A GENERALIZED PICTURE FUZZY DISTANCE MEASURE FOR RESEARCH TOPIC RECOMMENDATION IN MATHEMATICS
Abstract
Selecting an appropriate research topic is a critical yet challenging task for mathematics students, often hindered by misalignment between student interests, academic competencies, and supervisor availability. Traditional recommendation systems fail to capture the inherent uncertainty and ambiguity in human preferences, leading to suboptimal topic matches and prolonged study durations. This paper develops a research topic recommendation system specifically designed for mathematics students using an innovative Picture Fuzzy Distance Measure (PFDM). The picture fuzzy approach was selected for its comprehensiveness and detail in decision-making. Unlike traditional binary or even intuitionistic fuzzy models, this approach uniquely and simultaneously accommodates three degrees of consideration: positive membership, neutral membership, and negative membership degrees, thereby enabling more comprehensive representation of the complexity and ambiguity in human preferences. The proposed method integrates three main criteria through this approach: student interest measured through structured questionnaires, academic competence based on transcript analysis, and supervisor suitability based on expertise and availability. The developed PFDM has been proven to satisfy all basic metric axioms—non-negativity, identity, symmetry, and triangle inequality—with values bounded within the [0,1] interval. This paper not only provides a theoretical contribution to the development of fuzzy distance measures but also offers a practical solution for research topic recommendation.
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References
L. A. Zadeh, “FUZZY SETS,” Information and Control, vol. 8, no. 3, pp. 338-353, June 1965. doi: https://doi.org/10.1016/S0019-9958(65)90241-X.
C. Kahraman, S. Cevik, O. Basar, and O. S. Cebi, "ROLE OF FUZZY SETS ON ARTIFICIAL INTELLIGENCE METHODS: A LITERATURE REVIEW," Transactions on Fuzzy Sets and Systems, vol. 2, no. 1, pp. 158–178, Mar. 2023.
P. Dutta and A. Konwar, "QUINTIC FUZZY SETS: A NEW CLASS OF FUZZY SETS FOR SOLVING MULTI-CRITERIA DECISION-MAKING PROBLEMS UNDER UNCERTAINTY," Decision Analytics Journal, vol. 11, p. 100449, June 2024. doi: https://doi.org/10.1016/j.dajour.2024.100449.
I. Couso, C. Borgelt, E. Hullermeier, and R. Kruse, "FUZZY SETS IN DATA ANALYSIS: FROM STATISTICAL FOUNDATIONS TO MACHINE LEARNING," IEEE Computational Intelligence Magazine, vol. 14, no. 1, pp. 31–44, Feb. 2019. doi: https://doi.org/10.1109/MCI.2018.2881642.
K. T. Atanassov, "INTUITIONISTIC FUZZY SETS," Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, Aug. 1986. doi: https://doi.org/10.1016/S0165-0114(86)80034-3.
D. Rahma Oktaviani, M. Habiburrohman, I. Kamilia Amalina, and A. History, "APPLICATION OF INTUITIONISTIC FUZZY SETS IN DETERMINING THE MAJOR IN SENIOR HIGH SCHOOL," Desimal: Jurnal Matematika, vol. 5, no. 3, pp. 247–254, Oct. 2022. doi: https://doi.org/10.24042/djm.v5i3.13018.
BB. C. Cuong and V. Kreinovich, "PICTURE FUZZY SETS - A NEW CONCEPT FOR COMPUTATIONAL INTELLIGENCE PROBLEMS," in Proc. Third World Congress on Information and Communication Technologies (WICT’2013), Hanoi, Vietnam, pp 1-6, Dec. 15-18, 2013. doi: https://doi.org/10.1109/WICT.2013.7113099
D. Rahma Oktaviani, "SUATU KAJIAN PICTURE FUZZY SUBGRUP," Jurnal Riset dan Aplikasi Matematika, vol. 7, no. 1, pp. 66–79, Apr. 2023. doi: https://doi.org/10.26740/jram.v7n1.p66-79.
R. Xue, "EVALUATING PHYSICAL EDUCATION QUALITY IN HIGHER EDUCATION USING A PICTURE FUZZY DECISION FRAMEWORK WITH MUIRHEAD MEAN OPERATOR AND MULTIMOORA METHOD," IEEE Access, vol. 13, pp. 18277–18293, Jan. 2025. doi: https://doi.org/10.1109/ACCESS.2025.3532949.
Z. Chen, W. Liang, and S. Luo, "A NOVEL INTEGRATED PICTURE FUZZY MACONT METHOD AND ITS APPLICATION IN TEACHING QUALITY EVALUATION IN HIGHER EDUCATION," IEEE Access, vol. 12, pp. 88345–88356, June 2024. doi: https://doi.org/10.1109/ACCESS.2024.3418035.
R. Zhao, M. Luo, and S. Li, "A DYNAMIC DISTANCE MEASURE OF PICTURE FUZZY SETS AND ITS APPLICATION," Symmetry, vol. 13, no. 3, p. 436, Mar. 2021. doi: https://doi.org/10.3390/sym13030436.
A. K. Adak, M. K. Gunjan, and A. M. Haghighi, "DISTANCE MEASURE OF PICTURE FUZZY SETS AND ITS APPLICATION IN MULTI-CRITERIA DECISION MAKING PROBLEM," Journal of Fuzzy Extension and Applications, vol. 5, no. 4, pp. 594–604, Dec. 2024.
J. Bahasa et al., "PENERAPAN METODE INKUIRI DALAM PEMILIHAN TOPIK TULISAN AKADEMIK," Jurnal Pendidikan dan Pembelajaran, vol. 18, no. 1, pp. 45–56, Feb. 2023.
R. Untari, N. Alawiyah, L. Permatasari, F. Sulistiyarini, and S. Q. Melati, "FAKTOR-FAKTOR PENGHAMBAT MAHASISWA DALAM MENYUSUN SKRIPSI," Academia: Journal of Multidisciplinary Studies, vol. 6, no. 2, pp. 189–204, Dec. 2022. doi: https://doi.org/10.22515/academica.v6i2.5712
J. Yuan, Z. Chen, and M. Wu, "A NOVEL DISTANCE MEASURE AND CRADIS METHOD IN PICTURE FUZZY ENVIRONMENT," International Journal of Computational Intelligence Systems, vol. 16, no. 1, p. 150, Dec. 2023. doi: https://doi.org/10.1007/s44196-023-00354-y.
A. H. Ganie, "A PICTURE FUZZY DISTANCE MEASURE AND ITS APPLICATION TO PATTERN RECOGNITION PROBLEMS," Iranian Journal of Fuzzy Systems, vol. 20, no. 1, pp. 71–85, Jan. 2023, doi: https://doi.org/10.22111/ijfs.2023.7347.
K. Naeem and S. Memiş, "PICTURE FUZZY SOFT SIGMA-ALGEBRA AND PICTURE FUZZY SOFT MEASURE AND THEIR APPLICATIONS TO MULTI-CRITERIA DECISION-MAKING," Granular Computing, vol. 8, no. 2, pp. 397–410, Mar. 2023. doi: https://doi.org/10.1007/s41066-022-00333-2.
G. E. Mostafa, S. Boulaaras, and R. Jan, "NOVEL PICTURE FUZZY DISTANCE MEASURE ρ∗ AND ITS APPLICATION IN MEDICAL DIAGNOSIS," Partial Differential Equations in Applied Mathematics, vol. 10, p. 100679, June 2024. doi: https://doi.org/10.1016/j.padiff.2024.100679.
S. Singh and A. H. Ganie, "APPLICATIONS OF A PICTURE FUZZY CORRELATION COEFFICIENT IN PATTERN ANALYSIS AND DECISION-MAKING," Granular Computing, vol. 7, no. 2, pp. 353–367, Apr. 2022. doi: https://doi.org/10.1007/s41066-021-00269-z.
S. S. Geetha and K. Selvakumari, "A PICTURE FUZZY APPROACH TO SOLVING TRANSPORTATION PROBLEM," European Journal of Molecular & Clinical Medicine, vol. 7, no. 2, pp. 4982–4990, 2020.
S. Singh and S. Kumar, "AN INNOVATIVE DISTANCE MEASURE FOR PICTURE FUZZY SETS AND APPLICATIONS IN MEDICAL DIAGNOSIS AND PATTERN ANALYSIS," International Journal of Fuzzy Systems, 2025. [Online]. Available: https://internationalpubls.com (accessed Apr. 7, 2025)
A. R. Mishra, S.-M. Chen, and P. Rani, "MULTI-ATTRIBUTE DECISION-MAKING BASED ON PICTURE FUZZY DISTANCE MEASURE-BASED RELATIVE CLOSENESS COEFFICIENTS AND MODIFIED COMBINED COMPROMISE SOLUTION METHOD," Information Sciences, vol. 664, p. 120325, Apr. 2024. doi: https://doi.org/10.1016/j.ins.2024.120325.
V. Sanchez-Anguix, R. Chalumuri, R. Aydoğan, and V. Julian, "A NEAR PARETO OPTIMAL APPROACH TO STUDENT-SUPERVISOR ALLOCATION WITH TWO SIDED PREFERENCES AND WORKLOAD BALANCE," Applied Soft Computing, vol. 107, p. 107485, Aug. 2021. doi: https://doi.org/10.1016/j.asoc.2021.107485.
G. Tabansız-Göç, A. Sebatlı-Sağlam, and F. Çavdur, "ANALYZING THE EFFECTS OF DIFFERENT PROBLEM SETTINGS ON THE SATISFACTION LEVELS OF STUDENTS AND SUPERVISORS IN THE STUDENT-SUPERVISOR ALLOCATION PROBLEM," Journal of the Faculty of Engineering and Architecture of Gazi University, vol. 40, no. 2, pp. 1131–1146, Feb. 2025. doi: https://doi.org/10.17341/gazimmfd.1430498.
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