Aggregation of fuzzy vector spaces

Carlos Bejines

Kybernetika (2023)

  • Volume: 59, Issue: 5, page 752-767
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Bejines, Carlos. "Aggregation of fuzzy vector spaces." Kybernetika 59.5 (2023): 752-767. <http://eudml.org/doc/299161>.

@article{Bejines2023,
abstract = {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.},
author = {Bejines, Carlos},
journal = {Kybernetika},
keywords = {aggregation function; vector spaces; algebraic structures; monotone functions},
language = {eng},
number = {5},
pages = {752-767},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Aggregation of fuzzy vector spaces},
url = {http://eudml.org/doc/299161},
volume = {59},
year = {2023},
}

TY - JOUR
AU - Bejines, Carlos
TI - Aggregation of fuzzy vector spaces
JO - Kybernetika
PY - 2023
PB - Institute of Information Theory and Automation AS CR
VL - 59
IS - 5
SP - 752
EP - 767
AB - 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.
LA - eng
KW - aggregation function; vector spaces; algebraic structures; monotone functions
UR - http://eudml.org/doc/299161
ER -

References

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  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. MR3675898
  2. Bejines, C., Ardanza-Trevijano, S., Chasco, M., Elorza, J., , Fuzzy Sets Systems 446 (2022), 53-67. MR4473741DOI
  3. Bejines, C., Ardanza-Trevijano, S., Elorza, J., , Axioms 10 (2021), 3, 201. DOI
  4. Bejines, C., Chasco, M. J., Elorza, J., , Fuzzy Sets Systems 418 (2021), 170-184. MR4266805DOI
  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. MR1936384
  8. Das, P., , Fuzzy Sets Systems 25 (1988), 1, 73-85. MR0918011DOI
  9. Das, P. S., , J. Math. Anal. Appl. 84 (1981), 1, 264-269. MR0639537DOI
  10. Dixit, V., Kumar, R., Ajmal, N., , Fuzzy Sets Systems 37 (1990), 3, 359-371. MR1077151DOI
  11. Drewniak, J., Dudziak, U., Preservation of properties of fuzzy relations during aggregation processes., Kybernetika 43 (2007), 2, 115-132. MR2343390
  12. Iranmanesh, A., Naraghi, H., The connection between some equivalence relations on fuzzy subgroups., Iranian J. Fuzzy Systems 8 (2011), 5, 69-80. MR2907795
  13. Jain, A., Fuzzy subgroups and certain equivalence relations., Iranian J. Fuzzy Systems 3 (2006), 2, 75-91. MR2286681
  14. Katsaras, A., Liu, D., 10.1016/0022-247X(77)90233-5, J. Math. Anal. App. 58 (1977), 135-146. MR0440481DOI10.1016/0022-247X(77)90233-5
  15. Kouchakinejad, F., Šipošová, A., , Kybernetika 53 (2017), 1, 129-136. MR3638560DOI
  16. Mordeson, J. N., Bhutani, K. R., Rosenfeld, A., Fuzzy Group Theory., Springer, 2005. 
  17. Murali, V., Makamba, B. B., , Fuzzy Sets Systems 123 (2001), 2, 259-264. MR1849411DOI
  18. Pedraza, T., Ramos-Canós, J., Rodríguez-López, J., , Symmetry 13 (2021), 10, 1908. DOI
  19. Pedraza, T., Rodríguez-López, J., Valero, Ó., , Inform. Sci. 581 (2021), 362-389. MR4319806DOI

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