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<p>This paper explores Pythagorean fuzzy triangular norms and conorms using the theory of residual implicator and co-implicator, respectively. The Archimedean and nilpotent Pythagorean fuzzy triangular norms and conorms within a complete lattice (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathfrak {L}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">L</mi> </math></EquationSource> </InlineEquation>) are presented. Representation theorems in Pythagorean fuzzy sets leverage these techniques to handle uncertainty efficiently, improving fuzziness’s comprehension and practical implementation. The theoretical insights, backed by illustrative examples and mathematical proofs, provide a thorough comprehension of how Pythagorean fuzzy implications are represented within the context of Pythagorean fuzziness.</p>

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Encoding Residuation Principle and Representation Theorem Under Pythagorean Fuzzy Using Triangular Norm and Conorm

  • 期刊论文

  • 发表日期：

    2025年2月19日

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  • V. Keerthana,
  • B. Baranidharan,
  • G. S. Mahapatra

摘要

This paper explores Pythagorean fuzzy triangular norms and conorms using the theory of residual implicator and co-implicator, respectively. The Archimedean and nilpotent Pythagorean fuzzy triangular norms and conorms within a complete lattice ( \({\mathfrak {L}}\) L ) are presented. Representation theorems in Pythagorean fuzzy sets leverage these techniques to handle uncertainty efficiently, improving fuzziness’s comprehension and practical implementation. The theoretical insights, backed by illustrative examples and mathematical proofs, provide a thorough comprehension of how Pythagorean fuzzy implications are represented within the context of Pythagorean fuzziness.