The socioeconomic or political structures of countries and investment costs play a crucial role in investor decisions, especially in developing countries where the environment is unstable. In this regard, fuzzy models that consider the investment amount and cost may enable making more realistic decisions rather than the deterministic models used in portfolio optimization (PO). Hence, the objective of this paper is to examine the effects of the environment, investment amount and cost on PO in a politically, socially and economically unstable environment. Konno-Yamazaki PO model was fuzzified by adopting fuzzy linear programming (FLP) approaches of Verdegay and Werners for this purpose. Afterward, extended models were created. To do that, investment amount, tax and transaction costs were integrated into the return constraint of the fuzzified models. Mean-Variance Model (MVM) of Markowitz was also used for comparatively interpreting the results of the optimization. Results show that the fuzzified models based on Verdegay and Werners FLP approaches can be suggested as a decision-making tool, respectively for risk-averse and risk-taker investors. The extended models provide much better results compared to the fuzzified models. On the other hand, they are not more successful than the MVM in an unstable environment but the stable environment. The main contributions are considering political, social and economic events in the optimization, comparatively analyzing fuzzified Konno-Yamazaki model with its extended versions and the MVM, investigating the relationship between optimization models and investor types.