Aggregation of fuzzy vector spaces

Abstract

This paper contributes to the ongoing investigation of aggregating algebraic structures, with a particular focus on the aggregation of fuzzy vector spaces. The article is structured into three distinct parts, each addressing a specific aspect of the aggregation process.The first part of the paper explores the self-aggregation of fuzzy vector subspaces. It delves into the intricacies of combining and consolidating fuzzy vector subspaces to obtain a coherent and comprehensive outcome.The second part of the paper centers around the aggregation of similar fuzzy vector subspaces, specifically those belonging to the same equivalence class. This section scrutinizes the challenges and considerations involved in aggregating fuzzy vector subspaces with shared characteristics.The third part of the paper takes a broad perspective, providing an analysis of the aggregation problem of fuzzy vector subspaces from a general standpoint. It examines the fundamental issues, principles, and implications associated with aggregating fuzzy vector subspaces in a comprehensive manner.By elucidating these three key aspects, this paper contributes to the advancement of knowledge in the field of aggregation of algebraic structures, shedding light on the specific domain of fuzzy vector spaces.

Analysis of Fuzzy Vector Spaces as an Algebraic Framework for Flag Codes

“…Additionally, in the context of understanding the algebraic structures, a fruitful research line is the analysis of the aggregation of these structures. Some papers have recently been published on the aggregation of fuzzy algebraic structures considering some of these partitions of fuzzy sets [12,15,43,44]. This current area is being explored and there are many issues with no answer at the moment.…”

“…The study of fuzzy algebraic structures originated soon after the first appearance of Fuzzy Set Theory [10]. Since then, several authors have devoted their efforts to examining the properties of fuzzy algebras [11], fuzzy subgroups [12,13], fuzzy vector spaces [14,15], fuzzy rings [16] or fuzzy semirings [17]. In the context of fuzzy vector spaces (introduced in [14]), the focus is on understanding the distinct fuzzy vector subspaces that can be defined within a vector space.…”