On direct sums of (L, M)-fuzzy convex spaces

Key Points

• To generalize the concept of direct sums within (L, M)-fuzzy convex spaces and explore their properties.
• Generalization of direct sum concepts for (L, M)-fuzzy convex spaces.
• Discussion of properties between direct sums and factor spaces.
• Characterization of (L, M)-fuzzy direct sum convex spaces using level L-direct sums.
• Investigation into additivity of different separability types.
• Identified key properties linking direct sums of (L, M)-fuzzy convex spaces and their factor spaces.
• Established characterizations of (L, M)-fuzzy direct sum convex spaces.
• Examined the additivity conditions related to separability types, revealing new insights.