An intuitionistic fuzzy approach to S-approximation spaces
Journal of Intelligent & Fuzzy SystemsPublished 30 April 2016
Ali Shakiba, M. R. Hooshmandasl, Bijan Davvaz, Seyed Abolfazl Shahzadeh Fazeli
Citations13
SJR quartileQ2
SJR score0.36
SNIP0.62
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TL;DR
The concept of intuitionistic fuzzy S-approximation spaces is investigated to manage the uncertainty in the intuitionistic fuzzy problems which are not expressible in terms of intuitionistic fuzzy inclusion relations.
Abstract
In this paper, we will investigate the concept of intuitionistic fuzzy S-approximation spaces. This concept can be employed to manage the uncertainty in the intuitionistic fuzzy problems which are not expressible in terms of intuitionistic fuzzy inclusion relations. Also, we have studied these stru ctures from a three-way decisions approach. The monotone intuitionistic fuzzy S-approximation spaces capture some interesting properties which are discussed as well as complement compatible ones.
Keywords
Computer ScienceDecision SciencesMathematics
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Rough Sets: Theoretical Aspects of Reasoning about Data
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