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Structure learning is the core of graph model Bayesian Network learning, and the current mainstream single search algorithm has problems such as poor learning effect, fuzzy initial network, and easy falling into local optimum. In this paper, we propose a heuristic learning algorithm HC-PSO combining the HC (Hill Climbing) algorithm and PSO (Particle Swarm Optimization) algorithm, which firstly uses HC algorithm to search for locally optimal network structures, takes these networks as the initial networks, then introduces mutation operator and crossover operator, and uses PSO algorithm for global search. Meanwhile, we use the DE (Differential Evolution) strategy to select the mutation operator and crossover operator. Finally, experiments are conducted in four different datasets to calculate BIC (Bayesian Information Criterion) and HD (Hamming Distance), and comparative analysis is made with other algorithms, the structure shows that the HC-PSO algorithm is superior in feasibility and accuracy. [ABSTRACT FROM AUTHOR]

Currently, the digital economy continues to deepen its development, and it has become a consensus among all sectors as the direction of global future development. Digital finance, as a fleet in the wave of digital economy, is rapidly heading towards the sunny shore of benefiting the public and serving entities driven by the digital technology engine. Xinwang Bank is a fast boat in the digital finance fleet, always adhering to the principle of technology, building an open platform, and actively promoting the construction of an open, shared, and secure digital credit ecosystem from three levels: institutional, industry, and ecological, to assist in the development of the digital economy. The digital commercial bank security evaluation is a classical multiple attribute group decision making (MAGDM) problems. Recently, the Evaluation based on Distance from Average Solution (EDAS) method has been employed to manage MAGDM issues. The intuitionistic fuzzy sets (IFSs) are used as a tool for portraying uncertain information during the digital commercial bank security evaluation. In this paper, the intuitionistic fuzzy nunmber EDAS (IFN-EDAS) method is cultivated to manage the MAGDM based on Hamming distance and Euclidean distance under IFSs. In the end, a numerical case study for digital commercial bank security evaluation is supplied to validate the proposed method. The main contributions of this paper are outlined: (1) the EDAS method has been extended to IFSs based on Hamming distance and Euclidean distance; (2) the CRITIC method is used to derive weight based on Hamming distance and Euclidean distance under IFSs. (3) the IFN-EDAS method based on Hamming distance and Euclidean distance is founded to manage the MAGDM based on the Hamming distance and Euclidean distance under IFSs; (4) a numerical case study for digital commercial bank security evaluation and some comparative analysis is supplied to validate the proposed method. [ABSTRACT FROM AUTHOR]

In the information age, teachers are no longer the only source of information for students, and the problems of the traditional lecture mode are becoming more and more obvious. Especially in the process of teaching English in colleges and universities, students' personalized and diversified needs for English learning are becoming more and more obvious, and if traditional theoretical lectures or theoretical indoctrination are continued, students' needs and goals will be affected. As a new form of teaching, blended teaching can integrate the advantages of classroom teaching and online teaching and improve the overall quality and effectiveness of English teaching under the premise of changing the orientation of teachers and students. The English blended teaching quality evaluation is a multiple-attribute group decision-making (MAGDM) problem involving multiple qualitative and quantitative attributes. In this paper, on basis of EDAS technique, a novel spherical fuzzy number EDAS (SFN-EDAS) technique based on SFN Hamming distance (SFNHD) and SFN Jaccard similarity measure (SFNJSM) is built for dealing with MAGDM. Moreover, the MEREC technique with SFNHD and SFNJSM is extended to SFSs to acquire the attribute weights. Finally, SFN-EDAS technique is used for English blended teaching quality evaluation to prove practicability of the developed SFN-EDAS technique and SFN-EDAS technique is compared with existing techniques to further demonstrate its superiority. Hence, the research main achievements for this paper are outlined: (1) the novel EDAS technique is extended to the SFSs environment based on the SFNHD and SFNJSM; (2) the MEREC technique is extended to SFSs to acquire the attribute weights based on the SFNHD and SFNJSM; (3) a novel spherical fuzzy number EDAS (SFN-EDAS) technique based on the SFNHD and SFNJSM is built for dealing with MAGDM; (4) an empirical example and several comparative analysis for English blended teaching quality evaluation is offered to demonstrate the SFN-EDAS technique. [ABSTRACT FROM AUTHOR]

Sports events, as large-scale events that provide products and services, have received widespread attention for their economic benefits and influence. Event organizers expect to achieve high efficiency by providing high-quality products and services. The quality of competition products and services is mainly evaluated through the subjective feelings of the audience, and usually the audience's evaluation of service quality is vague. Therefore, this article intends to establish an evaluation index system for the quality of spectator service in sports events, in order to provide a reasonable evaluation of the service products provided by sports event organizers. The audience service quality evaluation for large-scale sports-events is a MAGDM problems. Recently, the EDAS and CRITIC technique has been employed to cope with MAGDM issues. The interval neutrosophic sets (INSs) are employed as a tool for characterizing uncertain information during the audience service quality evaluation for large-scale sports-events. In this paper, the interval neutrosophic number EDAS (INN-EDAS) technique based on the Hamming distance and Euclid distance is founded to manage the MAGDM under INSs. The CRITIC technique is employed to obtain the weight information based on the Hamming distance and Euclid distance under INSs. Finally, a numerical case study for audience service quality evaluation for large-scale sports-events is employed to validate the proposed technique. The main contributions of this paper are proposed: (1) The INN-EDAS technique based on the Hamming distance and Euclid distance is founded to manage the MAGDM under INSs; (2) The CRITIC technique is employed to obtain the weight information based on the Hamming distance and Euclid distance under INSs; (3) a numerical case study for audience service quality evaluation for large-scale sports-events is employed to validate the proposed technique. [ABSTRACT FROM AUTHOR]

As the rapidly progressing applications of uncertainty theories, the need for modifications to some of their existing mathematical tools or creating new tools to deal correctly with them in various environments is also exposed. Hesitant fuzzy numbers (HFNs), as a particular case of fuzzy numbers, are not an exception to this rule. Considering the necessity of determining the distance between given HFNs in many of their practical applications, this article shows that the existing methods either do not provide correct results or are not able to meet the needs of users. This paper aims to present new methods for distance measures of hesitant fuzzy numbers. To do them, three prevalent distance measures, i.e., the generalized distance measure, the Hamming distance measure, and the Euclidean distance measure, will be optimized into three distinct trinal categories. With the approach of reducing error propagation via reducing some unnecessary mathematical computations, new distance measures on HFNs will be introduced, first. The middle is the modification of the first category, which is more suitable when the given HFNs are equal-distance by the previous formula. Also, as the third category, the weighted form of these distance measures has been proposed, to be used where the real and membership parts of HFNs are not of equal importance. As an application of these, a TOPSIS-based technique for solving multi-attribute group decision-making problems with HFNs has been proposed. A numerical example will be implemented to describe the presented method. Finally, along with the validation of the proposed method, its numerical comparison with some other existing methods will be discussed in detail. [ABSTRACT FROM AUTHOR]

The financial management capability of enterprises, as an important component of their soft power, has a decisive impact on the success or failure of their operations. In the increasingly fierce market competition, enterprises must continuously improve their financial management capabilities in order to ensure efficient operation and achieve better economic benefits. Insufficient financial management capabilities in enterprises can seriously affect the stability of production and operation, hinder the realization of profits, and hinder the long-term development of enterprises. In order to better improve the financial management level of enterprises and promote the standardization of financial management, it is necessary to use scientific techniques to evaluate the financial management ability of enterprises, so as to accurately grasp the key links in the financial management process of enterprises and implement targeted effective measures. The enterprise financial management capability evaluation is a classical multiple attribute group decision making (MAGDM). In recent years, the MAGDM problem has become an important research field in modern decision science. This paper extends the EDAS technique to the 2-tuple linguistic Pythagorean fuzzy sets (2TLPFSs). On the basis of the original EDAS technique, 2-tuple linguistic Pythagorean fuzzy number EDAS (2TLPFN-EDAS) technique based on cosine similarity measure (CSM) and Hamming distances is managed for MAGDM. Finally, a case study for enterprise financial management capability evaluation and some comparative analysis with the other techniques show that the new technique proposed in this paper is effective, reasonable and accurate. The main contribution of the paper is summarized: (1) the 2TLPFN-EDAS technique based on CSM and Hamming distances is managed for MAGDM under 2TLPFSs; (2) The entropy is employed to manage the attribute weight based on cosine similarity measure(CSM) and Hamming distances under 2TLPFSs; (3) the 2TLPFN-EDAS technique is employed for enterprise financial management capability evaluation and were compared with some existing techniques; (4) Through the comparison, it is found that 2TLPFN-EDAS technique for enterprise financial management capability evaluation proposed are effective. [ABSTRACT FROM AUTHOR]

Ceramic art has a long history of development in China and is an important component of the inheritance and development of traditional culture. The highly distinctive ceramic art expression content has been sought after by many international research enthusiasts and applied to product design, highlighting different social backgrounds and special cultural connotations of different eras, while also laying an important theoretical foundation for the inheritance and development of culture. The quality evaluation of ceramic product modeling design could be deemed as a classic multiple attribute group decision making (MAGDM) problem. Recently, the EDAS and CRITIC method has been used to cope with MAGDM issues. Spherical fuzzy sets (SFSs) can excavate the uncertainty and fuzziness in MAGDM more effectively and deeply. In this article, on basis of evaluation based on distance from average solution (EDAS), a novel spherical fuzzy number EDAS (SFN-EDAS) method based on Hamming distance and Euclid distance is built for dealing with MAGDM. Moreover, when the attribute weights are completely unknown, the CRITIC method is extended to SFSs to acquire the attribute weights. Finally, SFN-EDAS method is used for quality evaluation of ceramic product modeling design to prove practicability of the developed method and compare SFN-EDAS method with existing methods to further demonstrate its superiority. [ABSTRACT FROM AUTHOR]

With the proposal of the "Double First Class" construction concept in Chinese universities, cultivating high-quality talents has become the main direction of university education. At present, local universities in China are actively adapting to the changes of the times, taking the construction of the Double First Class as an opportunity, continuously adjusting and deepening the reform of the double innovation and innovation talent cultivation mode, further improving the curriculum system, increasing investment in professional practical teaching, stimulating students' enthusiasm for innovation and entrepreneurship (IAE), and focusing on improving students' comprehensive abilities, achieving significant results in talent cultivation. The "Entrepreneurship and Entrepreneurship" career ability evaluation of local college students could be considered as multiple attribute decision-making (MADM). Recently, the Combined Compromise Solution (CoCoSo) method and information entropy method was employed to deal with MADM. The triangular fuzzy neutrosophic sets (TFNSs) are employed as a better tool for expressing uncertain information during the "Entrepreneurship and Entrepreneurship" career ability evaluation of local college students. In this paper, the triangular fuzzy neutrosophic number CoCoSo (TFNN-CoCoSo) based on the Hamming distance and Euclid distance is constructed to cope with the MADM under TFNSs. The information entropy method is employed to compute the weight values based on the Hamming distance and Euclid distance under TFNSs. Finally, a numerical example of "Entrepreneurship and Entrepreneurship" career ability evaluation of local college students is constructed and some decision comparisons are constructed to verify the TFNN-CoCoSo method. [ABSTRACT FROM AUTHOR]

The energy consumption of mechanical products in China is enormous, and the energy utilization rate is low, which is increasingly receiving people's attention. Conducting product design for energy optimization is of great significance for improving energy utilization efficiency. The scheme design of a product is the key to achieving innovation in product design, and the evaluation and decision-making of the design scheme directly affect the results of the later stage of the design. Therefore, correctly evaluating and making reliable decisions on product design schemes that are oriented towards fuzzy decision optimization is an important aspect of product innovation conceptual design. The product modeling design quality evaluation is a multiple attribute group decision making (MAGDM) problems. Recently, the Combined Compromise Solution (CoCoSo) method and information entropy method has been employed to cope with MAGDM issues. The interval neutrosophic sets (INSs) are employed as a tool for portraying uncertain information during the product modeling design quality evaluation. In this paper, the CoCoSo method is designed for MAGDM under INSs. Then, the interval neutrosophic numbers CoCoSo (INN-CoCoSo) method based on the Hamming distance and Euclidean distance is built for MAGDM. The information Entropy method is employed to produce the weight information based on the Hamming distance and Euclidean distance under INNSs. Finally, a practical numerical example for product modeling design quality evaluation is supplied to show the INN-CoCoSo method. The main contributions of this paper are constructed: (1) This paper builds the novel MAGDM based on CoCoSo model under INSs; (2) The information Entropy method is employed to produce the weight information based on the Hamming distance and Euclidean distance under INNSs; (3) The new MAGDM method is proposed for product modeling design quality evaluation based on INN-CoCoSo. [ABSTRACT FROM AUTHOR]

With the continuous development of China's economic system, the development of the construction industry is becoming more and more rapid, and the number and scale of construction projects are increasing. Due to the characteristics of large projects and long cycles, there are a large number of construction parties involved in construction projects. The increase in the number of participating partners makes it difficult for their projects to be integrated and managed by management departments such as owners, let alone for various parties to collaborate in the construction of projects. In order to effectively solve this problem, the engineering procurement construction (EPC) general contracting model has emerged. The risk assessment of EPC project is classical multiple attributes group decision making (MAGDM). The probabilistic hesitancy fuzzy sets (PHFSs) are used as a tool for characterizing uncertain information during the risk assessment of EPC project. In this paper, the classical grey relational analysis (GRA) method is extended to PHFSs. Firstly, the basic concept, comparative formula and Hamming distance of PHFSs are introduced. Then, the definition of the score values is employed to obtain the attribute weights based on the information entropy. Then, probabilistic hesitancy fuzzy GRA (PHF-GRA) method is built for MAGDM under PHFSs. Finally, a practical case study for risk assessment of EPC project is designed to validate the proposed method and some comparative studies are also designed to verify the applicability. [ABSTRACT FROM AUTHOR]

Radial distribution system is an important link connecting power supply and users, and its power supply reliability is directly related to users. Radial distribution network reconfiguration can transform the network structure by changing the switching state of the distribution network lines, and achieve the goals of reducing network operational losses, improving power quality, and power supply reliability while meeting various constraints such as radial operation, power supply and demand balance, capacity, and voltage. Radial distribution systems have the characteristics of multiple components and complex structures. How to quickly and accurately evaluate the health performance of radial distribution systems and find an optimal solution for network reconfiguration are important issues in distribution network analysis. The network health performance evaluation of radial distribution system is classical multiple attributes group decision making (MAGDM). The probabilistic hesitancy fuzzy sets (PHFSs) are used as a tool for characterizing uncertain information during the network health performance evaluation of radial distribution system. In this paper, we extend the classical grey relational analysis (GRA) method to the probabilistic hesitancy fuzzy MAGDM with unknown weight information. Firstly, the basic concept, comparative formula and Hamming distance of PHFSs are briefly introduced. Then, the definition of the score values is employed to compute the attribute weights based on the information entropy method. Then, probabilistic hesitancy fuzzy GRA (PHF-GRA) method is built for MAGDM under PHFSs. Finally, a practical case study for network health performance evaluation of radial distribution system is designed to validate the proposed method and some comparative studies are also designed to verify the applicability. [ABSTRACT FROM AUTHOR]

Combinative distance-based assessment (CODAS) is a multi-criteria decision-making (MCDM) method that is based on the Euclidean and Hamming distances of alternatives from the average scores of attributes. Spherical fuzzy sets, as the recent extensions of ordinary fuzzy sets, were developed based on Pythagorean and neutrosophic sets and enable decision-makers to express their membership, non-membership, and hesitancy degrees independently and in a larger domain than most other fuzzy extensions. This paper proposes a new interval-valued spherical fuzzy CODAS method and provides extra space for catching the vagueness in the nature of the problem. The feasibility and practicality of the proposed model are illustrated with an application for evaluating the reopening readiness of academic units for campus education in the era of COVID-19. Three decision-makers from a higher education institution evaluate four academic units with respect to five strategic criteria and prioritize them according to their readiness levels for the campus type of education. Sensitivity and comparative analyses, theoretical and practical contributions, limitations, and future research avenues are also presented in the study. [ABSTRACT FROM AUTHOR]

A risky large group decision-making method based on FCM clustering and cloud models is proposed for risky large group decision-making problems with linguistic evaluation scales, unknown attribute weights, and many decision members with unknown weights, considering the psychological behavioral characteristics of decision makers' regret avoidance. The method first uses the golden partition method to improve the cloud model to transform the uncertain linguistic evaluation matrix into a comprehensive cloud model, which quantifies the fuzziness and randomness of linguistic values. The cloud model expectation values are then extracted to determine the attribute weights using the entropy weighting method. Secondly, the three numerical features of the cloud model are extracted as sample features for FCM clustering to obtain the decision maker's preference clustering information, and the initial weights of decision-makers are determined according to the majority principle, which improves the existing studies that simply use the expected value of the cloud model for clustering analysis, ignoring the entropy and super entropy for portraying the ambiguity and randomness. On this basis, the Hamming distance is introduced to calculate the closeness to adjust the initial weights of decision-makers, improving the way that the weights of aggregation members are equally distributed in previous studies. Finally, considering the influence of the decision maker's psychological behavior on decision information in the risky decision-making process, regret theory is introduced to construct a decision maker's perceived utility matrix, which is combined with the decision maker's weights to determine and rank the combined perceived utility. Through comparison with existing methods, it is found that the proposed method of recalibration of decision-maker preference clustering, while considering the psychological behavior of decision-maker regret avoidance, not only solves the situation of large group decision making in which expert information is easily distorted but also satisfies the convenience of the calculation process and is more suitable for the situation where there are many decision-makers and their preferences are complicated. [ABSTRACT FROM AUTHOR]

In this paper, considering the traditional geometric operation laws and Pythagorean fuzzy information, a varies of new distance measures of Pythagorean fuzzy set are proposed, such as generalized Pythagorean fuzzy ordered geometric distance (GPFOWGD) measures and generalized Pythagorean fuzzy hybrid weighted geometric distance (GPFHWGD) measures. Besides, some special issues including Hamming distance, Euclidean distance and Hausdorff distance of these raised geometric distance measures are investigated. To testify the valid of these new presented distance measures, a decision-making model is built and illustrated by a mathematical calculation example to evaluate the service quality of sports clubs using Pythagorean fuzzy information. The results display that the approach is uncomplicated, valid and simple to compute. The example illustrates that the method presented in the paper can be used to deal with problems of uncertainty such as dynamic multiple attribute decision making. [ABSTRACT FROM AUTHOR]

This study proposes a two-sided matching decision-making (TSMDM) approach by combining the regret theory under the intuitionistic fuzzy environment. At first, according to the Hamming distance of intuitionistic fuzzy sets and regret theory, superior and inferior flows are defined to describe the comparative preference of subjects. Hereafter, the satisfaction degrees are obtained by integrating the superior and inferior flows of the subjects. The comprehensive satisfaction degrees are calculated by aggregating the satisfaction degrees, based on which, a multi-objective TSMDM model is built. Furthermore, the multi-objective TSMDM model is converted to a single-objective model, the optimal solution of the latter is derived. Finally, an illustrative example and several analyses are provided to verify the feasibility and the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

With the aggravation of market competition, strategic supplier is becoming more and more critical for the success of manufacturing enterprises. Suppler selection, being the critical and foremost activity must ensure that selected suppliers are capable of supporting the long-term development of organizations. Hence, strategic supplier selection must be restructures considering the long-term relationships and prospects for sustainable cooperation. This paper proposes a novel multi-stage multi-attribute group decision making method under an interval-valued q-rung orthopair fuzzy linguistic set (IVq-ROFLS) environment considering the decision makers' (DMs) psychological state in the group decision-making process. First, the initial comprehensive fuzzy evaluations of DMs are represented as IVq-ROFLS. Subsequently, two new operators are proposed for aggregating different stages and DMs' preferences respectively by extending generalized weighted averaging (GWA) to IVq-ROFLS context. Later, a new hamming distance based linear programming method based on entropy measure and score function is introduced to evaluate the unknown criteria weights. Additionally, the Euclidean distance is employed to compute the gain and loss matrix, and objects are prioritized by extending the popular Prospect theory (PT) method to the IVq-ROFLS context. Finally, the practical use of the proposed decision framework is validated by using a strategic supplier selection problem, as well as the effectiveness and applicability of the framework are discussed by using comparative analysis with other methods. [ABSTRACT FROM AUTHOR]

Quality function deployment (QFD) is an useful tool to solve Multi-criteria decision making, which can translate customer requirements (CRs) into the technical attributes (TAs) of a product and helps maintain a correct focus on true requirements and minimizes misinterpreting customer needs. In applying quality function deployment, rating technical attributes from input variables is a crucial step in fuzzy environments. In this paper, a new approach is developed, which rates technical attributes by objective penalty function and fuzzy technique for order preference by similarity to an ideal solution (TOPSIS) based on weighted Hamming distance under the case of uncertain preference characteristics of decision makers in fuzzy quality function deployment. A pair of nonlinear programming models with constraints and a relevant pair of nonlinear programming models with unconstraints called objective penalty function models are proposed to gain the fuzzy important numbers of technical attributes. Then, this paper compares the fuzzy numbers by fuzzy technique for order preference by similarity to an ideal solution (TOPSIS) method based on weighted Hamming distance in consideration of the uncertain preference characteristics of decision makers. To end with, the developed method is examined with the numerical examples. [ABSTRACT FROM AUTHOR]

Selecting an appropriate robot among the alternative robots is a difficult problem for decision makers, since it is complicated to express attributes as crisp numbers in multiple attribute decision making problems. Generalized trapezoidal hesitant fuzzy numbers(GTHF-numbers) can be efficiently used to estimate information in the decision making process. This paper proposes an advanced type of TOPSIS (Technique for order preference by similarity to ideal solution) method, called TOPSIS method of GTHF-numbers. To do this, we introduce some novel distance measures including Hamming distance measure, Euclidean distance measure, λ-generalized distance measure, λ-generalized Hausdorff distance measure, γ-hybrid Hamming distance, hybrid Euclidean distance and λ-generalized hybrid distance measure on GTHF-numbers. Then, we develop a novel TOPSIS method of GTHF-numbers based on introduced distance measures. Finally, we provide a real example, for an auto company which desires to select a suitable robot for its production process, based on the proposed TOPSIS method of GTHF-numbers to prove the efficiency and the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

A Pythagorean fuzzy soft set is a parameterized family of Pythagorean fuzzy sets and a generalization of intuitionistic fuzzy soft sets. In this paper, the notions of entropy and distance measures are defined for the Pythagorean fuzzy soft sets (PFSSs). Since, the already existing techniques for finding entropy and distance measures are not working for PFSSs, it is necessary to introduce these techniques in the contest of PFSSs. This work proposes a characterization of the Pythagorean fuzzy soft entropy. Also, the expressions for the standard distance measures like Hamming distance and Euclidean distance are obtained. Further, the applications of PFSSs in decision making problem and pattern recognition problem are discussed. Finally, comparative studies with other existing equations are also carried out. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the picture fuzzy multiple attribute decision making problems where the information about attribute weights is partly known or completely unknown. We introduce some notions, such as picture fuzzy ideal point, the normalized Hamming distance of picture fuzzy numbers. We also introduce the grey relational coefficient between the attribute value vectors of each alternative and the picture fuzzy ideal point. Then we establish the grey relational analysis models to measure the grey relational degree between each alternative and the picture fuzzy ideal point. Based on the grey relational analysis models, we can rank the given alternatives and then select the most desirable one. Finally, we illustrate the developed grey relational analysis models with a numerical example for potential evaluation of emerging technology commercialization. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Hamming distance, the Hausdorff distance with Pythagorean fuzzy sets (PFSs) to define the generalized Pythagorean fuzzy normalized Hamming distance, the generalized Pythagorean fuzzy normalized Hausdorff distance and the generalized hybrid Pythagorean fuzzy normalized distance. According to the relation between distance and similarity measure, we can obtain similarity measure. Furthermore, we study the Pythagorean fuzzy weighted distance and similarity measures. On the basis of the set-theoretic approach, the matching function, the notion of complement and the continuous functions, we extend other similarity measures. In the end, we utilize an applicable example to prove the proposed methods. [ABSTRACT FROM AUTHOR]

The multiple attribute decision making (MADM) with interval grey uncertain linguistic (IGUL) is a topic of current interest, and various methods have been developed. However, few approaches taking the behavioral characteristics of the decision maker into account. In this paper, an extension of TODIM (i.e., an acronym in Portuguese of interactive and multiple attribute decision making) method, in which three behavioral characteristics of the decision maker (i.e., risk aversion, reference dependence and loss aversion) are considered, is proposed. First, the δ-Hamming distance is defined to deal with the interval grey uncertain linguistic variables by considering the level of the decision maker's risk aversion, and its distinguish ability is validated by compared to the classical Hamming distance. Then, the details of the TODIM· SIR method is demonstrated: (i) considering the reference dependence behaviour of the decision maker, the positive-ideal alternative (i.e., PIA) and the negative-ideal alternative (i.e., NIA) are defined, and the gain and loss degrees of each alternative relative to NIA and PIA are computed based on the δ-Hamming distance; (ii) taking the loss aversion behaviour of the decision maker into account, the perceived dominance degree of the decision maker for the gain and the loss is calculated; (iii) according to the idea of the Superiority and Inferiority Ranking method (i.e., SIR, an outranking method), the Gain-flow and the Loss-flow are defined, and the partial ranking orders and the complete ranking order are obtained. Finally, two numerical examples are given to illustrate the robustness and validity of the method, and a comparative analysis is also conducted to compare the TODIM· SIR method with both the classical TODIM method and the classical SIR method. [ABSTRACT FROM AUTHOR]

Neutrosphic sets define the uncertainty with three parameters, namely truthiness, indeterminacy and falsity. COmbinative Distance-based ASsessment (CODAS) method computes the Euclidean as the primary measure and Hamming distances as the secondary measure to assess alternatives based on predetermined criteria. In this paper, CODAS method is extended to its interval-valued neutrosophic CODAS version for handling the vagueness and impreciseness in human thoughts. A fuzzy inference system can be used as a decision making process of mapping from a given input to an output using fuzzy logic. The inputs of the used ordinary fuzzy Mamdani type inference system are crisp while the rules are fuzzy. The applicability of the proposed methodology is illustrated through the assessment of livability index of urban districts. Sensitivity analysis demonstrates the robustness of the decision-making methodology. [ABSTRACT FROM AUTHOR]

In the study of intuitionistic fuzzy clustering, the construction of an intuitionistic fuzzy similarity matrix (IFSM) is a fundamental and important issue in the direct clustering analysis, since it determines clustering results and computational efforts. Many methods based on the axioms of intuitionistic fuzzy similarity relations are applicable to IFSM construction. However, most of existing methods may yield a "counterintuitive result" in some cases and consume much computational time. In this paper, we propose a novel intuitionistic fuzzy clustering method to deal with such problems. First, based on the normalized Hamming distance, we define a similarity measure between intuitionistic fuzzy numbers (IFNs), by which a similarity measure between intuitionistic fuzzy sets (IFSs) is induced. Second, a divergence measure between IFSs is obtained by extending the dissimilarity of IFNs. Third, we construct an IFSM by using together the similarity and divergence measures so as to cluster the intuitionistic fuzzy information. Finally, two examples are presented to show the effectiveness and advantages of our method. [ABSTRACT FROM AUTHOR]

Intuitionistic Fuzzy Sets (IFSs) have extensively been employed in multi-criteria decision making (MCDM). COmbinative Distance-based Assessment (CODAS) method, which is relatively a new MCDM technique, aims to select the alternative having the largest Euclidean and Taxicab (Hamming) distances to the negative- ideal point. This paper develops an intuitionistic fuzzy CODAS method, namely Interval-Valued Intuitionistic Fuzzy CODAS (IVIF-CODAS), and introduces it to the literature first time. The objective of our paper is to make a multi-criteria decision under intuitionistic fuzzy uncertainty by taking the hesitancy of decision makers into consideration based on both Euclidean and Taxicab distances according to the negative-ideal point. To show the effectiveness of the developed method, an application is given for wave energy facility location selection in Turkey and the obtained results are compared with crisp CODAS method's. [ABSTRACT FROM AUTHOR]

As a foundation to study the similarity measure with applications in pattern recognition, (normalized) Hamming distances and (normalized) Euclidean distances between hyper structures based on two and three parameters are established. An example to show that these distances are not metrics in general is provided, and conditions for these distances to be metrics are considered. The notions of length fuzzy ideals with four types are introduced, and related properties and their relations are investigated. Relations between length fuzzy ideals and length fuzzy subalgebras are investigated. Conditions for a length fuzzy subalgebra to be a length fuzzy ideal are provided. Characterizations of a length fuzzy ideal are considered. [ABSTRACT FROM AUTHOR]

In this paper, a new version of distance measure for hesitant fuzzy linguistic term sets is developed. The new version of distance measure provides an objective way to handle the diverse dimensions of two HFLTSs, i.e., without shortening the HFLTS to be a linguistic interval or extending the shorter one by adding linguistic terms. The Hamming distance, the Euclidean distance and the corresponding forms are put forward. By the relationship between the distance measure and the similarity measure, some parallel similarity measures are also investigated. As applications of the proposed measures, the issues of pattern recognition, clustering analysis and multi-criteria decision making are considered. [ABSTRACT FROM AUTHOR]

In this paper, with respect to multiple criteria group decision making (MCGDM) problems in which criteria values are expressed by Pythagorean fuzzy uncertain linguistic variables (PFULVs), we propose an extended TODIM method. Firstly, we define the Pythagorean fuzzy uncertain linguistic set, and propose the operational laws, Hamming distance, score function and accuracy function of PFULVs. Then an extended TODIM method is presented to solve the MCGDM problems under the Pythagorean fuzzy uncertain linguistic environment, and a numerical example with the Pythagorean fuzzy uncertain linguistic information is given to show the effectiveness of the proposed method. Further, we analyze the influence of the different parameter on the MCGDM, and test the practicality of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of triangular cubic fuzzy numbers. We discuss some basic operational laws of triangular cubic fuzzy numbers and then develop triangular cubic fuzzy weighted average (TCFWA) operator. We also define crisp weighted possibility means of TCFNs and hamming distance between TCFNs. Furthermore, we extend the classical VIKOR method to solve the MCDM method based on triangular cubic fuzzy numbers. The new ranking method for TCFNs is used to rank the alternatives. Finally, an illustrative example is given to verify and demonstrate the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

An extension of TOPSIS, a multi-criteria dual hesitant fuzzy decision making technique, to a group decision environment is investigated, where the importance of combinations or their ordered positions is not only globally considered, but also overall focus on the correlations among combinations or their ordered positions. Firstly, to get a broad view of the techniques used, some operational laws on dual hesitant fuzzy numbers are introduced. Based on these operational laws, motivated by the ideas of Choquet integral and Shapley index, two dual hesitant fuzzy aggregation operators called the Shapley dual hesitant fuzzy Choquet averaging operator (SDHFCA) and Shapley dual hesitant fuzzy Choquet geometric operator (SDHFCG) are proposed. Then, some desirable properties of the two operators are discussed, such as idempotency, monotonicity, boundary and commutativity. Secondly, the Shapley Choquet integral-based Hamming distance between any dual hesitant fuzzy numbers is defined. Combining the SDHFCA operator and the SDHFCG operator with Shapley Choquet integral-based Hamming distance, an extension of TOPSIS method is developed to deal with a multi-criteria dual hesitant fuzzy group decision making problems. Finally, a green chain supplier selection example is used to illustrate the developed procedures. [ABSTRACT FROM AUTHOR]

This paper applies the interval neutrosophic set theory to express fuzzy formal concept. A new interval neutrosophic fuzzy concept lattice is proposed. Furthermore, interval-distance and interval-similarity measure are discussed. We can find some interval neutrosophic fuzzy concepts to meet particular similarity range given by users. The result of this paper may enhance the flexibility of extracting knowledge and expand the capacity of knowledge. [ABSTRACT FROM AUTHOR]

Neutrosophic hesitant fuzzy set (NHFS) is an extension of neutrosophic set and the hesitant fuzzy set, which can easily express the uncertain, incomplete and inconsistent information, and the VIKOR (from Serbian: VIseKriterijumska Optimizacija I Kompromisno Resenje) method is an effective decision making tool which can select the optimal alternative by the maximizing "group utility" and minimizing "individual regret" with cognitive computation. In this paper, we firstly introduced some operational laws, comparison rules and the Hamming distance measure of neutrosophic hesitant fuzzy set, and described the traditional VIKOR method which only processes the crisp numbers. Then we extended the VIKOR method to process the Neutrosophic hesitant fuzzy information (NHFI), and proposed an extended VIKOR method for the multiple criteria decision making (MCDM) problems with NHFI, and an illustrative example shows the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The cloud model, which mainly reflects the uncertainty in the real life and the concepts in human knowledge: fuzziness and randomness. Actually, many practical problems occur in uncertain environments, especially in the situations where the information about all the criteria weights, criteria values and expert weights are uncertain linguistic variables called uncertain pure linguistic problems. For this purpose, In this paper, we present an approach to multi-criteria group decisionmaking with uncertain pure linguistic information based on the cloud model. To do so, firstly, the uncertain linguistic values are converted into integrated cloud and interval integrated cloud, respectively, and the cloud decision-making information are converted into generating floating cloud and generating floating interval cloud by the cloud operational laws. Secondly, by means of the Hamming distance and closeness degree, the ranking of all alternatives is determined. Finally, a numerical example and comparative analysis with related decision-making methods are provided to illustrate the practicality and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new method for intuitionistic fuzzy decision making problems with induced aggregation operators and distance measures. Firstly, we introduce the intuitionistic fuzzy induced ordered weighted averaging distance (IFIOWAD) operator. It is an extension of the ordered weighted averaging (OWA) operator that uses the main characteristics of the induced OWA (IOWA), the distance measures and uncertain information represented by intuitionistic fuzzy numbers. The main advantage of this operator is that it is able to consider complex attitudinal characters of the decision-maker by using order-inducing variables in the aggregation of the distance measures. We further generalize the IFIOWAD by using weighted average. The result is the intuitionistic fuzzy induced ordered weighted averaging weighted average distance (IFIOWAWAD) operator. Finally, a practical example about the selection of investments is provided to illustrate the developed intuitionistic fuzzy aggregation operators. [ABSTRACT FROM AUTHOR]

Uncertainty measures can supply new points of view for analyzing data and help us to disclose the substantive characteristics of data sets. Accuracy and roughness proposed by Pawlak are mainly two important measures to deal with uncertainty information in rough set theory. However, these measures are constructed by set operations, which bring about poor efficiency. In this paper, we proposed a binary granule representation by a conversion from a set to a binary granule. Correspondingly, set operations are converted to binary granule computing. Besides, we investigate how to understand measures from rough set framework in the viewpoint of binary granule representation by introducing Hamming distance between granules. Moreover, a concept of granule swarm distance is defined for measuring uncertainty between two granule swarms, which provides a more comprehensible perspective for measures in rough set theory. Theoretical analysis shows that the binary granule representation is valuable to understand rough set measures. [ABSTRACT FROM AUTHOR]

Molodtsov [35] initiated the soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. Maji [30] defined the concept of neutrosophic soft set which is based on a combination of the neutrosophic set and soft set models. In this paper, we give the notion of neutrosophic soft set with a new style and present some algebraic properties. We define several distance measures between neutrosophic soft sets and give an axiomatic definition of neutrosophic entropy for a neutrosophic soft set. To find the most ideal alternatives from all possible alternatives, we propose a method based on similarity measure. Thus we can rank all possible alternatives. Finally, the proposed similarity measure is applied to a multicriteria decision making problem. [ABSTRACT FROM AUTHOR]

As generalize of the hesitant fuzzy sets, hesitant interval-valued fuzzy sets (HIVFSs), which permits the memberships of an element to a given set having a few different interval values in [0,1] rather than real numbers, can be considered as a powerful tool to express uncertain information in the human decision making process. Based on the traditional Hamming distance, Euclidean distance, Hausdorff distance, and generalized distance, in this paper, we propose a variety of distance measures for hesitant interval-valued fuzzy sets, based on which the corresponding similarity measures can be obtained. We investigate the connections of the aforementioned distance measures and further develop a number of hesitant interval-valued ordered weighted distance measures and hesitant interval-valued ordered weighted similarity measures. They can alleviate the influence of unduly large (or small) deviations on the aggregation results by assigning them low (or high) weights. Finally, we shall present a numerical example to show potential evaluation of emerging technology commercialization with hesitant interval-valued fuzzy information in order to illustrate the method proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new fuzzy decision making technique called the fuzzy induced heavy ordered weighted averaging distance (FIHOWAD) operator. It is an extension of the ordered weighted averaging (OWA) operator that uses the main characteristics of the induced OWA (IOWA), the Hamming distance, the heavy OWA (HOWA) and uncertain information represented as fuzzy numbers. A key feature of the FIHOWAD operator is that it generalizes a wide range of aggregation operators such as the fuzzy minimum distance, the fuzzy weighted Hamming distance (FWHD), the fuzzy OWA distance (FOWAD), the fuzzy IOWA distance (FIOWAD) and the fuzzy heavy OWA distance (FHOWAD) operators. We studied some of its main properties and different particular cases. Finally, we present a numerical example to illustrate the new approach in a financial decision making problem. [ABSTRACT FROM AUTHOR]

An interval neutrosophic set is an instance of a neutrosophic set, which can be used in real scientific and engineering applications. In the paper, the Hamming and Euclidean distances between interval neutrosophic sets (INSs) are defined and the similarity measures between INSs are proposed based on the relationship between similarity measures and distances. In the applications of the similarity measures, a multicriteria decision-making method is established in interval neutrosophic setting, in which criterion values with respect to alternatives are evaluated by the form of interval neutrosophic values (INVs) and the criterion weights are known information. We utilize the similarity measures between each alternative and the ideal alternative to rank the alternatives and to determine the best one. Finally, an illustrative example demonstrates the applications of the proposed decision-making method. [ABSTRACT FROM AUTHOR]