insight - Mathematics - # Globular T-Spherical Fuzzy Sets

Innovative Extension of Fuzzy Sets: Globular T-Spherical Fuzzy (G-TSF) Sets

Q: How do Globular T-Spherical Fuzzy Sets compare to other extensions like PyFSs or IFSs

Globular T-Spherical Fuzzy Sets (G-TSFSs) offer a unique extension compared to other fuzzy set models like Pythagorean Fuzzy Sets (PyFSs) or Intuitionistic Fuzzy Sets (IFSs). While PyFSs introduce the concept of membership and non-membership degrees with specific conditions, G-TSFSs provide a more flexible approach by incorporating a globular/sphere bound. This allows for a more accurate representation of vague, ambiguous, and imprecise information. On the other hand, IFSs introduce degrees of membership and non-membership but face constraints in value allocation due to certain conditions. In contrast, G-TSFSs overcome these limitations by allowing decision-makers to assign values within a specified range that ensures their sum falls within the unit interval.

Q: What are the practical implications of using G-TSFSs in real-world decision-making scenarios

The practical implications of using G-TSFSs in real-world decision-making scenarios are significant. By employing structured representations on spheres with specific centers and radii, G-TSFS models enhance decision-making processes by enabling comprehensive evaluations within flexible regions. This leads to more sensitive decision-making capabilities over broader areas where uncertainty prevails. The application of similarity measures based on radius as well as Hamming distance and Euclidean distance for G-TSFS further enhances the evaluative capabilities for decision-makers. Additionally, introducing weighted aggregation operators tailored specifically for G-TSF values provides efficient ways to aggregate information from multiple sources into single outputs.

Q: How can the concept of G-TSFSs be applied to other fields beyond mathematics

The concept of Globular T-Spherical Fuzzy Sets can be applied beyond mathematics in various fields such as artificial intelligence, pattern recognition, data analysis, machine learning algorithms, expert systems design, risk assessment modeling in finance or insurance sectors among others. In artificial intelligence applications like image processing or natural language processing tasks where dealing with uncertain or imprecise data is common practice; utilizing G-TSFS could lead to improved accuracy and robustness in handling complex datasets effectively.

Core Concepts

The author introduces Globular T-Spherical Fuzzy (G-TSF) Sets as an innovative extension of existing fuzzy set models, offering a more precise representation of uncertainty and enhancing decision-making processes.

Abstract

The content discusses the concept of Globular T-Spherical Fuzzy (G-TSF) Sets as an extension of existing fuzzy set models. It introduces basic set operations, algebraic operations for G-TSF Values, similarity measures, and aggregation operators. The proposed G-TSFMCGDM model for multi-criteria group decision-making is demonstrated with practical applications.

The paper provides a detailed explanation of the theoretical framework behind G-TSF sets, including definitions, operations, and examples. It highlights the advantages of G-TSF sets in handling uncertainty and improving decision-making processes.

Key points include the introduction of G-TSFSs to represent vague information accurately, establishment of set operations and algebraic functions for G-TSF values, definition of similarity measures based on radius, introduction of weighted aggregation operators, and application in multi-criteria group decision-making scenarios.

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Stats

By employing a structured representation of data points on a sphere with a specific center and radius.
To quantify a similarity measure (SM) between GTSFVs.
Additionally, Hamming distance and Euclidean distance are introduced for G-TSFSs.
Introduction of G-TSF Weighted Average (G-TSFWA) and G-TSF Weighted Geometric (G-TSFWG) operators.
Leveraging the proposed SM, a Multi-Criteria Group Decision-Making (MCGDM) scheme for G-TSFSs is developed.

Quotes

Key Insights Distilled From

On Globular T-Spherical Fuzzy (G-TSF) Sets with Application to G-TSF Multi-Criteria Group Decision-Making

by Miin-Shen Ya... at arxiv.org 03-13-2024

https://arxiv.org/pdf/2403.07010.pdf

On Globular T-Spherical Fuzzy (G-TSF) Sets with Application to G-TSF Multi-Criteria Group Decision-Making

Deeper Inquiries

How do Globular T-Spherical Fuzzy Sets compare to other extensions like PyFSs or IFSs

Globular T-Spherical Fuzzy Sets (G-TSFSs) offer a unique extension compared to other fuzzy set models like Pythagorean Fuzzy Sets (PyFSs) or Intuitionistic Fuzzy Sets (IFSs). While PyFSs introduce the concept of membership and non-membership degrees with specific conditions, G-TSFSs provide a more flexible approach by incorporating a globular/sphere bound. This allows for a more accurate representation of vague, ambiguous, and imprecise information. On the other hand, IFSs introduce degrees of membership and non-membership but face constraints in value allocation due to certain conditions. In contrast, G-TSFSs overcome these limitations by allowing decision-makers to assign values within a specified range that ensures their sum falls within the unit interval.

What are the practical implications of using G-TSFSs in real-world decision-making scenarios

The practical implications of using G-TSFSs in real-world decision-making scenarios are significant. By employing structured representations on spheres with specific centers and radii, G-TSFS models enhance decision-making processes by enabling comprehensive evaluations within flexible regions. This leads to more sensitive decision-making capabilities over broader areas where uncertainty prevails. The application of similarity measures based on radius as well as Hamming distance and Euclidean distance for G-TSFS further enhances the evaluative capabilities for decision-makers. Additionally, introducing weighted aggregation operators tailored specifically for G-TSF values provides efficient ways to aggregate information from multiple sources into single outputs.

How can the concept of G-TSFSs be applied to other fields beyond mathematics

The concept of Globular T-Spherical Fuzzy Sets can be applied beyond mathematics in various fields such as artificial intelligence, pattern recognition, data analysis, machine learning algorithms, expert systems design, risk assessment modeling in finance or insurance sectors among others. In artificial intelligence applications like image processing or natural language processing tasks where dealing with uncertain or imprecise data is common practice; utilizing G-TSFS could lead to improved accuracy and robustness in handling complex datasets effectively.