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Journals / Journal of Universal Mathematics / 2026 / Cilt: 9 Sayı: 2

SCALAR MULTIPLICATION AND RELATED MEASURES FOR INTERVAL-VALUED INTUITIONISTIC FUZZY MATRICES

Gökhan Çuvalcıoğlu(MERSİN ÜNİVERSİTESİ)0000-0001-5451-3336
Gizem Efe0000-0001-9957-3252
Pages
124–146
Publication Date
2026-10-25
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

These findings extend the algebraic framework of interval-valued intuitionistic fuzzy matrices and offer a starting point for studying further operations and their relationships with matrix measures.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study several measures and algebraic properties of interval-valued intuitionistic fuzzy matrices.
📊
Key Findings & Data:Examples illustrate how scalar multiplication works and help explain the theoretical results.
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Conclusion & Impact:These findings extend the algebraic framework of interval-valued intuitionistic fuzzy matrices and offer a starting point for studying further operations and their relationships with matrix measures.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Intuitionistic fuzzy set · interval valued intuitionistic fuzzy set · interval valued intuitionistic fuzzy matrix

Abstract

In this paper, we study several measures and algebraic properties of interval-valued intuitionistic fuzzy matrices. We define the Hamming, generalized Hamming, Euclidean, and generalized Euclidean measures and prove their main properties. We also show that these measures remain unchanged when both matrices are transposed. Next, we introduce scalar multiplication using a pair of parameters and examine its associativity and distributive properties. We then establish several identities and inequalities relating this operation to the Hamming and Euclidean measures. Examples illustrate how scalar multiplication works and help explain the theoretical results. These findings extend the algebraic framework of interval-valued intuitionistic fuzzy matrices and offer a starting point for studying further operations and their relationships with matrix measures.

Özet

In this paper, we study several measures and algebraic properties of interval-valued intuitionistic fuzzy matrices. We define the Hamming, generalized Hamming, Euclidean, and generalized Euclidean measures and prove their main properties. We also show that these measures remain unchanged when both matrices are transposed. Next, we introduce scalar multiplication using a pair of parameters and examine its associativity and distributive properties. We then establish several identities and inequalities relating this operation to the Hamming and Euclidean measures. Examples illustrate how scalar multiplication works and help explain the theoretical results. These findings extend the algebraic framework of interval-valued intuitionistic fuzzy matrices and offer a starting point for studying further operations and their relationships with matrix measures.

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Cite This Article

Çuvalcıoğlu, G., Efe, G. (2026). SCALAR MULTIPLICATION AND RELATED MEASURES FOR INTERVAL-VALUED INTUITIONISTIC FUZZY MATRICES. Journal of Universal Mathematics, Cilt: 9 Sayı: 2, 124–146. https://doi.org/10.33773/jum.2059656

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References (8)

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