Geodesic
Aggregation of fuzzy vector spaces
Kybernetika, Tome 59 (2023) no. 5, pp. 752-767
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This paper contributes to the ongoing investigation of aggregating algebraic structures, with a particular focus on the aggregation of fuzzy vector spaces. The article is structured into three distinct parts, each addressing a specific aspect of the aggregation process. The first part of the paper explores the self-aggregation of fuzzy vector subspaces. It delves into the intricacies of combining and consolidating fuzzy vector subspaces to obtain a coherent and comprehensive outcome. The second part of the paper centers around the aggregation of similar fuzzy vector subspaces, specifically those belonging to the same equivalence class. This section scrutinizes the challenges and considerations involved in aggregating fuzzy vector subspaces with shared characteristics. The third part of the paper takes a broad perspective, providing an analysis of the aggregation problem of fuzzy vector subspaces from a general standpoint. It examines the fundamental issues, principles, and implications associated with aggregating fuzzy vector subspaces in a comprehensive manner. By elucidating these three key aspects, this paper contributes to the advancement of knowledge in the field of aggregation of algebraic structures, shedding light on the specific domain of fuzzy vector spaces.
This paper contributes to the ongoing investigation of aggregating algebraic structures, with a particular focus on the aggregation of fuzzy vector spaces. The article is structured into three distinct parts, each addressing a specific aspect of the aggregation process. The first part of the paper explores the self-aggregation of fuzzy vector subspaces. It delves into the intricacies of combining and consolidating fuzzy vector subspaces to obtain a coherent and comprehensive outcome. The second part of the paper centers around the aggregation of similar fuzzy vector subspaces, specifically those belonging to the same equivalence class. This section scrutinizes the challenges and considerations involved in aggregating fuzzy vector subspaces with shared characteristics. The third part of the paper takes a broad perspective, providing an analysis of the aggregation problem of fuzzy vector subspaces from a general standpoint. It examines the fundamental issues, principles, and implications associated with aggregating fuzzy vector subspaces in a comprehensive manner. By elucidating these three key aspects, this paper contributes to the advancement of knowledge in the field of aggregation of algebraic structures, shedding light on the specific domain of fuzzy vector spaces.
DOI : 10.14736/kyb-2023-5-0752
Classification : 03B52, 94D05
Keywords: aggregation function; vector spaces; algebraic structures; monotone functions 
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Bejines, Carlos. Aggregation of fuzzy vector spaces. Kybernetika, Tome 59 (2023) no. 5, pp. 752-767. doi: 10.14736/kyb-2023-5-0752

[1] Appiah, I. K., Makamba, B.: Counting distinct fuzzy subgroups of some rank-3 abelian groups. Iranian J. Fuzzy Systems 14 (2017), 1, 163-181. | MR

[2] Bejines, C., Ardanza-Trevijano, S., Chasco, M., Elorza, J.: Aggregation of indistinguishability operators. Fuzzy Sets Systems 446 (2022), 53-67. | DOI | MR

[3] Bejines, C., Ardanza-Trevijano, S., Elorza, J.: On self-aggregations of min-subgroups. Axioms 10 (2021), 3, 201. | DOI

[4] Bejines, C., Chasco, M. J., Elorza, J.: Aggregation of fuzzy subgroups. Fuzzy Sets Systems 418 (2021), 170-184. | DOI | MR

[5] Bejines, C., Chasco, M. J., Elorza, J., Montes, S.: Equivalence relations on fuzzy subgroups. In: Conference of the Spanish Association for Artificial Intelligence, Springer 2018, pp. 143-153.

[6] Beliakov, G., Pradera, A., Calvo, T., al., et: Aggregation Functions: A Quide for Practitioners, Vol. 221. Springer, 2007.

[7] Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation Operators. Chapter Aggregation Operators: Properties, Classes and Construction Methods, Physica-Verlag, Heidelberg 2002, pp. 3-104. | MR

[8] Das, P.: Fuzzy vector spaces under triangular norms. Fuzzy Sets Systems 25 (1988), 1, 73-85. | DOI | MR

[9] Das, P. S.: Fuzzy groups and level subgroups. J. Math. Anal. Appl. 84 (1981), 1, 264-269. | DOI | MR

[10] Dixit, V., Kumar, R., Ajmal, N.: Level subgroups and union of fuzzy subgroups. Fuzzy Sets Systems 37 (1990), 3, 359-371. | DOI | MR

[11] Drewniak, J., Dudziak, U.: Preservation of properties of fuzzy relations during aggregation processes. Kybernetika 43 (2007), 2, 115-132. | MR

[12] Iranmanesh, A., Naraghi, H.: The connection between some equivalence relations on fuzzy subgroups. Iranian J. Fuzzy Systems 8 (2011), 5, 69-80. | MR

[13] Jain, A.: Fuzzy subgroups and certain equivalence relations. Iranian J. Fuzzy Systems 3 (2006), 2, 75-91. | MR

[14] Katsaras, A., Liu, D.: Fuzzy vector spaces and fuzzy vector topological spaces. J. Math. Anal. App. 58 (1977), 135-146. | DOI | MR

[15] Kouchakinejad, F., Šipošová, A.: A note on the super-additive and sub-additive transformations of aggregation functions: The multi-dimensional case. Kybernetika 53 (2017), 1, 129-136. | DOI | MR

[16] Mordeson, J. N., Bhutani, K. R., Rosenfeld, A.: Fuzzy Group Theory. Springer, 2005.

[17] Murali, V., Makamba, B. B.: On an equivalence of fuzzy subgroups i. Fuzzy Sets Systems 123 (2001), 2, 259-264. | DOI | MR

[18] Pedraza, T., Ramos-Canós, J., Rodríguez-López, J.: Aggregation of weak fuzzy norms. Symmetry 13 (2021), 10, 1908. | DOI

[19] Pedraza, T., Rodríguez-López, J., Valero, Ó.: Aggregation of fuzzy quasi-metrics. Inform. Sci. 581 (2021), 362-389. | DOI | MR

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