Search

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]

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, 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]

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]

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]

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]

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]