While the rapid development of information technology has made easy to store and access the huge amount of data, it also brings another problem, that of how to extract potentially useful knowledge not only in an efficient way but also in a way that could be easily understandable by humans. One of the solutions to this problem is linguistic summarization, aim of which is to generate explicit and concise summaries from data that is more compatible with human cognitive mechanism. The most crucial step in linguistic summarization is certainly the evaluation of linguistic summaries since they are the most important element of fuzzy rule based systems commonly used in expert systems and intelligent systems. Therefore, the selection of appropriate method for evaluating linguistic summaries in sense of different views such as quality, quantity, relevance and simplicity becomes vital. The aim of this paper is to review the state of art on linguistic summarization in the framework of fuzzy sets, focusing on the methods for evaluating linguistic summaries and the current applications. A taxonomy is proposed to identify the existing methods depending on the type of fuzzy sets (i.e., type-1 fuzzy set and type-2 fuzzy set) and the type of cardinalities (i.e., scalar cardinality and fuzzy cardinality). The recent studies on linguistic summarization are also presented to give a comprehensive framework for the future directions. The paper ends with conclusions, addressing some important issues and open questions which can be subject for future research. (C) 2016 Elsevier Ltd. All rights reserved.