The discovery of association rule acquire an imperative role in data mining since its inception, which tries to find correlation among the attributes in a database. Classical algorithms/procedures meant for Boolean data and they suffer from sharp boundary problem in handling quantitative data. Thereby fuzzy association rule (i.e., association rule based on fuzzy sets) with fuzzy minimum support and confidence is introduced as an alternative tool. Besides, rule length, comprehensibility, and interestingness are also potentially used as quality metrics. Additionally, in fuzzy association rule mining, determining number fuzzy sets, tuning membership functions and automatic design of fuzzy sets are prominent objectives. Hence fuzzy association rule mining problem can be viewed as a multi-objective optimisation problem. On the other side, multi-objective genetic algorithms are established and efficient techniques to uncover Pareto front. Therefore, to bridge these two fields of research many methods have been developed. In this paper, we present some of the popular state-of-art multi-objective fuzzy-genetic algorithms for mining association rules. In addition, their novelty, strengths, and weaknesses have been analysed properly with a comparative performance. The indicative future research direction and an extensive bibliography of this paper may be an attracting point for researchers from diversified domains to explore and exploit further.