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<p>Recent advancements in the field have demonstrated that the ordinal sum of triangular norms on bounded lattices can be used to create new triangular norms. In this paper, we propose a new method for constructing triangular norms on bounded lattices by leveraging triangular subnorms defined on their sublattices and outline sufficient conditions for this construction. We also provide several examples to illustrate that our construction method differs from existing methods for obtaining ordinal sums of triangular norms on bounded lattices. Additionally, we demonstrate that this new construction method is generalized by induction to a modified ordinal sum construction for producing triangular norms on bounded lattices.</p>

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A new technique for developing triangular norms and triangular conorms on bounded lattices

  • 期刊论文

  • 发表日期：

    2026年7月3日

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  • Gül Deniz Çaylı

摘要

Recent advancements in the field have demonstrated that the ordinal sum of triangular norms on bounded lattices can be used to create new triangular norms. In this paper, we propose a new method for constructing triangular norms on bounded lattices by leveraging triangular subnorms defined on their sublattices and outline sufficient conditions for this construction. We also provide several examples to illustrate that our construction method differs from existing methods for obtaining ordinal sums of triangular norms on bounded lattices. Additionally, we demonstrate that this new construction method is generalized by induction to a modified ordinal sum construction for producing triangular norms on bounded lattices.