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- W2740407498 abstract "Three-way decision theory is an extension of the commonly used binary-decision model with an added third option. It is originally introduced to explain the three regions of probabilistic rough sets. Every object in a three-way decision model can be assigned to one of the three regions according to its evaluation value under an evaluation function. This paper first introduces three-way decision models based on subset-evaluation which generalize the original models. By the axiomatic approach, we characterize a matroid in terms of evaluation function and then define three-way matroids based on this characterization. Furthermore, three-way matroids are generalized to three-way fuzzy matroids and an equivalent description of three-way fuzzy matroid in terms of fuzzy independent set system is presented. Finally, we give the second description of three-way fuzzy matroid: a three-way fuzzy matroid is exactly the greatest element of an equivalence class. Additionally, relations of notions introduced in this paper are also pointed out. • This paper introduces two generalizations of matroids based on subset-evaluation based three-way decision models. • Two explanations of three-way fuzzy matroids are given. • Three-way matroids and three-way fuzzy matroids provide new context for some famous algorithms in matroid theory." @default.
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- W2740407498 date "2017-11-01" @default.
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- W2740407498 title "Generalized matroids based on three-way decision models" @default.
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- W2740407498 doi "https://doi.org/10.1016/j.ijar.2017.07.012" @default.
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