Distribution linguistic preference relations (DLPRs) with complete symbolic proportions have been recently investigated to record the comparison information coming from decision makers (DMs) in the context of linguistic decisions. Due to various reasons such as a lack of experience and partial knowledge about the pairs of decision alternatives, it is not always easy for DMs to provide complete symbolic proportions in DLPRs. In this paper, we propose a new style of pairwise comparison called DLPR with incomplete symbolic proportions to represent DMs’ comparison information. Two aggregation operators for DLPRs with incomplete symbolic proportions and their desirable properties are presented. An expectation-based numerical preference relation (EBNPR) is deduced from a DLPR with incomplete symbolic proportions using numerical scale models. The consistency of DLPR with incomplete symbolic proportions is defined via its associated EBNPR. On the other hand, solving linguistic decision problems implies the need for invoking the principles of computing with words (CW). The key point about CW is that words might exhibit different meaning for different people. Hence, another aim of this paper is to deal with the point about CW by setting personalized numerical scales of linguistic terms for different DMs in group decision making (GDM) with the newly introduced preference relations. Several numerical scale computation models are developed to personalize numerical scales for each DM to show their individual difference in understanding the meaning of words. Finally, we present the applications of the aforesaid theoretical results to GDM situations, which are demonstrated by solving a GDM problem of evaluating and selecting research projects.