of the proposed method is presented in applying pairwise learning, which transforms the original complex problem into simple subproblems. With this process, the complexity of the problem to be solved is greatly reduced, which increases the feasibility for industrial applications. Furthermore, the fuzzy computing technique is used to aggregate the output for each single subproblem, and the nondominance degree of each class is determined from the fuzzy preference relation matrix, which can be directly used for the determination of the input instance. Based on several industrial-based classification experiments, the proposed BPA generation method and decision-making algorithm present the effectiveness and improvement in terms of precision and Cohen's kappa. [ABSTRACT FROM AUTHOR]

Three-way decision (3WD) provides a new perspective and methodology for solving multi-attribute decision-making (MADM) problem. In this paper, we introduce 3WD into a multi-scale decision information system (MS-DIS), which provides a new idea for solving MADM issues in MS-DISs. By using fuzzy membership functions, a multi-scale evaluation information table is first converted into a numerical evaluation value table. To calculate loss functions at two states generated by the decision class partition, a distance-based cost measurement is then defined. With reference to fuzzy σ -neighborhood classes, conditional probabilities are further calculated and 3WD rules from MS-DISs can be unravelled. As a result, the ranking about all objects in the data is obtained according to expected losses. Finally, a specific numerical example is used to illustrate the effectiveness of the proposed method comparing with other ones. An experimental analysis is also used to describe the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

• We propose an information entropy measure for intuitionistic fuzzy values (IFVs). • We propose the IIFEWA operator for IFVs. • We propose a new multiattribute decision making (MADM) method. • The proposed MADM method is based on the proposed IIFEWA operator of IFVs. • It provides us with a very useful way for MADM in the intuitionistic fuzzy context. This paper proposes the improved intuitionistic fuzzy Einstein weighted averaging (IIFEWA) operator of intuitionistic fuzzy values (IFVs). The proposed IIFEWA operator can overcome the drawbacks of the intuitionistic fuzzy Einstein improved weighted averaging (IFEIWA) operator, the intuitionistic fuzzy Hamacher improved weighted averaging (IFHIWA) operator, the intuitionistic fuzzy Hamacher weighted averaging (IFHWA) operator, the intuitionistic fuzzy Einstein weighted averaging (I F W A ω ε) operator, the intuitionistic fuzzy weighted averaging (IFWA) operator and the intuitionistic fuzzy Hamacher interactive ordered weighted averaging (IFHIOWA) operator of IFVs, where they have the drawbacks that (1) the membership grades and the non-membership grades of their obtained aggregating IFVs are indeterminated in some situations and (2) if there is only one IFV whose membership grade is equal to 1, then the membership grade of the aggregated IFV of n IFVs becomes 1; if there is only one IFV whose non-membership grade is equal to 0, then the non-membership grade of the aggregated IFV of n IFVs becomes 0. Based on the proposed IIFEWA operator, we propose a new multiattribute decision making (MADM) method. The proposed MADM method overcomes the drawbacks of the existing MADM methods, where they cannot distinguish the ranking orders of alternatives in some situations. [ABSTRACT FROM AUTHOR]

This paper proposes a consensus model for multi-experts multi-criteria decision making (MEMCDM) problems with probabilistic linguistic term sets (PLTSs), which also considers the regret-rejoice emotions of decision makers (DMs) in their decision-making processes. Additionally, the Dempster-Shafer theory is applied to estimate the probability of the market status which is related to the perceived values of the alternatives. Moreover, an algorithm is given to determine the weight of each DM. Then, a detailed consensus procedure is proposed and an illustrative example is used to show the feasibility of the proposed model. Finally, some comparative analyses are carried out to demonstrate the advantages of the proposed consensus process. [ABSTRACT FROM AUTHOR]

In the crowdsourcing task allocation scheme, there is an emerging and realistic co-opetition phenomenon. To availably solve the crowdsourcing task allocation problem with co-opetition, this paper designs a two-stage co-opetition model by constructing novel three-way decision (TWD), including a competition-optimization model and a negotiation-cooperation model. Unlike the other studies, the two-stage co-opetition model with TWD can not only protect the profits of the task candidates, but also optimize the overall benefits. Specifically speaking, in the competition-optimization model, we construct an optimization model based on the data envelopment analysis (DEA) method in advance, which maximizes the personal benefit. By integrating information system and the loss function matrix, we consider the linkage of evaluation information and risk information and then improve the original TWD to make an initial allocation. In the negotiation-cooperation model, considering that the relationship among the candidates may influence the task performance, the fuzzy measure is introduced to describe a broader partnership. Meanwhile, we also design two different schemes to coordinate and optimize the best task allocations based on the initial allocation. In order to choose the best scheme, the selection strategy between schemes is further investigated under the guidance of the utility and the loss. Finally, we give an example of a medical supply chain crowdsourcing problem to illustrate and verify our proposed approach. [ABSTRACT FROM AUTHOR]