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All Journal Jurnal Matematika UNAND Square : Journal of Mathematics and Mathematics Education
Candra, Ainun Esti
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Computer Science & IT Education Mathematics

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Sifat-Sifat Matriks Normal dalam Aljabar Max-Plus Muanalifah, Any; Romadiastri, Yulia; Albab, Muhammad Ulil; Nurwan; Artes, Rosalio G.; Candra, Ainun Esti
Square : Journal of Mathematics and Mathematics Education Vol. 7 No. 2 (2025)
Publisher : UIN Walisongo Semarang

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Abstract

Dalam aljabar max-plus, matriks normal didefinisikan sebagai matriks persegi  dimana elemen pada diagonal utamanya adalah nol dan elemen non diagonal utamanya adalah bilangan real non positif. Struktur ini memberikan sifat keteraturan khusus terhadap operasi maksimum dan penjumlahan pada aljabar maxplus. Pada artikel ini akan di bahas review tentang matriks  normal dan perilaku stabil terhadap perpangkatan, termasuk kondisi tertentu yang menjamin sifat idempoten. Selain itu, diperoleh kriteria struktural yang memastikan kekomutatifan dua matriks normal terhadap perkalian max-plus.
ALGEBRAIC LAWS AND PROPERTIES OF PICTURE FUZZY SETS Oktaviani, Dinni Rahma; Habiburrohman, Muhammad; Norasia, Yolanda; Candra, Ainun Esti
Jurnal Matematika UNAND Vol. 15 No. 2 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.2.150-162.2026

Abstract

This paper investigates the fundamental algebraic laws and properties that hold in the framework of Picture Fuzzy Sets (PFS). Picture fuzzy sets extend classical fuzzy and intuitionistic fuzzy sets by incorporating an additional degree of neutrality, providing a more refined representation of uncertainty. We examine the validity of standard algebraic laws such as commutativity, associativity, distributivity, and idempotency under picture fuzzy operations, and identify the conditions under which these laws are preserved. The study contributes to a deeper understanding of the algebraic behavior of PFS and forms a theoretical basis for their further applications in fuzzy decision-making and information processing.
Co-Authors Albab, Muhammad Ulil Artes, Rosalio G. Dinni Rahma Oktaviani Habiburrohman, Muhammad Muanalifah, Any Norasia, Yolanda Nurwan Yulia Romadiastri