A Novel Weighted Fuzzy Harmonic Mean Aggregation Operator on Fuzzy Graphs for Multi-Criteria Decision Making and Its Application in AI-Based Recommendation Systems
DOI:
https://doi.org/10.68050/JAMS.2026.335Keywords:
Fuzzy Graph, Harmonic Mean, Aggregation Operator, Multi-Criteria Decision Making, Recommendation System, Artificial Intelligence, Fuzzy SetsAbstract
Multi-criteria decision making (MCDM) under uncertainty often uses aggregation operators to combine fuzzy criteria evaluations into a single score. However, commonly used weighted arithmetic and geometric operators tend to over-reward alternatives that perform well on some criteria while masking weak performance on others undesirable in risk-sensitive applications like recommendation systems. This paper proposes a Weighted Fuzzy Harmonic Mean Aggregation Operator (WFHMAO) defined over a fuzzy decision graph, where alternatives are vertices and criteria-wise satisfaction degrees are fuzzy edge memberships. Its harmonic mean structure penalizes low membership values more strongly than arithmetic or geometric aggregation, making it well-suited for cases where a single poor criterion should meaningfully lower an alternative's score. We formally establish idempotency, boundedness, monotonicity, and commutativity of the operator, and embed it as a fusion layer in a hybrid AI recommendation framework combining content-based similarity, collaborative-filtering scores, and popularity signals. A case study on online course recommendation, compared against weighted arithmetic mean (WAM) and weighted geometric mean (WGM), shows that WFHMAO produces more conservative, discrimination-sensitive rankings with reduced influence of criterion-specific outliers.
References
[1] Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
[2] Rosenfeld, A. (1975). Fuzzy graphs. In L. A. Zadeh, K. S. Fu, & M. Shimura (Eds.), Fuzzy Sets and Their Applications to Cognitive and Decision Processes (pp. 77–95). Academic Press.
[3] Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man, and Cybernetics, 18(1), 183–190.
[4] Saaty, T. L. (1980). The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation. McGraw-Hill.
[5] Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
[6] Xu, Z. (2007). Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems, 15(6), 1179–1187.
[7] Yager, R. R. (2013). Pythagorean fuzzy subsets. In Proceedings of the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (pp. 57–61). IEEE.
[8] Shit, C., Ghorai, G., Xin, Q., & Gulzar, M. (2022). Harmonic aggregation operator with trapezoidal picture fuzzy numbers and its application in a multiple-attribute decision-making problem. Symmetry, 14(1), 135.
[9] Ko, H., Lee, S., Park, Y., & Choi, A. (2022). A survey of recommendation systems: Recommendation models, techniques, and application fields. Electronics, 11(1), 141.
[10] Bhattacharya, A., & Pal, M. (2023). A fuzzy graph theory approach to the facility location problem: A case study in the Indian banking system. Mathematics, 11(13), 2992.
[11] Ahmad, U., & Sabir, M. (2023). Multicriteria decision-making based on the degree and distance-based indices of fuzzy graphs. Granular Computing, 8(4), 793–807.
[12] Karn, A. L., Karna, R. K., Kondamudi, B. R., Bagale, G., Pustokhin, D. A., Pustokhina, I. V., & Sengan, S. (2023). Customer centric hybrid recommendation system for e-commerce applications by integrating hybrid sentiment analysis. Electronic Commerce Research, 23(1), 279–314.
[13] Irvanizam, I., & Zahara, N. (2024). An improved Rafsi method based on single-valued trapezoidal neutrosophic number and its harmonic and arithmetic mean operators for healthcare service quality evaluation. Expert Systems with Applications, 248, 123343.
Deng, J., Chen, J., Wang, S., Ye, J., & Wang, Y. (2024). A novel fuzzy neural collaborative filtering for recommender systems. Expert Systems with Applications, 258, 125153.
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Articles published in the Journal of Advanced Multidisciplinary Studies (JAMS) are licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0), unless otherwise stated. Authors retain copyright of their work and grant JAMS the right of first publication.
