期刊
SOFT COMPUTING
卷 26, 期 7, 页码 3435-3454出版社
SPRINGER
DOI: 10.1007/s00500-021-06690-5
关键词
Multi-criteria decision-making; MULTIMOORA; Picture fuzzy sets; Schweizer-Sklar t-norm and t-conorm; Aggregation operator
资金
- Natural Science Foundation of Zhejiang Province [LY20G010006]
- Philosophy and Social Science Program in Zhejiang Province, China [21NDJC099YB]
- National Natural Science Foundation of China [71701065, 61972336, 71571193]
This paper proposes an extended picture fuzzy multi-objective optimization method based on Schweizer-Sklar prioritized aggregation operators and picture fuzzy set. The developed picture fuzzy Schweizer-Sklar operations and aggregation operators are used to construct an extended picture fuzzy MULTIMOORA method. An illustrative example is provided to demonstrate the effectiveness of the proposed method.
The purpose of this paper is to construct an extended picture fuzzy multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) method based on Schweizer-Sklar prioritized aggregation operators and picture fuzzy set. First, based on Schweizer-Sklar t-norm and t-conorm, picture fuzzy Schweizer-Sklar operations involving a variable parameter are defined to make the corresponding operations more flexible than other operations. Second, the picture fuzzy Schweizer-Sklar prioritized aggregation operators, namely the picture fuzzy Schweizer-Sklar prioritized weighted average operator and the picture fuzzy Schweizer-Sklar prioritized weighted geometric operator, are developed, and their related properties are investigated as well. Third, an extended picture fuzzy MULTIMOORA method with unknown weight information, which involves the ratio system, the reference point, and the multiplicative form methods simultaneously, is constructed based on the developed aggregation operators. Finally, an illustrative example with public-private-partnership investment project selection is presented to verify the feasibility and validity of the constructed method. The results indicate that the constructed method is effective to realize an optimal decision-making.
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