Neutrosophic sets and their variants
Sulima Ahmed Mohammed Zubair
Abstract
This study introduces an approach for Multiple Attribute Decision-Making (MADM) that deals with the complexity of Single-Valued Neutrosophic Uncertain Linguistic Variables (SVNULVs). This method is engineered to grasp the interconnectedness of multiple inputs and to meet the diverse requirements for ...
Read More
This study introduces an approach for Multiple Attribute Decision-Making (MADM) that deals with the complexity of Single-Valued Neutrosophic Uncertain Linguistic Variables (SVNULVs). This method is engineered to grasp the interconnectedness of multiple inputs and to meet the diverse requirements for semantic transformations. Due to the shortcomings of existing operational rules in terms of closeness and flexibility, this paper proposes a novel set of operational rules and a ranking process for SVNULVs, integrating the concept of a Linguistic Scale Function (LSF). We propose an innovative operator along with its weighted counterpart to amalgamate SVNULVs, thereby characterizing the dynamics among various inputs through these new operations. Concurrently, we scrutinize and discuss the unique cases and favorable properties of these proposed operators. Building upon this new operator, the paper also unveils a fresh MADM methodology leveraging SVNULVs. To validate the effectiveness of this proposed methodology, an illustrative example is employed, demonstrating the precision of the method and its advantages over existing MADM techniques.
Neutrosophic sets and their variants
Vakkas Uluçay; Necmiye Merve Şahin; Nisa İrem Toz; Enver Bozkurt
Abstract
Different frameworks can be chosen to solve Multi-Criteria Decision-Making (MCDM) problems emerging in business, cyber environment, economy, health care, engineering and other areas. Uncertainty, vagueness and non-rigid boundaries of the initial information are frequently noticed when dealing with the ...
Read More
Different frameworks can be chosen to solve Multi-Criteria Decision-Making (MCDM) problems emerging in business, cyber environment, economy, health care, engineering and other areas. Uncertainty, vagueness and non-rigid boundaries of the initial information are frequently noticed when dealing with the practicalities of the MCDM tasks. Single-valued neutrosophic sets are considered as the effective tool to express uncertainty of the information, however in some cases it lacks the desirable generality and flexibility. The Q-single-valued neutrosophic sets were recently proposed to deal with this situation. Then, we develop a VIKOR method based on the Q-single-valued neutrosophic sets for novel MCDM method. In the decision-making framework, the proposed method is not only a way to solve the problem of MCDM, but also contains an important mathematical idea as a different solution approach. By applying this method to the real-life problem of cyber warfare, demonstrated the flexibility, effectiveness and feasibility of the proposed VIKOR method and compare the obtained results with the results of other existing methods.
Picture fuzzy sets and their variants
Ngan Thi Roan; Salvador Coll; Marina Alonso; Juan Miguel Martínez Rubio; Pedro López; Fran Andujar; Son Hoang Le; Manh Van Vu; Florentin Smarandache
Abstract
In order to solve the complex decision-making problems, there are many approaches and systems based on the fuzzy theory were proposed. In 1998, Smarandache introduced the concept of single-valued neutrosophic set as a complete development of fuzzy theory. In this paper, we research on the distance measure ...
Read More
In order to solve the complex decision-making problems, there are many approaches and systems based on the fuzzy theory were proposed. In 1998, Smarandache introduced the concept of single-valued neutrosophic set as a complete development of fuzzy theory. In this paper, we research on the distance measure between single-valued neutrosophic sets based on the H-max measure of Ngan et al. [8]. The proposed measure is also a distance measure between picture fuzzy sets which was introduced by Cuong in 2013 [15]. Based on the proposed measure, an Adaptive Neuro Picture Fuzzy Inference System (ANPFIS) is built and applied to the decision making for the link states in interconnection networks. In experimental evaluation on the real datasets taken from the UPV (Universitat Politècnica de València) university, the performance of the proposed model is better than that of the related fuzzy methods.
