Fuzzy Systems and its Applications

Fuzzy Systems and its Applications

Intuitionistic soft L-preideals in EQ-algebras

Document Type : Original Article

Author
Mahmood Bakhshi
Department of Mathematics, University of Bojnord
10.22034/jfsa.2024.455888.1204
Abstract
In this paper, considering the concept of an L-set, where L is a complete lattice, we introduce the concepts of intuitionistic soft L-preideal and intuitionistic soft L-ideal in EQ-algebras and present their preliminary properties and equivalent conditions. We also investigate their lattice structure and show that they form a complete lattice under the set-inclusion relation. Furthermore, we introduce some algebraic operations on these concepts and study their properties.

Additionally, we introduce the concepts of intuitionistic soft L-prefilters and intuitionistic soft L-intuitive in EQ-algebras. We provide equivalent conditions for them and investigate the relationships between intuitionistic soft L-preideals/L-ideals and intuitionistic soft L-prefilters/L-filters.
Keywords
EQ-algebra
intuitionistic soft L-preideal
intuitionistic soft L-prefilter
complete lattice
[1] Akhlaghinia, N., Aaly Kologani, M., Borzooei, R. A., Xin, X. L. (2021) On the category of EQ[1]algebras. Bulletin of the Section Logic, 50, 397-419.
[2] Akhlaghinia, N., Borzooei, R. A. and Aaly Kologani, M. (2021) Preideals in EQ-algebras. Soft Computing, 25, 12703-12715.
[3] Atanassove, K., Stoeva, S. (1984) Intuitionistic L-fuzzy sets, in R. Trappl. Ed., Cybernetics and System Research 2 (Elsevier Sci. Publ., Amsterdam), 539-540.
[4] Bakhshi, M., Khavari, M. M. and Nazifi, M. (2020) Isomorphisms in EQ-algebras. Disscussiones Mathematicae: General Algebra and Applications, 40, 267-274.
[5] Blyth, T. S. (2005) Lattices and Ordered Algebraic Structures, Springer-Verlag: London.
[6] Borzooei, R. A., Akhlaginia, N., Xin, X. L., Aaly, M. (2021) Constructing some logical algebras from EQ-algebras. Filomat, 35, 2747-2760.
[7] Borzooei, R. A., Ganji, B. (2015) States on EQ-algebras. J. Intelligent & Fuzzy Systems, 29, 209- 221.
[8] Bouchon-Meunier, B., Yager, R. R., Zadeh, L. A. (1995) Fuzzy logic and soft computing. World Scientific Publisher, Singapore.
[9] El-Zekey, M. (2010) Representable good EQ-algebras. Soft Computing, 14, 1011-1023.
[10] El-Zekey, M., Novák, V. and Mesiar, R. (2011) On good EQ-algebras. Fuzzy Sets and Systems, 178, 1-23.
[11] Goguen, A. J. (1967) L-fuzzy sets. Journal of Mathematical Analysis and Applications, 18 (1), 145- 174.
[12] Maji, P. K., Biswas, R., Roy, A. R. (2003) Soft set theory, Computers and Mathematics with Applications, 45, 555-562.
[13] Ming Ma, Zh. and Qing Hu, B. (2012) Fuzzy EQ-filters of EQ-algebras. Quantitative Logic and Soft Computing, 528-535.
[14] Molodtsove, D. (1999) Soft set theory-First results, Computers and Mathematics with Applications, 37, 19-31.
[15] Novák, V. (2011) EQ-algebras-based fuzzy type theory and its extensions. Logic J. IGPL, 19, 512- 542.
[16] Novák, V. and De Baets, B. (2009) EQ-algebras. Fuzzy Sets and Systems, 160, 2956-2978.
[17] Xin, X. L. (2020) Residuated lattices may not be residuated lattices. Fuzzy Set and Systems, 382, 120-128.
[18] Zadeh, L. A. (1965) Fuzzy sets. Information and control, 8(3), 338-353.
[19] Zadeh, L. A. (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy sets and systems, 1(1), 3-28.
[20] Zadeh, L. A. (1994) Soft computing and fuzzy logic, IEEE software, 11(6), 48-56.
[21] Zadeh, L. A. (1996) Fuzzy logic, neural networks, and soft computing. Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers by Lotfi A Zadeh, 775-782
Fuzzy Systems and its Applications
Volume 7, Issue 1 - Serial Number 14
Open Access Statement
June 2024
Pages 25-51

  • Receive Date 05 May 2024
  • Revise Date 20 June 2024
  • Accept Date 18 August 2024