Some construction methods of interval-valued implications on bounded lattices
IRANIAN JOURNAL OF FUZZY SYSTEMS, vol.21, no.6, pp.33-54, 2024 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 21 Issue: 6
- Publication Date: 2024
- Doi Number: 10.22111/ijfs.2024.48572.8569
- Journal Name: IRANIAN JOURNAL OF FUZZY SYSTEMS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
- Page Numbers: pp.33-54
- Keywords: bounded lattice, construction method, Implications, interval-valued fuzzy set, lattice of closed intervals, order preserving function, order reversing function
- Karadeniz Technical University Affiliated: Yes
Abstract
In recent years, implication operators have been studied intensively from many perspectives. These include the study of construction methods of implication operators. Additionally, it has been investigated whether some aggregation operators such as t-norm in interval-valued L-fuzzy set theory are representable. In this paper, we present some construction methods to obtain interval-valued implications, which are i-representable or not depending on the lattice and fuzzy logic operators, via some fuzzy logic operators, order preserving and/or order reversing functions. Moreover, many illustrative examples are included.