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Extraneous growth of scientific information over the Internet makes the searching task non-trivial and as a consequence researchers are facing difficulties in finding relevant papers from the millions of research papers in digital repositories. The research paper recommendation systems have been advocated to address this problem. The existing research paper recommendation systems lack in exploiting prominent information of papers, such as relevancy with the current time, novelty, scientific contribution, writing complexity of the papers, etc. Further, the existing models emphasize only on user's preference rather than user's intention that may change with time. Furthermore, the existing models do not consider a sound ranking strategy to unleash the personalization aspect and relevancy of papers. This work aims to address the existing limitations and proposes a systematic hidden attribute-based recommendation engine (SHARE). SHARE utilizes a feature engineering technique to unfold valuable insights of papers through multiple hidden features. These features are used as a context for users as well as multiple criteria for ranking papers. Additionally, SHARE predicts a user's intention beyond the user's preference to capture the dynamic notion of a user. Finally, a novel ranking strategy is proposed to retrieve personalized and the most important papers. SHARE is flexible for recommending both old and new users. In order to evaluate the effectiveness of SHARE both user studies and system evaluations were performed. Experimental results substantiate the efficacy of the proposed approach and are comparable to the existing systems. [ABSTRACT FROM AUTHOR]

As an unsupervised learning method, clustering does not need to know prior knowledge of the datasets in advance. How determining the optimal number of clusters becomes an important method to judge the quality of clustering results. For fuzzy clustering algorithms, the introduction to fuzzy partition makes it more consistent with the structure of real datasets than hard clustering algorithms. Therefore, it is necessary to carry out the research on the validity evaluation methods of fuzzy clustering. At present, the research on fuzzy clustering validity mainly focuses on the fuzzy clustering validity index (FCVI) and the combined fuzzy clustering validity evaluation method (CFCVE). From these two aspects, this paper reviews fuzzy clustering validity functions and combined fuzzy clustering validity evaluation methods. Then FCVI and CFCVE are discussed in details from different points on fuzzy clustering validity functions, and the research status and construction strategies of different fuzzy clustering validity evaluation methods are analyzed. The accuracy and stability of each fuzzy clustering validity evaluation method are analyzed through comparative experiments. Finally, the paper summarizes the shortcomings and advantages of the current research on fuzzy clustering validity and looks forward to the research direction and improved methods of the evaluation methods. [ABSTRACT FROM AUTHOR]

• A many objective evolutionary algorithm based on decomposition and moth search is proposed. • Random and adaptive weights is used to break the limitation of uniform distribution weights. • Mutual evaluation value is used to evaluate the optimal individual in the neighborhood. • Improving scale factor α in MSA is to improve the performance of the proposed algorithm. Decomposition-based multi-objective evolutionary algorithm (MOEA/D) has good performance in solving multi-objective problems (MOPs) but poor performance in solving many-objective optimization problems (MaOPs). The weight vectors in MOEA/D are relatively fixed, which results in poor performance when dealing with complex MaOPs. In this paper, random and adaptive weights are introduced into MOEA/D to break the limitation of fixed weight vectors. And the moth search algorithm (MSA) is used as an operator to improve global search ability. The updating strategies in MSA are more consistent with the neighborhood learning strategy adopted in MOEA/D. In addition, to enable MSA to find the optimal solution in the neighborhood on the MaOPs to update other individuals. This paper introduces mutual evaluation value for evaluating the optimal individual in the neighborhood, and the proposed algorithm is abbreviated as MOEA/DMS. In comparative experiments on the MaF test suite, hypervolume (HV) and inverted generational distance (IGD) are used to measure MOEA/DMS and other many-objective evolutionary algorithms (MaOEAs). The results show that MOEA/DMS has an excellent performance in dealing with MaOPs. Besides, MOEA/DMS is compared with other state-of-the-art MaOEAs on two combinatorial MaOPs. The results show that MOEA/DMS also has significant advantages in dealing with combinatorial MaOPs. [ABSTRACT FROM AUTHOR]

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]

Although conventional dynamic surface filters can eliminate the issue of complexity explosion in backstepping design, the convergence of filter errors significantly influences the overall control performance. This paper proposes a unified design framework of an event-triggered adaptive fuzzy design scheme with fixed-time performance for unmodeled strict-feedback nonlinear systems, where the tracking performance, filter error, and parameter learning convergence are considered simultaneously. The unified framework guarantees the smoothness of all the closed-loop signals. A novel dynamic surface filter is designed to avoid the repeated differentiation of recursive virtual control while the filter error converges in fixed time. Compared with the conventional backstepping design, the proposed adaptive fuzzy controller design in this paper can guarantee fixed-time tracking performance. An event-triggered condition with intermittent feedback is developed to decrease the computational and communication burden. Two simulation examples are provided to validate the effectiveness of the unified fixed-time framework. [ABSTRACT FROM AUTHOR]

In this paper, we develop a novel multiattribute decision making (MADM) approach based on Fermatean hesitant fuzzy sets (FHFSs) and the modified VIKOR method. Firstly, we propose the definition of distance measures of FHFSs and present its properties. Further, taking the effectiveness of FHFSs for dealing with ambiguous and imprecise data in MADM problems, this paper proposes the remoteness index-based Fermatean hesitant fuzzy-VIKOR (FHF-VIKOR) MADM method. The generalized distance measure for FHFSs is subsequently employed to establish the notions of remoteness indices with the positive ideal and the negative ideal remoteness indices. The objective weighting procedure is developed using the maximum deviation principle and the generalized distance measure to obtain the attributes' weights. Some examples are discussed to reveal the performance of the proposed MADM method. Finally, the advantages of the proposed MADM method in terms of the robustness and the flexibility are shown by a comparative study. The proposed MADM method based on FHFSs and the modified VIKOR method can overcome the drawbacks of the existing MADM methods. [ABSTRACT FROM AUTHOR]

Given a finite set of alternatives, the ranking problem statement builds a preference pre-order (partial or complete) on this set. In this paper, we are interested in multiple criteria ranking problems with a hierarchical structure of criteria; more precisely, we are interested in the existing hierarchical E lectre III method. This method requires eliciting several preference parameters (namely, the weights and the veto thresholds). A direct elicitation of such parameters can be cognitively very demanding; thus, it is adequate to define the parameters in a way that requires much less cognitive effort from the decision-maker. The model parameters can be indirectly elicited by using holistic information provided by the decision-maker; this information can be given in the form of a ranking on a set of reference alternatives and some additional preference information. This paper proposes an aggregation-disaggregation approach for inferring the model parameters of the hierarchical E lectre III based on an evolutionary algorithm. To verify the applicability and validity of the proposed preference disaggregation methodology, an illustrative example is addressed regarding the ranking of a set of universities. [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]

• 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]

Internet hospitals are platforms that provide medical information, prescription, and treatment by combining online and offline medical resources. Well-development Internet hospitals can reduce operational pressure of offline hospitals and unnecessary waste of medical resources. Evaluating the performance of Internet hospitals is helpful for their development. In this paper, we introduce a linguistic Z-number-based gained and lost dominance score (GLDS) method to evaluate Internet hospitals. Firstly, to ensure the reliability of evaluation information, we extend the GLDS method to the linguistic Z-number environment. To model the risk preference of an expert, we depict the negative performance of an alternative over other alternatives under each criterion by a lost dominance score function, and represent the individual regret of a expert to the worst alternative by a net lost dominance score function. A weighting method that combines the best worst method and correlation coefficient method is developed to determine the weights of criteria. To verify the validity and practicability of the proposed method, a case study of ranking Internet hospitals is provided. Comparative analysis shows that the solutions of the proposed method reflect the preferences of experts. [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]

Currently, more and more researchers use the idea and strategy of three-way decision to guide scientific research. In this paper, we propose two comprehensive fuzzy concepts and apply them to construct a new three-way decision model. Firstly, with the TOPSIS method, this paper regards the optimal distance and the worst distance as the cost fuzzy concept and the benefit fuzzy concept, respectively. Then, based on the fuzzy concepts with opposite characteristics, two comprehensive fuzzy concepts (i.e., the comprehensive benefit fuzzy concept and the comprehensive cost fuzzy concept) are proposed, and the relationship between the decision-making regions corresponding to the two comprehensive fuzzy concepts is discussed. Further, four fuzzy neighborhood operators are used to describe the relationship between any two schemes and the relative loss function is used to compute the loss value of each scheme with different behaviors in different states. Afterwards, we introduce a new three-way decision model to solve the multi-criteria decision-making (MCDM) problem. Comparing analysis, Kendall analysis and Spearman analysis show that our method is feasible and stable. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new score function of Fermatean fuzzy numbers (FFNs). The proposed score function of FFNs can conquer the drawbacks of the existing score function of FFNs. We develop a new multicriteria decision making (MCDM) method based on the proposed score function of FFNs, the criteria importance through intercriteria correlation (CRITIC) method and the gained and lost dominance score (GLDS) method with Fermatean fuzzy information. The developed MCDM method can conquer the shortcomings of the existing MCDM methods for MCDM in the environments of FFNs. It provides us a very useful way for MCDM in the context of FFNs. [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]

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 outranking multi-criteria decision-making (MCDM) method focuses on the systematic comparison of alternatives and the non-compensation among criteria to conduct decision analysis. Z-numbers are powerful tools for characterizing decision-making information and identifying information reliability. This paper aims to explore Z-number outranking theories and the corresponding MCDM method on the basis of the idea of Elimination and Choice Translating Reality (ELECTRE) III, which is a very popular and capable outranking model. The concordance and discordance indices of Z-numbers are defined by processing their bimodal uncertainty fully. And an objective computation method is investigated to determine the values of thresholds in these indices. Further, three types of novel outranking relations, including dominance, support and opposition relations, for Z-numbers are presented by comparing these indices systematically. Then, an extended MCDM method with the distillation and flow ranking rules is proposed by detecting the outranking relations among alternatives under multiple criteria and carrying out the outranking aggregation and exploitation. To verify the applicability and effectivity of the proposed method, an illustrative example is provided, and a simulation test and a comparison discussion are conducted [ABSTRACT FROM AUTHOR]

Z-numbers are efficient tools to represent uncertain information through restriction and reliability measurement. Z-numbers and their variants have been integrated with diverse decision-analysis methods to solve practical decision-making problems. To make researchers understand the research status and challenges in this area, this paper provides an overview of publications related to Z-number-based decision analysis methods and applications. Firstly, a bibliometric analysis is conducted to present the trends and hotspots in this research domain. To uncover theoretical developments of Z-numbers, concepts and operation rules of Z-numbers and their variants are then recalled. Furthermore, decision analysis methods regarding multiple criteria decision analysis, optimization, prediction, and reasoning within the context of Z-numbers are summarized. Applications of Z-number-based decision analysis methods are categorized into six different fields including business and financial management, industrial engineering and management, energy management, medical and healthcare management, environment and sustainable development, and others. Findings, challenges, and future research directions are further discussed. It is hoped that this paper can provide insights for scholars and practitioners in the fields of Z-number-based decision analysis and applications. [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]

Evolving fuzzy systems (EFSs) are a type of adaptive fuzzy rule-based systems which can self-adapt both their structures and parameters simultaneously. However, the existing EFSs suffer from two drawbacks: 1) classical EFSs usually use all input features to model systems, resulting in lengthy fuzzy rules; 2) some redundant information in fuzzy rules may hinder high generalization. To address these two issues, a promising method is proposed in this paper by combining very sparse random projection (VSRP) with a class of EFSs based-on data clouds, called VSRP-AnYa-EFS. The proposed method introduces: 1) a random sparse-Bernoulli (RSB) matrix based-on VSRP is utilized to compress the lengthy antecedent part into a tighter form, triggering a feature-reduction mechanism. By employing VSRP in RSB matrix, some redundant information in fuzzy rules can be filtered; 2) Local learning is used for consequent parameter optimization to suit decoupled behavior of rules after redundant information between rules is deleted. By adopting VSRP and local learning, the proposed VSRP-AnYa-EFS owns a compact structure and fast learning speed. Numerical examples presented in this paper demonstrate that the proposed method can significantly reduce training time from hours to minutes while the accuracy can be improved up to 5%. [ABSTRACT FROM AUTHOR]

• In the proposed IVIF-BWM, we build weight-determining models concerning expert's attitudes. • A bi-objective programming model is proposed to derive experts' dynamic weights. • Develop an IVIF-DBWM to determine the global weights of all criteria. • IVIF-SPA is proposed to evaluate the overall resumption risk of each alternative. Currently, China has achieved a remarkable achievement on the containment of COVID-19, which creates a favorable condition for the gradual resumption of normal life. However, COVID-19 infections continue to rise in many nations and some sporadic cases occur from time to time in China, which still poses some risks to the resumption. Hence, it is imperative to develop some reasonable techniques to assess the resumption risk. This paper aims to investigate an integrated interval-valued intuitionistic fuzzy (IVIF) technique to adroitly assess the resumption risk based on DEMATEL (decision making trial and evaluation laboratory), BWM (best-worst method) and SPA (set pair analysis). This integrated technique is called IVIF-DBWM-SPA, where the IVIF-DBWM (combined by the IVIF-DEMATEL and IVIF-BWM) is used to determine the global criteria weights and the IVIF-SPA is employed to generate the ranking order of the alternatives. The IVIF-DEMATEL and IVIF-BWM are used to determine the weights of dimensions and the weights of criteria under each dimension, respectively. In this IVIF-BWM, two bi-objective programming models are constructed by regarding experts' pessimistic and optimistic attitudes, respectively. Combined experts' intrapersonal and interpersonal uncertainties simultaneously, a bi-objective programming model is proposed to derive the dynamic weights of experts. Based on the determined weights of experts and criteria, an IVIF-SPA is developed to assess the risk levels of all alternatives. The validity of the proposed technique is demonstrated with a real case of college resumption risk assessment amid COVID-19. Some sensitivity and comparison analyses are provided to show the merits of the proposed technique. [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]

Complex evidence theory, as a generation model of the Dempster-Shafer evidence theory, has the ability to express uncertainty and perform uncertainty reasoning. One of the key issues in complex evidence theory is the complex basic belief assignment (CBBA) generation method. But, how to model uncertainty information in complex evidence theory is still an open issue. In this paper, therefore, we propose a CBBA generation method by taking advantage of the triangular fuzzy number. Moreover, an algorithm for decision making is devised based on the proposed CBBA generation method. Finally, the decision making algorithm is applied in classification to verify its effectiveness. In summary, the proposed method can handle uncertainty modeling and reasoning both in the real number domain and the complex number domain, which provides a promising way in decision making theory. [ABSTRACT FROM AUTHOR]

Recently the useful redefinition of the intuitionistic and interval-valued intuitionistic fuzzy set theories (A − I F S , A − I V I F S) based on the Dempster-Shafer theory of evidence (DST) was developed. It was named the "Belief-Plausibility" (BP) approach as only the basic mathematical tools of the DST were used for its foundation. In this paper, a new approach to compare the real, interval and fuzzy-valued intuitionistic fuzzy and BP numbers is proposed. Among known approaches to compare intuitionistic fuzzy objects, most justified and used in applications are those based on the so-called score and accuracy functions. The observed multiplicity of these functions treatments and modifications indicates that the source of such a divergence is the impossibility to solve this problem exclusively in the framework of the A − I F S. Therefore, to develop the reliable methods for the considered types of comparison, a redefinition of this problem based on the BP approach is proposed. This redefinition allows us to develop new two and three criteria methods for comparison of real, interval and fuzzy-valued intuitionistic fuzzy and BP numbers, based on the local criteria with transparent interpretation in the framework of the BP approach. [ABSTRACT FROM AUTHOR]

Multi-Criteria Decision Aiding arises in many industrial applications where the user needs an explanation of the recommendation. We consider, in particular, an explanation taking the form of a contribution level assigned to each variable. Decision models are often hierarchical, and the influence is computed by the Winter value, which is an extension of the Shapley value on trees. The contribution of the paper is to propose two exact methods to efficiently compute the Winter values for a very general class of decision models known as the Choquet integral. The first one is an analytical expression for a flat model. The second one is an exact algorithm for a hierarchical model. The main idea of this algorithm is to prune the combinatorial structure on which the Winter value is computed, based on the upper and lower bounds of the utility on subtrees. Extensive simulations show that this new algorithm provides very significant computation gains compared to the state of the art. [ABSTRACT FROM AUTHOR]

Color is one of the most used features for image analysis. However, two uncertainty problems arise in this scope: first, color computer representation does not match with how humans understand the color concept; second, the color feature is imprecise by nature. For this reason, fuzzy colors and fuzzy color spaces were developed as a suitable way to model color categories. The most recent and best accurate approaches use crisp color prototypes to build fuzzy color spaces, considering standard and fixed set of colors prototypes (such as ISCC-NBS system) for this purpose. The use of these types of general purpose prototypes may not be flexible enough to collect particular colors of a given image (or a set of images); in addition, image colors may be context dependent in some cases (for example, red color in winery or medicine context). In order to solve these drawbacks, in this paper we propose to learn fuzzy color spaces by analyzing the relevant colors in a given set of representative images for a specific context and/or application; then, we will use them as prototypes in order to build adaptive fuzzy color spaces. Some real experiments are performed in order to illustrate the advantages of our proposal. [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]

• A restrictive requirement that the input channel of the NDS is a constant matrix is removed, by proposing a novel fuzzy integral sliding mode parallel controller. • The universality of the proposed fuzzy controllers is rigorously discussed for two kinds of NDSs. This paper considers the stabilization problem of nonlinear descriptor systems through Takagi–Sugeno (T-S) fuzzy models of type 1. A novel fuzzy integral sliding mode parallel control strategy is proposed, where the T-S fuzzy model is employed to equivalently approximate any nonlinear descriptor system. A fuzzy sliding-mode parallel controller is constructed to robustly control the T-S fuzzy model and, consequently, to semi-globally stabilize the corresponding nonlinear descriptor system. The developed control scheme can remove a restrictive assumption on the system input channel and is applicable to general nonlinear descriptor systems. Moreover, universality discussion of the developed controller for two kinds of nonlinear descriptor systems is provided, which endows the proposed method with more confidence in real industrial applications. Finally, two examples numerically demonstrate the feasibility and advantages of the developed controller. [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]

• The new landscape in the longitudinal research of type-2 fuzzy sets (T2FS) domain are presented. • The multi-criteria decision making has gradually developed into moto theme. • The knowledge diffusion trajectory and thematic evolution of T2FS domain are presented. • The application of T2FSs in decision-making may the possible development directions. Nowadays, more scholars and practitioners are committed to improving and applying type-2 fuzzy sets (T2FSs) in various domains because of the stronger ability to handle the uncertainty of fuzzy complex systems. To explore the status and internal laws of development of this field, this paper presents the development overview based on the bibliometric analysis, then the dynamic evolution of main topics and the knowledge diffusion trajectory are also displayed on the basis of the strategy diagram and main path analysis (MPA). From 1997 to 2019, 1749 documents are retrieved from Web of Science (WoS) repository for the analysis. The results show that there are four stable collaborative communities existing in the countries/regions' collaborative network and the collaboration is affected by geographical factors to some degree. Three main evolution paths of hot topics are also presented in this paper and the multi-criteria decision-making (MCDM) has gradually developed into the moto theme. Furthermore, articles appearing on the main path mainly focus on the research of basic concept and framework, self-optimization and applications in various domains of T2FSs. In general, this paper provides a new landscape in the longitudinal research based on the development overview, thematic evolution and the knowledge diffusion trajectory. [ABSTRACT FROM AUTHOR]

This paper explores the elliptic entropy and the elliptic semi-entropy of a coherent fuzzy number and discusses several of their properties. We propose a methodology that incorporates the adaptive index, k , of the coherent fuzzy number representing an individual investor's stock market assessment (pessimistic, optimistic, or neutral). We combine the adaptive index with the elliptic entropy and semi-entropy to obtain risk measures incorporating investor attitude. We use the proposed risk measures in a portfolio optimization problem that uses coherent fuzzy numbers to model the asset returns. The optimization models are solved using a genetic algorithm. We apply the proposed methodology to a large-scale case study involving 100 assets to demonstrate its effectiveness. The real-world performance of the proposed approach is illustrated using an out-of-sample analysis. Based on the results we obtained, we discuss the advantages and disadvantages of elliptic entropy and semi-entropy. Finally, we compare the proposed methodology with other approaches in the literature and demonstrate its superiority. [ABSTRACT FROM AUTHOR]

• Obtaining the optimal discounting weights of BPAs is proposed using the BWM method by considering consistency ratio. • A new way to determine the best and worst BPA is presented based on the distance of evidences. • Partially decrease the computing cost of fusion system by decreasing the number of comparisons using the BWM method. • More reasonable results in decision making are obtained by the proposed methodology. Dempster-Shafer evidence theory (DST) could show its advantages during the process of data fusion. In DST, the determination of the weight of evidence in conflict management is attracting growing interest. Limited work has been done based on the discount model, the consistency of the weight is still virgin and may become a fascinating question. In this paper, a novel strategy about how to ascertain the optimal weight of basic probability assignment (BPA) using BWM method is proposed, which provides a promising way to ascertain the best BPA and the worst BPA. Then, a consistency ratio is utilized for BPA, which has the ability of inspecting the reliability of the comparisons and producing more rational results. Some numerical experiments and application examples are used to illustrate the effectiveness and practicability of the proposed methodology. [ABSTRACT FROM AUTHOR]