Search

In this article, multiple attribute decision-making problems are solved using the vague normal set (VNS). It is possible to generalize the vague set (VS) and q-rung fuzzy set (FS) into the q-rung vague set (VS). A log q-rung normal vague weighted averaging (log q-rung NVWA), a log q-rung normal vague weighted geometric (log q-rung NVWG), a log generalized q-rung normal vague weighted averaging (log Gq-rung NVWA), and a log generalized q-rungnormal vagueweightedgeometric (logGq-rungNVWG) operator are discussed in this article. Adescription is provided of the scoring function, accuracy function and operational laws of the log q-rung VS. The algorithms underlying these functions are also described. A numerical example is provided to extend the Euclidean distance and the Humming distance. Additionally, idempotency, boundedness, commutativity, and monotonicity of the log q-rung VS are examined as they facilitate recognizing the optimal alternative more quickly and help clarify conceptualization. We chose five anemia patients with four types of symptoms including seizures, emotional shock or hysteria, brain cause, and high fever, who had either retrograde amnesia, anterograde amnesia, transient global amnesia, post-traumatic amnesia, or infantile amnesia. Natural numbers q are used to express the results of the models. To demonstrate the effectiveness and accuracy of the models we are investigating, we compare several existing models with those that have been developed. [ABSTRACT FROM AUTHOR]

This article presents the circular Pythagorean fuzzy set (C-PFS) model, a generalization of the circular intuitionistic fuzzy set model that improves its performance thanks to the acclaimed extension of intuitionistic fuzzy sets to Pythagorean fuzzy sets. Then, we generalize C-PFSs to produce the novel disc Pythagorean fuzzy sets (D-PFSs). The constituent elements of both C-PFSs and D-PFSs are circular Pythagorean fuzzy values, either with a common or a distinctive radius. We lay out some fundamental algebraic and arithmetic operations on D-PFSs (hence on C-PFSs), namely union, intersection, addition, multiplication, and scalar multiplication, and we explore the main features of these operations. We propose and investigate the properties of the novel circular Pythagorean fuzzy weighted average/geometric aggregation operators. The "COmbinative Distance based ASsesment" approach, which is based on the Hamming and Euclidean distances, is expanded to the D-PFS framework. To justify its implementability, we apply the new methodology to a case study (selection of the best supermarkets to buy fresh fruit for a hotel) and then we compare it to related solutions. [ABSTRACT FROM AUTHOR]

Novel methods for multiple attribute decision-making problems are presented in this paper using Type-Ⅱ Fermatean normal numbers. Type-Ⅱ Fermatean fuzzy sets are developed by further generalizing Fermatean fuzzy sets and neutrosophic sets. The Type-Ⅱ Fermatean fuzzy sets with basic aggregation operators are constructed. The concept of a Type-Ⅱ Fermatean normal number is compatible with both commutative and associative rules. This article presents a new proposal for Type-Ⅱ Fermatean normal weighted averaging, Type-Ⅱ Fermatean normal weighted geometric averaging, Type-Ⅱ generalized Fermatean normal weighted averaging, and Type-Ⅱ generalized Fermatean normal weighted geometric averaging. Furthermore, these operators can be used to develop an algorithm that solves MADM problems. Applications for the Euclidean distance and Hamming distances are discussed. Finally, the sets that arise as a result of their connection to algebraic operations are emphasized in our discourse. Examples of real-world applications of enhanced Hamming distances are presented. A sensor robot's most important components are computer science and machine tool technology. Four factors can be used to evaluate the quality of a robotics system: resolution, sensitivity, error and environment. The best alternative can be determined by comparing expert opinions with the criteria. As a result, the proposed models' outcomes are more precise and closer to integer number δ . To demonstrate the applicability and validity of the models under consideration, several existing models are compared with the ones that have been proposed. Novel methods for multiple attribute decision-making problems are presented in this paper using Type-Ⅱ Fermatean normal numbers. Type-Ⅱ Fermatean fuzzy sets are developed by further generalizing Fermatean fuzzy sets and neutrosophic sets. The Type-Ⅱ Fermatean fuzzy sets with basic aggregation operators are constructed. The concept of a Type-Ⅱ Fermatean normal number is compatible with both commutative and associative rules. This article presents a new proposal for Type-Ⅱ Fermatean normal weighted averaging, Type-Ⅱ Fermatean normal weighted geometric averaging, Type-Ⅱ generalized Fermatean normal weighted averaging, and Type-Ⅱ generalized Fermatean normal weighted geometric averaging. Furthermore, these operators can be used to develop an algorithm that solves MADM problems. Applications for the Euclidean distance and Hamming distances are discussed. Finally, the sets that arise as a result of their connection to algebraic operations are emphasized in our discourse. Examples of real-world applications of enhanced Hamming distances are presented. A sensor robot's most important components are computer science and machine tool technology. Four factors can be used to evaluate the quality of a robotics system: resolution, sensitivity, error and environment. The best alternative can be determined by comparing expert opinions with the criteria. As a result, the proposed models' outcomes are more precise and closer to integer number . To demonstrate the applicability and validity of the models under consideration, several existing models are compared with the ones that have been proposed. [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]

• 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]

Combinative Distance based ASsesment (CODAS) method aims to perform multi-criteria selection process according to the largest Euclidean and Taxicab distance with respect to negative ideal solutions. Recently, several CODAS methods have been applied to multi-criteria decision making problems with interval valued intuitionistic fuzzy sets. This paper demonstrates the weaknesses of using Euclidean and Taxicab distance on interval valued intuitionistic fuzzy sets and provides alternative strategies to model the vagueness and uncertainty in decision maker evaluations more effectively. The contribution of this paper is twofold. First, a new selection metric is defined in order to eliminate the disadvantages of using Euclidean and Taxicab distance in interval valued intuitionistic fuzzy CODAS. Second, a new fuzzy aggregation operator is proposed for aggregating decision maker evaluations by using fuzzy weights rather than using crisp weights. To show the effectiveness of the modified CODAS method, an application is given for multi-criteria selection of renewable energy alternatives in Turkey and the results are compared with two other interval valued intuitionistic fuzzy CODAS methods in the literature. • This paper criticizes the existing IVIF-CODAS methods in the literature. • The drawbacks of using Euclidean and Hamming distance are highlighted. • A new distance metric and fuzzy aggregation operator for IVIF CODAS is proposed. • The proposed IVIF-CODAS method does not have any user-defined parameters. • Results show the difference between existing and proposed IVIF CODAS methods. [ABSTRACT FROM AUTHOR]