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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vira Hari Krisnawati
Brawijaya University
Mathematics

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An Integrated Circular Intuitionistic Fuzzy SWARA-TOPSIS Framework for Supplier Selection: Evidence from Pia Cap Mangkok Putri Rosmerry Retno Sahabir; Vira Hari Krisnawati; Marsudi Marsudi
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.36728

Abstract

In food industries, supplier evaluation and selection are strategic activities that influence product freshness, operational continuity, and supply chain sustainability. However, this process is often hindered by uncertainty and ambiguity in expert judgments. In response to these challenges, the present study proposes an integrated decision-making method that combines Circular Intuitionistic Fuzzy Set (CIFS), the Stepwise Weight Assessment Ratio Analysis (SWARA), and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). CIFS capture uncertainty in expert opinions, SWARA determines systematic criteria weights, and TOPSIS—enhanced with the Garg et al. distance measure—ranks suppliers based on aggregated evaluations. The evaluation involves seven key criteria: flexibility, capacity, quality, service, reputation, price, and lead time, assessed across five potential suppliers. Applied to Toko Pia Cap Mangkok, a traditional snack producer in Malang, Indonesia, the method identifies lead time, capacity, and reputation as the most critical criteria. Among the alternatives, Supplier $A_1$ consistently ranks first across optimistic, pessimistic, and combined scenarios, confirming its robustness and reliability, followed by Supplier $A_2$, while others perform less competitively. This study advances fuzzy-based multi-criteria decision-making by integrating CIFS–SWARA–TOPSIS, ensuring reliable supplier selection under uncertainty and offering a replicable framework for decision-makers in the food industry.
Energy and Topological Indices of Complete Bipartite Subgraphs Kiki Amanda Eka Meilina; Noor Hidayat; Vira Hari Krisnawati
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.32765

Abstract

This paper investigates the complete bipartite subgraphs induced within the zero-divisor graph of a commutative ring formed by the direct product of three distinct modular integer rings. The set of nonzero zero-divisors is partitioned into six disjoint subsets based on the position of the zero component in each element. Six complete bipartite subgraphs are constructed and analysed by pairing subsets with zeros in different positions. For each subgraph, we compute the energy, Laplacian energy, and three degree-based multiplicative topological indices, namely the Narumi–Katayama index, and the first and second multiplicative Zagreb indices. The results are expressed in closed-form formulas and reveal consistent structural patterns, highlighting the relationship between the algebraic properties of the ring and the graph theoretic characteristics of the induced subgraphs.
Co-Authors Hidayat, Noor Kiki Amanda Eka Meilina Marsudi Marsudi Putri Rosmerry Retno Sahabir