Journal
SYMMETRY-BASEL
Volume 13, Issue 3, Pages -Publisher
MDPI
DOI: 10.3390/sym13030436
Keywords
picture fuzzy set; picture fuzzy point operator; distance measure; multi-criteria decision-making
Categories
Funding
- National Natural Science Foundation of China [61773019, 11771263]
- Fundamental Research Funds For the Central Universities [2018TS059, GK201503013]
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The paper proposes a dynamic distance measure of picture fuzzy sets based on a picture fuzzy point operator to address some unreasonable and counterintuitive cases in existing distance measures. Through numerical comparisons and multi-criteria decision-making problems, it is shown that the proposed distance measure is reasonable and effective.
Picture fuzzy sets, which are the extension of intuitionistic fuzzy sets, can deal with inconsistent information better in practical applications. A distance measure is an important mathematical tool to calculate the difference degree between picture fuzzy sets. Although some distance measures of picture fuzzy sets have been constructed, there are some unreasonable and counterintuitive cases. The main reason is that the existing distance measures do not or seldom consider the refusal degree of picture fuzzy sets. In order to solve these unreasonable and counterintuitive cases, in this paper, we propose a dynamic distance measure of picture fuzzy sets based on a picture fuzzy point operator. Through a numerical comparison and multi-criteria decision-making problems, we show that the proposed distance measure is reasonable and effective.
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