The lattice generated by hesitant fuzzy filters in pseudo-BCI algebras
- Authors
- Bo, Chunxin; Zhang, Xiaohong; Shao, Songtao; Park, Choonkil
- Issue Date
- Oct-2018
- Publisher
- IOS PRESS
- Keywords
- Hesitant fuzzy set; pseudo-BCI algebra; hesitant fuzzy filter; anti-grouped hesitant fuzzy filter; lattice
- Citation
- JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, v.35, no.3, pp.3333 - 3345
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
- Volume
- 35
- Number
- 3
- Start Page
- 3333
- End Page
- 3345
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/149215
- DOI
- 10.3233/JIFS-172024
- ISSN
- 1064-1246
- Abstract
- The notion of hesitant fuzzy set is introduced by V. Torra, which is a very useful tool to express peoples’ hesitancy in daily life. The notion of pseudo-BCI algebra is introduced by W. A. Dudek and Y. B. Jun, which is a kind of nonclassical logic algebra and close connection with various non-commutative fuzzy logic algebras. In this paper, hesitant fuzzy theory is applied to pseudo-BCI algebras. The new concepts of hesitant fuzzy filter and anti-grouped hesitant fuzzy filter in pseudo-BCI algebras are proposed, and their characterizations are presented. Also, the relationships between fuzzy filters and hesitant fuzzy filters are discussed. Moreover, by introducing the notion of tip-extended pair of hesitant fuzzy filters, a new union operation (generated by the union of two hesitant fuzzy filters) is defined and it is proved that the set of all hesitant fuzzy filters in pseudo-BCI algebras forms a bounded distributive lattice about intersection and the new union.
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