Fuzzy Prediction Strategies for Gene-Environment Networks - Fuzzy Regression Analysis for Two-Modal Regulatory Systems

Abstract

Target-environment networks provide a conceptual framework for the analysis and prediction of complex regulatory systems such as genetic networks, eco-finance networks or sensor-target assignments. These evolving networks consist of two major groups of entities that are interacting by unknown relationships. The structure and dynamics of the hidden regulatory system have to be revealed from uncertain measurement data. In this paper, the concept of fuzzy target-environment networks is introduced and various fuzzy possibilistic regression models are presented. The relation between the targets and/or environmental entities of the regulatory network is given in terms of a fuzzy model. The vagueness of the regulatory system results from the (unknown) fuzzy coefficients. For an identification of the fuzzy coefficients' shape, methods from fuzzy regression are adapted and made applicable to the bi-level situation of target-environment networks and uncertain data. Various shapes of fuzzy coefficients are considered and the control of outliers is discussed. A first numerical example is presented for purposes of illustration. The paper ends with a conclusion and an outlook to future studies.