“…Since APP problem always involves several criteria (objectives) and due to the vagueness of the available information, fuzzy multi-objective programming has been widely used in this area. Lee (1990), Gen, Tsujimura and Ida (1992), Wang and Fang (2001), Wang and Liang (2004), Ghasemy Yaghin, Torabi and Fatemi Ghomi (2012), Madadi and Wong (2014), Gholamian et al (2015), Gholamian, Mahdavi and Tavakkoli-Moghaddam (2016), Kalaf et al (2015), Sisca, Fiasché and Taisch (2015), Fiasché et al (2016) and Zaidan et al (2017) utilised various kinds of fuzzy multi-objective optimisation models to study APP under uncertainty. Gholamian et al (2015) and Gholamian, Mahdavi and Tavakkoli-Moghaddam (2016) developed a fuzzy multi-site multi-objective mixed integer nonlinear APP model in a supply chain under uncertainty with fuzzy demand, fuzzy cost parameters, etc.…”