Introducing Interpolative Boolean algebra into Intuitionistic fuzzy sets
Authors
Pavle Miloševic, Ana Poledica, Aleksandar Rakicevic, Bratislav Petrovi, Dragan Radojevi
Corresponding Author
Pavle Miloševic
Available Online June 2015.
- DOI
- 10.2991/ifsa-eusflat-15.2015.196How to use a DOI?
- Keywords
- Interpolative Boolean algebra, Intuitionistic fuzzy sets, IFS operations, law of excluded middle, law of contradiction.
- Abstract
In this paper, we introduce Interpolative Boolean alge-bra (IBA) as a suitable algebra for intuitionistic fuzzy sets (IFSs). IBA is [0,1]-valued realization of Boolean algebra, consistent with Boolean axioms and theorems. IFS theory takes into account both membership and non-membership function, so it can be viewed as a ge-neralization of the traditional fuzzy set theory. We pro-pose a realization of IFS conjunction and disjunction operations based on IBA. This may be viewed as a ge-neralized framework for IFS-IBA calculus. Finally, we investigate the validity of the laws of contradiction and excluded middle in our approach.
- Copyright
- © 2015, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - CONF AU - Pavle Miloševic AU - Ana Poledica AU - Aleksandar Rakicevic AU - Bratislav Petrovi AU - Dragan Radojevi PY - 2015/06 DA - 2015/06 TI - Introducing Interpolative Boolean algebra into Intuitionistic fuzzy sets BT - Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology PB - Atlantis Press SP - 1389 EP - 1394 SN - 1951-6851 UR - https://doi.org/10.2991/ifsa-eusflat-15.2015.196 DO - 10.2991/ifsa-eusflat-15.2015.196 ID - Miloševic2015/06 ER -