Interval-Valued Intuitionistic Fuzzy Decision With Graph Pattern in Big Graph

Abstract

Graph pattern matching (GPM) in big graph has been widely used in decision making, such as expert finding, social group discovery, etc. However, these existing works consider neither the preference of the decision maker (DM), nor the subjectivity of constraints during the process of GPM. Therefore, this paper proposes an interval-valued intuitionistic fuzzy decision (IVIFD) with graph pattern in big graph. As traditionally IVIFD can maximally reduce the uncertainty of decision making and it is only valid for small datasets, which makes it impossible to be applied in big graph. In this paper, GPM is adopted to prune the searching space, which makes it possible to process IVIFD under the preference of the DM later. Technically, firstly, each DM selects the preferred vertices and/or edges in big graph, and the interval-valued intuitionistic fuzzy preference (IVIFP) is calculated and used to form the contextual constraints to conduct GPM. Secondly, a probability-certainty density function is introduced to capture the subjective probability of the contextual preference of subgraphs via the bijection from rating space of the context to preference space of the context, which leads to an interval-valued intuitionistic fuzzy set (IVIFS). In addition to the IVIFS, the IVIFD is made through interval-valued intuitionistic fuzzy cross entropy and grey relation degree. Moreover, the weight problem between different contexts is taken into account and handled respectively as three cases. Finally, numerical experiments and perturbation analysis validate the effectiveness and stability of our proposed method, and verify its necessity and efficiency through ablation experiments.