The concept of interval-valued q-rung orthopair fuzzy graph (IVq-ROFG) is a major recent extension in the field of fuzzy graph. However, traditional IVq-ROFG imposes strict restrictions on the lower and upper bounds of membership degree and non-membership degree, which narrows its scope of applicability. This paper proposes a new graph called possibility degree-based interval-valued q-rung orthopair fuzzy graph (PDIVq-ROFG) and generalizes the traditional IVq-ROFG. Firstly, the concept of PDIVq-ROFG is given and some basic terms, such as complement, self-complement, bridge, degree and total degree, are discussed. Secondly, product operations on PDIVq-ROFG are presented, including tensor product, Cartesian product, semi-strong product and strong product. Moreover, some theorems about the degree and total degree under these product operations are given and elaborated with several examples. Finally, the application of PDIVq-ROFG to the network of oil pipelines is provided and the feasibility and effectiveness of the PDIVq-ROFG are verified.
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This research has been supported by the National Natural Science Foundation of China (No. 11626079), the Natural Science Foundation of Hebei Province (No. A2020402013), the Social Science Foundation of Hebei Province (No. HB19GL061), the 2019 Social Science Research and Development Project of Hebei Province (No. 2019031201011), the Scientific Research Project of Department of Education of Hebei Province (No. BJ2017031) and the Research Foundation for Young key Scholars at Hebei University of Engineering (No. 16121002016).
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Yin, S., Yang, Y., Yao, N. et al. Possibility degree-based interval-valued q-rung orthopair fuzzy graphs. Soft Comput 25, 15005–15020 (2021). https://doi.org/10.1007/s00500-021-06412-x
- Interval-valued q-rung orthopair fuzzy graph
- Possibility degree
- Product operations
- Total degree