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<p>This paper introduces a topology on fuzzy directed graphs without loops and extends it to a generalized topology based on the non-empty membership edge set. We define the directed maximal path along the edges and select a subset collection from its edge set. The topology is formed by arbitrary unions of these subsets, including the empty set. We present examples of this topology and examine the induced topological space, focusing on connectedness in both connected and disconnected fuzzy graphs. We also analyze how the space reacts to conditions on the fuzzy graph structure. Finally, we apply the framework to stock market analysis and mutual fund investment decisions by optimizing risk factors, integrating current market positions, and analyzing average past 5-years profits to support high-profit strategies.</p>

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On generalized topological spaces derived from maximal path edges in fuzzy graphs

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Swarnakamal Adhikari,
  • Ganesh Ghorai

摘要

This paper introduces a topology on fuzzy directed graphs without loops and extends it to a generalized topology based on the non-empty membership edge set. We define the directed maximal path along the edges and select a subset collection from its edge set. The topology is formed by arbitrary unions of these subsets, including the empty set. We present examples of this topology and examine the induced topological space, focusing on connectedness in both connected and disconnected fuzzy graphs. We also analyze how the space reacts to conditions on the fuzzy graph structure. Finally, we apply the framework to stock market analysis and mutual fund investment decisions by optimizing risk factors, integrating current market positions, and analyzing average past 5-years profits to support high-profit strategies.