Journal
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
Volume 83, Issue -, Pages 142-159Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ijar.2017.01.005
Keywords
Matroids; Rough sets; Three-way decision; Three-way decision space
Categories
Funding
- National Natural Science Foundation of China [61202178, 61472471, 11571012]
- Fundamental Research Funds for the Central Universities [JB150709]
- China Postdoctoral Science Foundation [2016M602851]
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The notion of three-way decisions was originally introduced based on the need to explain the three regions of probabilistic rough sets. In a three-way decision model, every object can be evaluated by a function and according to the evaluation value, the object can be arranged in one of the three regions (i.e., positive, negative, and boundary regions). In this study, we generalize Yao's three-way decision models to a case where every subset in the universe can be evaluated by the evaluation function, and we then propose generalized three-way models. The properties and examples of these new models are presented, as well as extensions of these models. We also give some remarks regarding Hu's three-way decision spaces. Three-way matroids are introduced based on Hu's axiomatic approach and our generalized three-way models. Furthermore, three-way matroids are generalized to three fuzzy matroids as an application of our new model. Finally, we suggest future research related to our new models and three-way fuzzy matroids. (C) 2017 Elsevier Inc. All rights reserved.
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