AIMS Mathematics

2022, Issue 2: 2061-2083. doi: 10.3934/math.2022118
Research article

Three-way decision based on canonical soft sets of hesitant fuzzy sets

• Received: 28 July 2021 Accepted: 29 October 2021 Published: 08 November 2021
• MSC : 03E72, 62A86, 68T35, 90B50, 06D72, 94D05

• The theory of three-way decision is built on the philosophy of thinking in threes. The essence of three-way decision is trisecting the whole and taking different strategies for different parts accordingly. The theory of three-way decision has been successfully implemented to diverse fields since it provides an elegant and efficient solution for solving complicated problems. In this paper, a useful representation for hesitant fuzzy sets is obtained by means of canonical soft sets. We also define unit interval parameterized soft sets and their derived hesitant fuzzy sets. Mutual representations and inner connections between hesitant fuzzy sets and soft sets are examined. With the help of soft rough sets, a generalized rough model based on hesitant fuzzy sets is established. A novel three-way decision method is presented for solving decision-making problems by means of hesitant fuzzy sets and canonical soft sets. Finally, a numerical example regarding peer review of research articles is given to illustrate the validity and efficacy of the proposed method.

Citation: Feng Feng, Zhe Wan, José Carlos R. Alcantud, Harish Garg. Three-way decision based on canonical soft sets of hesitant fuzzy sets[J]. AIMS Mathematics, 2022, 7(2): 2061-2083. doi: 10.3934/math.2022118

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• The theory of three-way decision is built on the philosophy of thinking in threes. The essence of three-way decision is trisecting the whole and taking different strategies for different parts accordingly. The theory of three-way decision has been successfully implemented to diverse fields since it provides an elegant and efficient solution for solving complicated problems. In this paper, a useful representation for hesitant fuzzy sets is obtained by means of canonical soft sets. We also define unit interval parameterized soft sets and their derived hesitant fuzzy sets. Mutual representations and inner connections between hesitant fuzzy sets and soft sets are examined. With the help of soft rough sets, a generalized rough model based on hesitant fuzzy sets is established. A novel three-way decision method is presented for solving decision-making problems by means of hesitant fuzzy sets and canonical soft sets. Finally, a numerical example regarding peer review of research articles is given to illustrate the validity and efficacy of the proposed method.

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