Black-Litterman model with intuitionistic fuzzy posterior return

The main objective is to present a some variant of the Black - Litterman model. We consider the canonical case when priori return is determined by means such excess return from the CAPM market portfolio which is derived using reverse optimization method. Then the a priori return is at risk quantified uncertainty. On the side, intensive discussion shows that the experts' views are under knightian uncertainty. For this reason, we propose such variant of the Black - Litterman model in which the experts' views are described as intuitionistic fuzzy number. The existence of posterior return is proved for this case.We show that then posterior return is an intuitionistic fuzzy probabilistic set.Comment: SSRN Electronic Journal 201

Introduction to Plithogenic Logic as generalization of MultiVariate Logic

A Plithogenic Logical proposition P is a proposition that is characterized by many degrees of truth-values with respect to many corresponding attribute-values (or random variables) that characterize P. Each degree of truth-value may be classical, fuzzy, intuitionistic fuzzy, neutrosophic, or other fuzzy extension type logic. At the end, a cumulative truth of P is computed

Studying Neutrosophic Variables

We present in this paper the neutrosophic randomized variables, which are a generalization of the classical random variables obtained from the application of the neutrosophic logic (a new nonclassical logic which was founded by the American philosopher and mathematical Florentin Smarandache, which he introduced as a generalization of fuzzy logic especially the intuitionistic fuzzy logic ) on classical random variables. The neutrosophic random variable is changed because of the randomization, the indeterminacy and the values it takes, which represent the possible results and the possible indeterminacy. Then we classify the neutrosophic randomized variables into two types of discrete and continuous neutrosophic random variables and we define the expected value and variance of the neutrosophic random variable then offer some illustrative examples