2995-3162ISSN (Online)
Volume 6 , Issue 1 , PP: 22-34, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
Takaaki Fujita 1 * , Ajoy Kanti Das 2
Doi: https://doi.org/10.54216/PMTCS.060102
A Functorial Structure is defined as a covariant functor F : C → Set, assigning sets to objects and functions to morphisms, ensuring functoriality. In this paper, we introduce and formally define two new concepts: the HybridFunctorial Structure and the MultiFunctorial Structure. A HybridFunctorial Structure combines two functors on the same category, linked by a natural transformation, ensuring consistent pushforward compatibility. A MultiFunctorial Structure involves multiple functors indexed by a preorder, coherently related via natural transformations, forming compatible families with functorial consistency.
Functorial Structure , HybridFunctorial Structure , MultiFunctorial Structure
[1] Takaaki Fujita and Florentin Smarandache. A unified framework for u-structures and functorial structure: Managing super, hyper, superhyper, tree, and forest uncertain over/under/off models. Neutrosophic Sets and Systems, 91:337–380, 2025.
[2] Lotfi A Zadeh. Fuzzy sets. Information and control, 8(3):338–353, 1965.
[3] John N Mordeson and Premchand S Nair. Fuzzy graphs and fuzzy hypergraphs, volume 46. Physica, 2012.
[4] Prem Kumar Singh et al. Dark data analysis using intuitionistic plithogenic graphs. International Journal of Neutrosophic Sciences, 16(2):80–100, 2021.
[5] S Gomathy, D Nagarajan, S Broumi, and M Lathamaheswari. Plithogenic sets and their application in decision making. Infinite Study, 2020.
[6] Vicenc¸ Torra and Yasuo Narukawa. On hesitant fuzzy sets and decision. In 2009 IEEE international conference on fuzzy systems, pages 1378–1382. IEEE, 2009.
[7] Zeshui Xu. Hesitant fuzzy sets theory, volume 314. Springer, 2014.
[8] Sina Salimian and Seyed Meysam Mousavi. A multi-criteria decision-making model with interval-valued intuitionistic fuzzy sets for evaluating digital technology strategies in covid-19 pandemic under uncertainty. Arabian Journal for Science and Engineering, 48:7005-7017, 2022.
[9] Krassimir T Atanassov. Circular intuitionistic fuzzy sets. Journal of Intelligent & Fuzzy Systems, 39(5):5981–5986, 2020.
[10] Aiwu Zhang, Jianguo Du, and Hongjun Guan. Interval valued neutrosophic sets and multi-attribute decision-making based on generalized weighted aggregation operator. J. Intell. Fuzzy Syst., 29:2697–2706, 2015.
[11] Pu Ji, Jian qiang Wang, and Hong yu Zhang. Frank prioritized bonferroni mean operator with single-valued neutrosophic sets and its application in selecting third-party logistics providers. Neural Computing and Applications, 30:799–823, 2018.
[12] V Divya, J Jesintha Rosline, and A Anthoni Amali. Regularity of fermatean quadripartitioned neutrosophic fuzzy graph. In International Conference on Intelligent and Fuzzy Systems, pages 39–47. Springer, 2025.
[13] M Ramya, S Murali, and R Radha. Fermatean quadripartitioned neutrosophic lie algebra. Fuzzy, Intuitionistic and Neutrosophic Set Theories and their Applications in Decision Analysis, page 72, 2025.
[14] Zhouming Ma and Jusheng Mi. Boundary region-based rough sets and uncertainty measures in the approximation space. Information Sciences, 370:239–255, 2016.
[15] Zdzisław Pawlak. Rough sets. International journal of computer & information sciences, 11:341–356, 1982.
[16] Pradip Kumar Maji, Ranjit Biswas, and A Ranjan Roy. Soft set theory. Computers & mathematics with applications, 45(4-5):555–562, 2003.
[17] Dmitriy Molodtsov. Soft set theory-first results. Computers & mathematics with applications, 37(4-5):19 31, 1999.
[18] Kaoru Hirota. Concepts of probabilistic sets. Fuzzy sets and systems, 5(1):31–46, 1981.
[19] Hans-J¨urgen Zimmermann. Fuzzy set theory—and its applications. Springer Science & Business Media, 2011.
