**1. Introduction**

Eutrophication is a common water pollution phenomenon caused by excessive nutrients and is accompanied by ecological problems such as algal blooms, oxygen depletion, aquatic organism death, and aquatic ecosystem deterioration [1]. With the increase of population and rapid urbanization, nutrient loading in lots of urban lakes has increased and exceeded their corresponding natural carrying capacities [2–4]. Especially, urban lake eutrophication poses a serious threat to regional economic development, the ecological environment, and drinking water security [5,6]. Furthermore, heavy metal pollutants are discharged into urban lakes through industrial, agricultural, and domestic waste-water discharges, precipitation, and the release of contaminated sediment [7–9]. To a certain extent, toxic metal accumulation in urban lakes can do serious harm to the "water—aquatic plant—aquatic animal" system which will affect human health directly or indirectly through drinking water, food chains, etc. [10].

In recent years, various works have been done to explore the heavy metal or eutrophication distributions and sources in urban lakes [11,12], as well as toxic metal eco-risk and health risk levels [13,14], environmental managemen<sup>t</sup> strategies [15,16], and corresponding remediation technologies [17]. Obviously, eutrophication and heavy metal pollution play key roles in urban lake health. Environmental assessment of eutrophication or heavy metals in urban lakes is an important reference for identifying the degree of pollution and formulating pollution prevention strategies. Unfortunately, most research on lake risk is often evaluated from a single angle for toxic metals pollution or eutrophication using the standard comparison method [18–20] for both, the comprehensive trophic level index (TLI) [21,22], and the health risk assessment for toxic metals [23,24]. Moreover, the above deterministic methods probably lead to biased or unreliable assessments due to the randomness and fuzziness in environment systems caused by natural change and human activities [25–28]. Frankly, when there are different theoretical foundations, the evaluation results and conclusions differ to some extent, which makes it challenging for decision-makers to make scientific and synthetic managemen<sup>t</sup> decision under consideration of separate assessment methods. Therefore, in order to implement appropriate environmental managemen<sup>t</sup> strategies and measures, it is important to explore a feasible lake health assessment method synthetically considering lake eutrophication and corresponding health risks posed by heavy metals, together with evaluation of systematic uncertainty.

The objectives of this study were (i) to investigate and analyze the state of eutrophication and the health risk posed by heavy metals in the selected lakes from the total 143 lakes in the Chinese Wuhan city as a study case; (ii) to develop a fuzzy comprehensive lake health assessment method (FCLHAM) integrating quantitative eutrophication and health risk consideration; (iii) to test and verify FCLHAM by assessing the integrated lake health states of the studied lakes; and (iv) to introduce a novel hierarchical managemen<sup>t</sup> system for lakes based on the FCLHAM results.
