Adaptive Clustering and Expert-Weighted Fuzzy Evaluation for Personalized Cold-Start Recommendation of Electricity Retail Packages

Satisfying the diverse electricity-consumption needs of heterogeneous users is central to refined operation in competitive retail markets. Existing package-recommendation methods remain limited by subjective specification of cluster numbers, incomplete representation of fuzzy preferences, and the absence of reliable package matching for new users without historical package-interaction records. This study develops an application-oriented personalized recommendation framework that integrates an adaptive Gaussian Mixture Model (GMM), a Weighted Interval-Valued Intuitionistic Hesitant Fuzzy Element (WIVIHFE)-based preference representation, and a similarity-based recommendation mechanism. K-means++ initialization and a comprehensive clustering evaluation metric (CEM) are first incorporated into the GMM to improve clustering stability and determine the number of user groups adaptively. Multi-attribute package evaluations are then mapped into five-dimensional WIVIHFE coordinates, where expert support weights represent differences in the credibility of evaluation information. Finally, Gaussian-kernel similarity transfers the package preferences of comparable historical users to a new user and yields expected-satisfaction rankings. In the case study, the proposed method achieved a root mean square error of 0.076 and a mean absolute error of 0.058, outperforming the benchmark configurations considered. This study provides a data-driven solution for cold-start package matching and differentiated marketing in electricity retail markets.