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Similarity and distance measures play important roles in fuzzy environments, helping to quantify the degree of similarity or concepts that may not have clear limits. They are used in various fields, including fuzzy logic, fuzzy clustering, and fuzzy decision-making. The cubic Fermatean fuzzy set (CFFS), which is a type of fuzzy set (FS), is highly favoured as an extension for expressing uncertainty through degrees of membership (η) and non-membership (υ). This article introduces novel measures for cosine similarity and distance in CFFSs. These measures are designed to improve the accuracy and efficiency of similarity and distance calculations in CFFSs. Also, a novel method is introduced for developing alternate similarity measures for CFFSs utilizing the proposed similarity measures that adhere to the similarity measures axiom. In addition, the connection between similarity and distance measures is utilized to construct a cosine distance metric for CFFSs. This newly suggested cosine similarity measure can not only provide solutions to decision-making problems from a geometric perspective but also from an algebraic point of view. To conclude, a case study is presented to showcase the practicality and effectiveness of the proposed approach, followed by a comparison of the outcomes of the suggested technique with some existing methodologies. This analysis helps to validate the proposed method and demonstrates its potential for outperforming other available approaches in terms of efficiency and accuracy. [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]

The aim of this paper is to define some new operation laws for the trapezoidal linguistic cubic fuzzy number and Hamming distance. Furthermore, we define and use the trapezoidal linguistic cubic fuzzy TOPSIS method to solve the multi criteria decision making (MCDM) method. The new ranking method for trapezoidal linguistic cubic fuzzy numbers (TrLCFNs) are used to rank the alternatives. Finally, an illustrative example is given to verify and prove 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]

In this paper, we construct an extended version of the TOPSIS method by using cubic information, and provide a numerical application to verify and demonstrate the practicality of the method. A new extension of the gray relation analysis (GRA) method is introduced by using cubic information. We also propose the cubic fuzzy multi-attribute group decision-making model, and the relation between the cubic TOPSIS method and the cubic gray relation analysis (CGRA) method is introduced. Finally, the proposed method is used for selection in sol–gel synthesis of titanium carbide nanopowders. We analyzed the proposed method by using a numerical application to sol–gel synthesis of titanium carbide nanopowders. [ABSTRACT FROM AUTHOR]

In this paper, we describe the idea of trapezoidal cubic hesitant fuzzy number. We discuss some basic operational laws of trapezoidal cubic hesitant fuzzy number and hamming distance of trapezoidal cubic hesitant fuzzy numbers (TrCHFNs). We introduce the new concept of the trapezoidal cubic hesitant fuzzy TOPSIS method. Furthermore, we extend the classical trapezoidal cubic hesitant fuzzy TOPSIS method to solve the MCDM method based on the trapezoidal cubic hesitant fuzzy TOPSIS method. The new ranking method for TrCHFNs is used to rank the alternatives. Finally, an illustrative example is given to verify and prove the practicality and effectiveness of the proposed method. We compared the proposed method to the existing methods, which shows the trapezoidal cubic hesitant Fuzzy TOPSIS method is more flexible to deal uncertainties and fuzziness. The main advantage of these operators is that it is to provide more accurate and significant results. [ABSTRACT FROM AUTHOR]

In this paper, we describe the new idea of trapezoidal linguistic uncertain cubic fuzzy number. We discuss some basic operational laws of trapezoidal linguistic uncertain cubic fuzzy number and hamming distance of TrLUCFNs. We introduce the new concept of trapezoidal linguistic uncertain cubic fuzzy TOPSIS method. Furthermore, we extend the classical trapezoidal linguistic uncertain cubic fuzzy TOPSIS method to solve the MCDM method based on trapezoidal linguistic uncertain cubic fuzzy TOPSIS method. The new ranking method for TrLUCFNs is used to rank the alternatives. Finally, an illustrative example is given to verify and prove the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we define hesitant cubic TOPSIs method. We develop the numerical application and different method. We define the new idea of Hesitant Cubic Gray Analysis Set. We proposed the HCF-MAGDM model and relationships among hesitant cubic TOPSIS method with hesitant cubic gray relation analysis method being introduced. Finally, using the proposed method to Sol–Gel synthesis of titanium carbide (TiC) nanopowders for selection, we analyzed the proposed method by using a numerical application to Sol–Gel synthesis of TiC nanopowders. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define some new operation laws for the trapezoidal linguistic cubic fuzzy number and Hamming distance. Furthermore, we define and use the trapezoidal linguistic cubic fuzzy TOPSIS method to solve the multi criteria decision making (MCDM) method. The new ranking method for trapezoidal linguistic cubic fuzzy numbers (TrLCFNs) are used to rank the alternatives. Finally, an illustrative example is given to verify and prove the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Pythagorean Hesitant fuzzy set (PHFS) which permits the membership degree and non-membership degree of an element to a set represented by several possible values is deliberated as a powerful tool to express uncertain information in the process of multi-attribute decision making (MADM) problems. In this paper, we propose a novel approach based on TOPSIS method and the maximizing deviation method for solving MADM problems where the evaluation information provided by the decision makers (DMs) is expressed in form of Pythagorean hesitant fuzzy numbers and the information about attribute weights is incomplete. To determine the attribute weight we develop an optimization model based on maximizing deviation method. Finally we provide a practical decision-making problem to demonstrate the implementation process of the proposed method. [ABSTRACT FROM AUTHOR]