RESUMEN
The concept of interval-valued intuitionistic fuzzy sets is intellectually stimulating and holds significant utility in the representation and analysis of real-world problems. The development of similarity measures within the class of interval-valued intuitionistic fuzzy sets possesses significant importance across various academic disciplines, particularly in the fields of decision-making and pattern recognition. The utilization of similarity measures is of utmost importance in the decision-making process when implementing interval-valued intuitionistic fuzzy sets. This is due to its inherent capability to quantitatively assess the level of resemblance or similarity between two interval-valued intuitionistic fuzzy sets. In this article, the drawbacks of the existing similarity measures in the context of an interval-valued intuitionistic fuzzy environment are addressed, and a novel similarity measure is presented. Many fundamental properties of this new interval-valued intuitionistic fuzzy similarity measure are also established, and the effectiveness of this similarity measure is illustrated by presenting a useful example. Moreover, a comparison is given to demonstrate the validity of the newly proposed similarity measure within the existing knowledge of similarity measures in the interval-valued intuitionistic fuzzy environment. In addition, an algorithm is designed to solve multi-criteria decision making problems by means of the proposed measure in the interval-valued intuitionistic fuzzy setting. Furthermore, this newly defined similarity measure is successfully applied to select an optimal renewable energy source to reduce energy crises. Finally, we conduct a comparative study to showcase the authenticity of the recently defined technique within the existing knowledge of similarity measures in the interval-valued intuitionistic fuzzy environment.
RESUMEN
In this paper, we define the notion of a t-intuitionistic fuzzy conjugate element and determine the t-intuitionistic fuzzy conjugacy classes of a t-intuitionistic fuzzy subgroup. We propose the idea of a t-intuitionistic fuzzy p- subgroup and prove the t-intuitionistic fuzzy version of the Cauchy theorem. In addition, we present the idea of a t-intuitionistic fuzzy conjugate subgroup and investigate various fundamental algebraic characteristics of this notion. Furthermore, we provide the idea of the t-intuitionistic fuzzy Sylow p- subgroup and prove the t-intuitionistic fuzzification of Sylow's theorems.
RESUMEN
This paper explains the idea of t-intuitionistic fuzzy graphs as a powerful way to analyze and display relationships that are difficult to understand. The article also illustrates the ability of t-intuitionistic fuzzy graphs to establish complex relationships with multiple factors or dimensions of a physical situation under consideration. Moreover, the fundamental set operations of t-intuitionistic fuzzy graphs are proposed. The notions of homomorphism and isomorphism of t-intuitionistic fuzzy graphs are also introduced. Furthermore, the paper highlights a practical application of the proposed technique in the context of poverty reduction within a specific society. By employing t-intuitionistic fuzzy graphs, the research demonstrates the potential to address the multifaceted nature of poverty, considering various contributing factors and their interdependencies. This application showcases the versatility and effectiveness of t-intuitionistic fuzzy graphs as a tool for decision-making and policy planning in complex societal issues.