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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]

Quality control is paramount in product manufacturing as it ensures consistent production to meet customer expectations, regulatory requirements and maintain a company's reputation and profitability. Distance measures within fuzzy sets serve as powerful tools for quality control, allowing for data comparison and identification of potential defects or outliers within a system. This study aims to develop a hybrid concept by combining a Cubic Intuitionistic Fuzzy Set (CIFS) with Soft Set (SS) and extending it to Cubic Intuitionistic Fuzzy Hypersoft Set (CIFHSS). CIFHSS enables handling multiple distinct attributes at the sub-attribute level within a cubic set environment. The concept includes operations like internal, partial internal, external, complement, direct sum, and product. Additionally, six distance metrics are defined within CIFHSS and applied to establish a quality control management system for industrial applications. The versatility of CIFHSS in quality control management stems from its ability to capture and model uncertainty, vagueness, and imprecision in data. This makes it an effective tool for decision-making, risk analysis, and process optimization across a wide range of industrial applications. [ABSTRACT FROM AUTHOR]

Interior decoration design can refine its functions, improve environmental quality, improve spatial form, and is closely related to buildings, structures, equipment, etc. The quality of interior decoration design directly affects a series of issues such as safety, quality, cost savings, environmental protection, and aesthetic practicality of the project, and the quality inspection of interior decoration design can control the safety, quality, cost savings, environmental protection, and aesthetic practicality of the interior decoration project in advance, reducing the occurrence of safety and quality accidents during construction and use, And it plays a proactive role in cost saving and environmental protection of decoration projects, and can also provide reasonable suggestions in terms of aesthetics, practicality, etc., so as to make indoor decoration projects safer and more perfect. The quality evaluation of interior decoration design is a classical multiple attribute group decision making (MAGDM) problem. This paper extends the EDAS method to the 2-tuple linguistic Pythagorean fuzzy sets (2TLPFSs). On the basis of the original EDAS method, 2-tuple linguistic Pythagorean fuzzy EDAS (2TLPF-EDAS) method based on the Hamming distance and Euclid distance is built for MAGDM. The information entropy method is used to obtain the weight information based on the score function and accuracy function under 2TLPFSs. Finally, a case study for quality evaluation of interior decoration design show that the new method proposed in this paper is reasonable. [ABSTRACT FROM AUTHOR]

We introduce and investigate neutrosophic soft contra e-continuous maps and contra e-irresolute maps in neutrosophic soft topological spaces with examples. Also, neutrosophic soft contra econtinuous maps are compared with neutrosophic soft continuous maps, d-continuous maps, d-semi continuous maps, d-pre continuous maps and e* continuous maps in neutrosophic soft topological spaces. We derive some useful results and properties related to them. An application in decision making problem using distance measure is given. An example of a candidate selection from a company interview is formulated as neutrosophic soft model problem and the hamming distance measure is applied to calculate the distance between the interview candidates and the ideal candidate. The candidate having less distance with the ideal solution is the desirable candidate. [ABSTRACT FROM AUTHOR]

We introduce a new class of sets called the generalized fuzzy sets as a generalization of fuzzy, intuitionistic fuzzy and the Pythagorean fuzzy sets. Together with their basic and important properties, we define the relations and distances on them. We demonstrate their importance by making their comparisons with other fuzzy sets available in the literature. We implement the idea of these sets on the examples in the fields of purchase satisfaction, personnel posting and disease diagnosis. By the comparison of their results with the results available in the literature, we suggest that this new category of sets is a more summarized form of all the fuzzy sets presented up to date, and has a wider scope of applications as compared to other fuzzy sets. The generalized fuzzy sets will entertain more applications than other sets. [ABSTRACT FROM AUTHOR]

In this article, we discuss a few fresh approaches to the spherical vague normal set (SVNS) approach to multiple attribute decision‐making (MADM) problems. A new generalization of the vague set (VS) and the spherical interval valued fuzzy set (SIVFS) is the spherical vague set (SVS). The spherical vague number (SVN) concepts consolidate normal fuzzy number (NFN) and we defined the spherical vague normal number (SVNN) and some of its intriguing fundamental operations. The purpose of this article is to discuss a novel idea of spherical vague normal weighted averaging (SVNWA), spherical vague normal weighted geometric (SVNWG), generalized spherical vague normal weighted averaging (GSVNWA) and generalized spherical vague normal weighted geometric (GSVNWG) operators. We talked about a flowchart with an algorithm that uses this operators and the MADM approach. With the help of a numerical example, we interact the extended euclidean and hamming distance measures. In this communication, it is also important to elaborate on some key SVN approach characteristics based on various algebraic operations, such as idempotency, boundedness, commutativity, and monotonicity. They are quicker to find the best option, more straightforward and practical. Think about five farmers. The four factors that are taken into account for each of the five farmers are climate, water, soil, disease, and flood, and their corresponding weights are displayed. We want to select the best option from a large number of choices by comparing expert assessments with the criteria. As a result, the conclusions of the defined models are more precise and closely related to Θ. We contrast some of the current models with the ones that have been proposed in order to demonstrate the dependability and utility of the models under investigation. The study's findings are also intriguing and fascinating. [ABSTRACT FROM AUTHOR]

Everything in the world almost resembles each other which could find out with the help of some measures. Similarity measure (SM) is one of them that play a dominant role in decision-making (D M g ). The higher the value of the SM, the more the things will match perfectly. Weights of criteria appear to specify that the decision-makers (DMs) recognize the significance of public views and their influence on reaching an ideal solution. Sometimes DMs hesitate or they are uncertain to assign the weights to the criteria because of their similar nature. Linear programming (LP) technique has been implemented to evaluate the weights of criteria to reduce the complexity of DMs so that they can avoid biasedness. An extension of fuzzy sets (FSs) named dual hesitant fuzzy sets (DHFSs) is utilized to handle ambiguous and uncertain information. Based on the Hausdorff metric and the Hamming distance, SM is developed to establish the multiple criteria decision-making (MCDM) approach to resolve the problems. Moreover, based on the proposed SM, the technique for order of preference similar to the ideal solution (TOPSIS) is extended to strengthen the obtained outcomes. The effectiveness of the suggested approach is validated by considering a practical example. To support the outcomes obtained by using the proposed model, sensitivity analysis (SA) and time complexity (TC) analysis have been performed. A comprehensive comparison with other techniques is performed to validate the proposed MCDM model. [ABSTRACT FROM AUTHOR]

Failure mode and effect analysis (FMEA), a multidisciplinary reliability analysis tool based on team evaluations, has been widely used in various industries. There are three critical issues in FMEA: the conversion of linguistic evaluations, the weights of risk factors, and the ranking mechanism of failure modes. Scholars have used various fuzzy theories and multi‐attribute decision‐making (MADM) methods to improve traditional FMEA, but there are still deficiencies. In this paper, the hesitant intuitionistic fuzzy set (HIFS), a concept that combines the intuitionistic fuzzy set (IFS) and the hesitant fuzzy set (HFS), is introduced into FMEA to convert linguistic evaluations. Some operators based on HIFS are proposed to process the converted data. Among them, a hesitant intuitionistic fuzzy comprehensive weighted Hamming distance (HIFCWHD) operator is proposed to compute the ordered comprehensive weight, effectively weakening the effect of extreme scores on results. The gray relational projection (GRP) method is adopted to determine the risk priority order of the failure modes. Finally, we give an illustrative case to demonstrate the effectiveness of the proposed FMEA method. [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]

In this paper, we present novel approaches to multi-attribute decision-making problems using q -rung normal fuzzy numbers. The q -rung normal fuzzy sets are an important way to express uncertain information, and they are superior to the intuitionistic fuzzy sets, Pythagorean fuzzy sets and normal Pythagorean fuzzy sets. A combination of the q -rung fuzzy number and the normal fuzzy number becomes q -rung normal fuzzy numbers. The new averaging and geometric operations of q -rung normal fuzzy numbers are studied using the general aggregation function. There are both commutative, associative, idempotent and boundedness compatible using q -rung normal fuzzy numbers. There are four new aggregating operators presented such as q -rung normal fuzzy interaction weighted averaging, q -rung normal fuzzy interaction weighted geometric, q -rung generalized normal fuzzy interaction weighted averaging and q -rung generalized normal fuzzy interaction weighted geometric. Usually, the aggregation functions are taken to be the Euclidean distance and Hamming distance. The existence of these operators enables the development of algorithms that solve multi-attribute decision-making problems. We demonstrate the application of enhanced Euclidean and Hamming distances to problems arising in real-world situations. An important component of a robot sensor is computer science and machine tool technology. There are four factors that can be used to evaluate robotics systems: resolution, sensitivity, error and accuracy. In order to determine the best alternative, expert opinions should be compared to the criteria. The accuracy of these models is better and they are closer to q. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods. [ABSTRACT FROM AUTHOR]

• A CODAS-based group decision model is designed for the T-spherical fuzzy context. • A T-spherical fuzzy Minkowski distance operator based on Heronian mean is proposed. • A novel ordered weighted Heronian Minkowski distance (TSFOWHMD) operator is advanced. • The TSFOWHMD operator is utilized to improve the CODAS method. • The applicability of the developed methodology is verified through a case study. T-spherical fuzzy sets (TSFSs) are more flexible and efficient tools to deal with ambiguous, uncertain and vague information in complex real-world decision-making problems than various extended intuitionistic fuzzy sets. This paper aims to develop a novel T-spherical fuzzy (TSF) Combinative Distance-Based ASsessment (CODAS) based on the Heronian Minkowski distance aggregation operator, this new method can capture interrelationship between input arguments. Some TSF weighted Heronian Minkowski distance (TSFWHMD) aggregation operators with generalization are developed based on Heronian mean and Minkowski-type distance, their properties are discussed as well as their families are analyzed. Furthermore, the TSF MAGDM methodology based on the improved CODAS is designed, where the Minkowski-type distance is used to define the TSF similarity for computing the expert weights and to construct the maximizing deviation method (MDM) for determining the attribute weights, respectively. The TSF ordered weighted Heronian Hamming distance (TSFOWHHD) and TSF ordered weighted Heronian Euclidean distance (TSFOWHED) operators derived from the TSFOWHMD operator are integrated into the CODAS method, which is an improved method for both measuring the deviation of the negative ideal solution from each alternative and capturing the correlation between attributes. Finally, the feasibility and practicality of developed methodology are illustrated with an example of CAE (Computer Aided Engineering) software selection for lithium-ion power battery (LiPB) design, sensitivity analysis and method comparisons are performed to elucidate the reliability and validity of the developed methodology. [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]

Generalized hesitant fuzzy numbers (GHFNs) are able to directly manage situations in which we may encounter a finite set of known values with a finite set of degrees of doubt as quantitative approximations of an uncertain situation/quantification of a linguistic expression. They are new extensions of hesitant fuzzy sets, which have been considered in this paper. In fact, in this paper, GHFNs will be utilized to model the uncertainty of the assessment values of options against criteria in multi-attribute decision making (MADM) problems. It means that all of the elements of decision matrix are GHFNs. Then, the technique for order of preference by similarity to ideal solution (TOPSIS) method, as a very successful method in solving MADM problems, will be updated to be used with GHFNs. To this end, the distance between GHFNs must be defined to obtain the distances between given alternatives from each of two subjective alternatives (positive/negative ideal solutions). Thus, three existing famous distance measures, i.e., general distance ( d g ), Hamming distance ( d h ), and Euclidean distance ( d e ) measures, have been updated for GHFNs firstly. Then, the new TOPSIS method will be proposed based on GHFNs. Finally, the numerical examples have been appointed to illustrate the proposed method, analyze comparatively and validate it. [ABSTRACT FROM AUTHOR]

In this paper, various E-learning Apps have been compared and analysed by two distance measures and formulate their comparison with limited number of students and factors with the scope of their extension. Hamming Distance and Euclidean Distance are two distance measures used in this paper. Moreover, the variables considered for this purpose follows the Intuitionistic Fuzzy Set (IFS) theory. [ABSTRACT FROM AUTHOR]

Fuzzy parameterized fuzzy soft matrices (fpfs-matrices) which can model problems involving fuzzy objects and parameters are one of the mathematical tools used to deal with decision-making problems. To utilize soft decision-making methods via fpfs-matrices in machine learning is likely to draw much scholarly attention. In this paper, we propose Comparison Matrix-Based Fuzzy Parameterized Fuzzy Soft Classifier (FPFS-CMC) in order to transfer modeling success of fpfs-matrices to machine learning. We then compare FPFS-CMC with Fuzzy Soft Set Classifier (FSSC), FussCyier, Fuzzy Soft Set Classification Using Hamming Distance (HDFSSC), and Fuzzy k-Nearest Neighbor (Fuzzy kNN) in consideration of accuracy, precision, recall, macro-F-score, and micro-F-score performance metrics, and 15 datasets in UCI Machine Learning Repository. Besides, we compare the proposed classifier with the state-of-the-art Support Vector Machine (SVM), Decision Tree (DT), and Adaptive Boosting (AdaBoost) in terms of five performance metrics herein. Afterward, the results from the experiments are analyzed by employing the Friedman and Nemenyi tests to assess the statistical significance of the differences in performances. Both experimental and statistical results show that FPFS-CMC outperforms the others. Finally, we provide the conclusive remarks and some suggestions for further research. [ABSTRACT FROM AUTHOR]

Game theory is a powerful tool in modeling actual decision-making problems. In many cases, it is difficult for players to give a crisp value of payoff. To conquer this issue, various extensions of fuzzy sets have been introduced to represent the payoffs. Although type-2 intuitionistic fuzzy (T2IF) set (T2IFS) can solve the game problem effectively, sometimes players prefer to give the primary (secondary) membership and non-membership degrees with some approximate ranges rather than crisp values. T2IFS cannot express such uncertain payoffs. Thus, this paper initiates a new concept called type-2 interval-valued intuitionistic fuzzy (T2IVIF) set (T2IVIFS) which has stronger ability than T2IFS and interval-valued intuitionistic fuzzy set (IVIFS) in representing uncertain information. Hamacher operations of T2IVIFSs are given. Hamming and Euclidean distances between T2IVIFSs are defined respectively. Some Hamacher aggregation operators for T2IVIFSs are developed and some desirable properties are analyzed. Afterwards, an effective method is proposed for solving T2IVIF matrix game, which can make game results more accurate and reliable. An example of new energy vehicle industry development is provided to validate the proposed T2IVIF matrix game. Comparative analyses reveal that the matrix game in T2IVIF environment has better flexibility and reliability than that in T2IF and IVIF environments. [ABSTRACT FROM AUTHOR]

Atanassov's intuitionistic fuzzy sets play a vital role in handling vagueness and uncertainty successfully as they associate an additional non-membership degree to each element of the universal set. Interval-valued intuitionistic fuzzy (IVIF) sets are more generalized quantities in this direction as they use intervals (⊂ [ 0 , 1 ]) to define the membership and non-membership grades of each element of the set. However, without defining basic arithmetic operations on the IVIF values/sets, the study is incomplete. This paper broadly examines the division and subtraction operations over any arbitrary IVIF values/sets using the concept of Hamming distance between them. A deterministic linear optimization model is proposed and solved in order to obtain the complete expressions for these operations. Next, various fundamental properties and relationships are examined and proved for the proposed arithmetic operations over IVIF values/sets. Furthermore, an example of a multi-criteria decision-making problem under uncertain conditions is studied and analyzed using the developed arithmetic operations on IVIF numbers. • Derived the generalized subtraction and division operations for IVIF values/sets. • The notion of Hamming distance and dual-simplex algorithm are used. • A deterministic LPP is proposed to obtain the expressions for the operations. • The fundamental properties and relationships for the basic operations are explored. • A case study of multi-criteria decision-making problems has been discussed. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy (IF) theory has become main approach to representing imprecision and vagueness. The IF divergence measure (IFDivM) based on Jensen–Shannon divergence is perhaps the most widely used measure to compare the similarity of multiple intuitionistic fuzzy sets (IFSs). In the present paper, this IFDivM is examined and applied to multiple examples. It is found that some extant IFDivMs hardly satisfy the axiomatic definition, and in a few cases even unable to show divergence of trivial IFSs. To address these inconsistencies, a new IFDivM based on Jensen–Shannon divergence is proposed, free from these problems. The effectiveness of the proposed IFDivM is tested on several critical cases, and precise analysis of its properties is performed. It is proved that the proposed IFDivM satisfies the axiomatic definition of IFDivMs. To illustrate the practical significance of the IFDivM, a novel intuitionistic fuzzy (IF) TODIM method, based on the proposed IFDivM, is developed, termed as GIF-TODIM method. Unlike the existing IF-TODIM methods, GIF-TODIM does not suffer from the revere ordering inconsistencies. The proposed GIF-TODIM method and the proposed IFDivM are applied to a real-world case study on supplier selection. A detailed comparative analysis is performed taking the TOPSIS method and other IFDivMs as baselines. The role of attitude on the final choice is analyzed in great detail. It is found that the proposed GIF-TODIM method is indeed useful, effective, and superior to the counterpart methods, when it comes to real-world situations. Concomitantly, in the present work, it is also revealed that the TOPSIS method based on the 2-D Hamming distance is a special form of the proposed GIF-TODIM method, when decision-makers have the same attitude towards losses and gains. Thus, an interesting relationship between TOPSIS and TODIM is identified under the intuitionistic fuzzy environment, which is bound to propel significant research in the area of decision making under uncertain conditions. As a whole, the article offers comprehensive analyses of IFDivMs and the TODIM method under the intuitionistic fuzzy environment. • Construct a new IF divergence measure (IFDivM) based on Jensen–Shannon divergence. • Develop a GIF-TODIM method based on the new IFDivM. • Apply the proposed GIF-TODIM method to a supplier selection problem. • Provide parameter analysis and comparative analysis with TOPSIS and other IFDivMs. • Show that TOPSIS based on 2-D Hamming distance is a special form of our GIF-TODIM. [ABSTRACT FROM AUTHOR]

A hesitant fuzzy number (HFN) is important as a generalization of the fuzzy number for hesitant fuzzy analysis and takes some applications that were discussed in recent literature. In this paper, we develop the hesitant fuzzy arithmetic, which is based on the extension principle for hesitant fuzzy sets. Employing this principle, standard arithmetic operations on fuzzy numbers are extended to HFNs and we show that the outcome of these operations on two HFNs are an HFN. Also we use the extension principle in HFSs for the ranking of HFNs, which may be an interesting topic. In this paper, we show that the HFNs can be ordered in a natural way. To introduce a meaningful ordering of HFNs, we use a new lattice operation on HFNs based upon extension principle and defining the Hamming distance on them. Finally, the applications of them are explained on optimization and decision-making problems. [ABSTRACT FROM AUTHOR]

The objective of this paper is to develop Pythagorean fuzzy (PF) multi‐objective optimization by ratio analysis (PF‐MOORA) plus full MULTIplicative form (PF‐MULTIMOORA) method for solving multicriteria decision making (MCDM) problems with completely unknown information of criteria weights. In the model formulation process, a new distance measure is defined to quantify the difference between PF sets by combining Hamming distance and Hausdorff metric. This distance measure is, subsequently, implemented in entropy weight model for determining unknown weights of criteria, and also in reference point approach for obtaining preference indices of alternatives. To overcome the deficiencies occurred in existing MULTIMOORA method, like multiple comparisons, circular reasoning, and so on, an aggregation‐based approach is recommended in the proposed PF‐MULTIMOORA. To demonstrate the feasibility and practicality of the proposed method, an example concerning strategy prioritization of a tiles manufacturing company is presented. In the strategy evaluation process, at first, the judgement values provided by the decision maker are expressed in linguistic terms, and then those are converted into PF numbers through a PF weighting scale. The sensitivity of the proposed model is validated by changing of weights of criteria which impact on the ranks of the strategies. To show robustness of the developed method, the result attained by applying PF‐MULTIMOORA is compared with existing techniques, not only in crisp and fuzzy quantitative strategic planning matrix context, but also using four other MCDM methods, namely, modified PF‐MOORA, as a particular case of the proposed PF‐MULTIMOORA technique, PF weighted sum, PF‐TOPSIS and PF‐VIKOR. [ABSTRACT FROM AUTHOR]

In this study, considering the traditional geometric operation laws and Pythagorean fuzzy information, we propose a variety of new distance measures of Pythagorean fuzzy sets such as generalized Pythagorean fuzzy geometric distance (GPFGD) measures and generalized Pythagorean fuzzy weighted geometric distance (GPFWGD) 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, we build a decision-making model illustrated by a mathematical calculation example to evaluate the sustainable development of new urbanization from the perspective of urban agglomeration using Pythagorean fuzzy information. [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]

As a generalization of complex fuzzy set (CFS), interval-valued complex fuzzy set (IVCFS) is a new research topic in the field of CFS theory, which can handle two different information features with the uncertainty. Distance is an important tool in the field of IVCFS theory. To enhance the applicability of IVCFS, this paper presents some new interval-valued complex fuzzy distances based on traditional Hamming and Euclidean distances of complex numbers. Furthermore, we elucidate the geometric properties of these distances. Finally, these distances are used to deal with decision-making problem in the IVCFS environment. [ABSTRACT FROM AUTHOR]

In this paper, we define the new concept of interval-valued triangular linguistic neutrosophic fuzzy set and operational laws. We discuss the IVTLNFWAA operator of IVTLNFS, and then the score function of IVTLNFS is introduced. We define the hamming distance of IVTLNFS. We define the triangular linguistic neutrosophic cubic fuzzy number and operational laws. We also discuss the triangular linguistic neutrosophic cubic fuzzy number, such as the TLNCFWAA operator. We define the score function and accuracy of TLNCFNs. We also discuss the hamming distance of TLNCFNs. We discuss some basic properties of the proposed operator, including idempotency and commutativity. The new concept of the triangular linguistic neutrosophic cubic fuzzy TOPSIS method is introduced. Furthermore, we extend the MCDM method based on the triangular linguistic neutrosophic cubic fuzzy TOPSIS method. Finally, an illustrative example is given to verify and demonstrate the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Currently, an important issue in multi-criteria decision-making (MCDM) problems are vagueness and lack of precision of decision- -making information because of insufficient data and incapability of the decision maker to process the information. Intuitionistic fuzzy sets (IFS) are a solution to eliminate the vagueness and the uncertainty. While fuzzy sets (FS) deal with ambiguity and vagueness problem, IFSs have more advantages. Moreover, the CODAS-SORT method cannot handle the uncertainty and ambiguity of information provided by human judgments. The aim of this study is to develop an IF extension of CODAS-SORT combining this method with the IFS theory. To achieve this, we use the fuzzy weighted Euclidean distance and fuzzy weighted Hamming distance instead of the crisp distances. A case study of a supplier selection assessment is used to clarify the details of our proposed method. [ABSTRACT FROM AUTHOR]

Neutrosophic set theory as a generalization of the fuzzy set theory and intuitionistic fuzzy set theory is an effective tool to deal with inconsistent, imprecise, and vague information. TOPSIS is a multiple attribute method to identify solutions from a finite set of alternatives based upon simultaneous minimization of distance from an ideal point and maximization of distance from a nadir point. In this paper, we first develop a new Hamming distance between single-valued neutrosophic numbers and then present an extension of the TOPSIS method for multi-attribute group decision-making (MAGDM) based on single-valued neutrosophic sets, where the inform ation about attribute values and attribute weights are expressed by decision-makers based on neutrosophic numbers. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the complex fuzzy ordered weighted distance (CFOWD) measure. It is a new measure that uses the main characteristics of the the ordered weighted averaging (OWA) operator and uncertain information represented as complex fuzzy values. This measure includes a wide range of distance measures such as the complex fuzzy maximum distance, the complex fuzzy minimum distance, the normalized complex fuzzy distance (NCFD), the complex fuzzy ordered weighted Hamming distance (CFOWHD), complex fuzzy ordered weighted Euclidean distance (CFOWED), complex fuzzy ordered weighted geometric distance (CFOWGD), the normalized complex fuzzy Ham- ming distance (NCFHD) and the normalized complex fuzzy Euclidean distance (NCFED). We study some of its main properties. Finally, based on CFOWD measures, we give an illustrative example regarding the selected problem. [ABSTRACT FROM AUTHOR]

The concept of distance between Pythagorean fuzzy sets (PFSs) has been proven to be relevant in the applications of PFSs as seen in the literature. The main purpose of this paper is to show that Zhang and Xu's distance measure between PFSs fails the conditions of distance measure; hence, it is not an appropriate distance measure for PFSs. Some numerical examples are used to validate this stance. In order to remedy this shortcoming, Zhang and Xu's distance measure for PFSs is normalised/modified to cater for the limitation by employing the technique used to normalise both Hamming and Euclidean distances between intuitionistic fuzzy sets by Szmidt and Kacprzyk. The modified Zhang and Xu's distance measure for PFSs satisfies the conditions of the axiomatic definition of distance measure for PFSs; hence, it is an appropriate/reliable distance measure for PFSs. Finally, the modified Zhang and Xu's distance measure for PFSs is applied to pattern recognition problems of classification of building materials and mineral fields. [ABSTRACT FROM AUTHOR]

It is doubtless that intuitionistic fuzzy set (IFS) theory plays an increasingly important role in solving the problems under uncertain situation. As one of the most critical members in the theory, distance measure is widely used in many aspects. Nevertheless, it is a pity that part of the existing distance measures has some drawbacks in practical significance and accuracy. To make up for their drawbacks and pursue more accuracy and effectiveness, in this paper, we propose a new inclusion relation of IFSs and a new definition called strict distance measure. Based on this new relation, an analysis is given to point out that the common shortcoming of Hamming distance measure and Euclidean distance measure is the mishandling of hesitancy degree. Therefore, the role of hesitancy degree in distance measure is studied deeply and then three strict distance measures are put forward to overcome the above shortcoming. In addition, a novel definition called the characteristic function of distance measure is defined to describe the character of strict distance measure. On this basis, a theorem is presented to illustrate the inevitability of the occurrence of unrecognized result in pattern recognition problems in some special cases. This theorem also shows that the problem cannot be entirely attributed to distance measures. In view of this condition, we provide an appropriate solution. Compared with other existing distance measures in some examples, the superiorities of our improved distance measures are demonstrated to be more effective and more significant. [ABSTRACT FROM AUTHOR]

Fuzzy set theory and fuzzy logic have been successfully developed in engineering and mathematics. However, these concepts have found great acceptance in social sciences in recent years since they provide an answer to those problems in the real world that cannot be modeled using classical mathematics. In this paper, we propose a new methodology for accounting science based on fuzzy triangular numbers. The methodology uses Hamming distance between fuzzy triangular numbers and arithmetic operations to evaluate corporate governance of multinational public stock corporations (PSCs) in the telecommunications sector. [ABSTRACT FROM AUTHOR]

In this paper, we define the new idea of triangular cubic hesitant fuzzy number (TCHFN). We discuss some basic operational laws of triangular cubic hesitant fuzzy number and hamming distance of TCHFNs. We introduce the new concept of triangular cubic hesitant TOPSIS method. Furthermore, we extend the classical cubic hesitant the technique for order of preference by similarity to ideal solution (TOPSIS) method to solve the Multi-Criteria decision-making (MCDM) method based on triangular cubic hesitant TOPSIS method. The new ranking method for TCHFNs 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]

In this paper, we define the idea of cubic linguistic uncertain fuzzy numbers. We define the idea of triangular cubic linguistic uncertain fuzzy number. We discuss some basic operational laws of triangular cubic linguistic uncertain fuzzy number and hamming distance of TCLUFNs. We introduce the new concept of triangular cubic linguistic uncertain fuzzy TOPSIS method. Furthermore, we extend the classical triangular cubic linguistic uncertain fuzzy TOPSIS method to solve the MCDM method based on triangular cubic linguistic uncertain fuzzy TOPSIS method. The new ranking method for TCLUFNs 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]

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 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]

An approach to solving complex decision-making problems based on IVIFNs: a case of comminution circuit design selection. • A complex interval-valued intuitionistic fuzzy reference point is introduced. • The procedure for ranking complex IVIFNs based on the Hamming distance is proposed. • IVIFNs based approach is used for the selection of a comminution circuit design. • The proposed complex IVIFNs approach is adapted to be used in a group environment. The comminution process is very important in the mineral processing industry. Some characteristics of ore particles which occur as a product of this process have a significant impact on the effects of further ore processing and the separation of valuable minerals in froth flotation. At the same time, this process requires a significant amount of energy, which significantly affects the overall processing costs, and a significant amount of heavy equipment and corresponding installations, which affects investment costs. In addition, it is not so easy to accurately determine the correlation between energy consumption, the consumption of the grinding media, the utilization of valuable materials and the comminution circuit throughput. Therefore, the selection of an adequate comminution circuit design is recognized as a complex decision-making problem and a new multiple-criteria decision-making approach based on the use of interval-valued intuitionistic fuzzy sets is proposed for its efficient selection. In contrast to the use of a number of more precisely defined criteria, the use of a smaller number of the more complex criteria evaluated on the basis of the satisfaction and dissatisfaction levels is also proposed in this approach. In order to enable its use for solving various complex decision-making problems, the proposed approach is adapted so as to be used in a group environment. In addition, a new procedure for ranking interval-valued intuitionistic fuzzy numbers based on the Hamming distance to a complex interval-valued intuitionistic fuzzy reference point is also proposed. The efficiency and usability of the proposed approach are considered on the illustrative example of the preliminary selection of three generic comminution circuit designs. The results obtained by applying the proposed approach are verified by the experts involved in the evaluation. The new procedure proposed for ranking interval-valued intuitionistic fuzzy numbers is also verified by comparing the results obtained by that procedure with those obtained by the proven procedure for ranking interval-valued intuitionistic fuzzy numbers based on an extension of the TOPSIS method. [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]

The main aim of the paper is to propose an application of Intuitionistic fuzzy set in medical field using new normalized Hamming distance method. This method was very useful to find the distance between patient and their Health problem. From this we find the solution is obtained by measuring the minimum distance between each patient and each health problem. Finally, an illustrative example is also included to demonstrate our proposed 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]

Interval-valued intuitionistic hesitant fuzzy sets (IVIHFSs) are useful to denote the decision makers' interval preferred, interval non-preferred and hesitant opinions simultaneously. Considering the application of IVIHFSs, this paper introduces a new decision-making method with interval-valued intuitionistic hesitant fuzzy information that extends the application scopes. To do this, the interval-valued intuitionistic hesitant fuzzy hybrid Shapley weighted averaging (IVIHFHSWA) operator and the interval-valued intuitionistic hesitant fuzzy hybrid Shapley weighted geometric (IVIHFHSWG) operator are defined to aggregate the collective attribute values of alternatives. To reflect the interactions and reduce the complexity of calculating the weights, the 2-additive measures are used to define these two hybrid Shapley weighted operators. To derive the exact weight information of attributes and ordered positions, the associated programming models for determining the optimal 2-additive measures are constructed that are based on the defined Hamming distance measure. To show the feasibility and efficiency of the new method, a practical decision-making problem is offered, which is also used to compare with the previous methods. [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]

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]