1. Fuzzy best-worst method based on generalized interval-valued trapezoidal fuzzy numbers for multi-criteria decision-making
- Author
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Jiu-Ying Dong, Shu-Ping Wan, and Shyi-Ming Chen
- Subjects
Mathematical optimization ,Information Systems and Management ,05 social sciences ,050301 education ,02 engineering and technology ,Multiple-criteria decision analysis ,Fuzzy logic ,Measure (mathematics) ,Computer Science Applications ,Theoretical Computer Science ,Multi criteria decision ,Artificial Intelligence ,Control and Systems Engineering ,Consistency (statistics) ,0202 electrical engineering, electronic engineering, information engineering ,Fuzzy number ,020201 artificial intelligence & image processing ,Weight ,Representation (mathematics) ,0503 education ,Software ,Mathematics - Abstract
This paper proposes a fuzzy best-worst method (BWM), called the GITrF BWM, based on generalized interval-valued trapezoidal fuzzy (GITrF) numbers (GITrFNs) for multi-criteria decision-making (MCDM). The reference comparisons between criteria are represented by GITrFNs and the weights of criteria are also taken the form of GITrFNs. The concept of normalized GITrF weight vector is proposed and a new graded mean integration representation (GMIR) of GITrFN is given. A goal programming model is built to obtain the optimal normalized GITrF weights of criteria. Furthermore, the GITrF consistency index and the GITrF consistency ratio are proposed. The GMIR of the GITrF consistency ratio is calculated to measure the acceptable consistency of all the reference comparisons between criteria. For the unacceptable consistent reference comparisons, we propose an approach to improve the consistency of reference comparisons between criteria. Finally, a GITrF BWM is proposed for MCDM. Three real examples are analyzed to illustrate the proposed GITrF BWM. The comparison analyses show that the proposed GITrF BWM outperforms the existing methods for MCDM in GITrF environments.
- Published
- 2021