Investigation of Mean-variance efficiency frontier patterns of portfolios under possible theory

One of the most important problems of the proposed methods in measuring the portfolio Efficiency frontier patterns is not considering the uncertainty in financial variables such as risk and return. In this regard, the development of various optimization theories and Extract optimal efficiency frontier of a portfolio in financial sciences to understand and identify aspects of uncertainty in the decision environment and possible events in space of uncertainty and ambiguity of capital markets have been invented and developed. Among the theories proposed in terms of uncertainties, the theory of possibility can be considered the most appropriate and accurate theory in interpreting and proving uncertainties in stock portfolio optimization. For this reason in the forthcoming research to further adapt portfolio optimization models And recognizing the efficient space congruous to reality to extract returns and portfolio risk by mathematical inference in an uncertainty space with emphasis on possible theory. In this study of the concept of fuzzy random variable and fuzzy theory and Fuzzy obligation, In order to cover the uncertainty existing in Cognition and determine the efficiency frontier Mean - portfolio variance Used under the theory of possibility.