The lattices of 𝔏-fuzzy state filters in state residuated lattices-Reference-Cited by-同舟云学术

The lattices of 𝔏-fuzzy state filters in state residuated lattices

Published:2020-12-01 Issue:6 Volume:70 Page:1289-1306
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

He Pengfei¹,Wang Juntao²,Yang Jiang³

Affiliation:

1. School of Mathematics and Information Science , Shaanxi Normal University , Xi’an , 710119 , China

2. School of Science , Xi’an Shiyou University , Xi’an , 710065 , China

3. School of Arts and Sciences , Shaanxi University of Science and Technology , Xi’an , 710021 , China

Abstract

Abstract In the paper, we introduce 𝔏-fuzzy state filters in state residuated lattices and investigate their related properties, where 𝔏 is a complete Heyting algebra. Moreover, we study the 𝔏-fuzzy state co-annihilator of an 𝔏-fuzzy set with respect to an 𝔏-fuzzy state filter. Finally, using the 𝔏-fuzzy state co-annihilator, we investigate lattice structures of the set of some types of 𝔏-fuzzy state filters in state residuated lattices. In particular, we prove that: (1) the set FSF[L] of all 𝔏-fuzzy state filters is a complete Heyting algebra; (2) the set Sν FSF[L] of all stable state filters relative to an 𝔏-fuzzy set ν is also a complete Heyting algebra; (3) the set Iμ FSF[L] of all involutory 𝔏-fuzzy state filters relative to an 𝔏-fuzzy state filter μ is a complete Boolean algebra.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0432/pdf

Reference36 articles.

1. Bahls, P.—Cole, J.—Jipsen, P.—Tsinakis, C.: Cancellative residuated lattices, Algebra Universalis 50 (2003), 83–106.

2. Blount, K.—Tsinakis, C.: The structure of residuated lattices, Internat. J. Algebra Comput. 13 (2003), 437–461.

3. Blyth, T. S.: Lattices and Ordered Algebraic Structures, Springer, London, 2005.

4. Chang, C. C.: Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467–490.

5. Ciungu, L. C.: Bosbach and Riečan states on residuated lattices, J. Appl. Funct. Anal. 2 (2008), 175–188.

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. ℒ-fuzzy Annihilators in Residuated Lattices;Mathematica Slovaca;2023-12-01

2. Some results on state ideals in state residuated lattices;Soft Computing;2023-10-17

3. The prime state ideal theorem in state residuated lattices;CATEG GEN ALGEBRAIC;2023

4. State monadic residuated lattices and their corresponding filters;Journal of Intelligent & Fuzzy Systems;2023-01-30

5. On State Ideals and State Relative Annihilators in De Morgan State Residuated Lattices;International Journal of Mathematics and Mathematical Sciences;2022-06-26