System effectiveness evaluation is an important part of constellation satellite communication system research, with applications in project verification and optimization as well as tactical and technical measurement argumentation. This paper presents a systematic and comprehensive effectiveness evaluation method for a constellation satellite communication system under a probabilistic hesitant intuitionistic fuzzy preference relationship (PHIFPR), aiming to better address the fuzziness and uncertainty in effectiveness evaluation. First, a proposed definition of PHIFPR describes the hesitancy of evaluators, provides hesitancy distribution information, and depicts the worst negative information and risk preferences in effectiveness evaluation. Then, we deduce the approximate consistency index of PHIFPR and establish a mathematical programming model to increase individual consistency when the approximate consistency index does not reach a predetermined level. In the sequel, a proposed group consensus index uses the PHIFPR-based Hausdorff distance to measure the closeness between evaluators' judgements. Afterwards, a consistency and consensus improvement model is designed to retain the original opinions of evaluators to make the consistency and consensus of PHIFPRs acceptable. Moreover, a goal programming model is established to gain the reliable scheme priority weights by regarding the approximate consistency condition of a PHIFPR as a fuzzy constraint. Finally, an experimental example is offered to highlight the practicability and feasibility of the proposed method, and some comparative analyses with other methods offer insights into the designed method.