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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]

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]

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]

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]

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]

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]