The solution of fuzzy linear systems by non-linear programming: a financial application

• DOI: 10.1016/j.ejor.2005.10.055
• Publication Date: 2006-02-10T01:44:19Z
• Authors: Silvia Muzzioli; Huguette Reynaerts
• Keywords: 0202 electrical engineering, electronic engineering, information engineering; Fuzzy sets; fuzzy linear systems; binary tree model; 02 engineering and technology

Abstract Fuzzy linear systems of equations play a major role in various financial applications. In this paper we analyse a particular fuzzy linear system: the derivation of the risk neutral probabilities in a fuzzy binary tree. This system has previously been investigated and different solutions to different forms of the same system have been proposed. The aim of this paper is twofold. First, we highlight that the different solutions proposed, arise from different forms of the same system. Second, in order to find a unique vector solution for the system, we propose a practical algorithm that boils down to the solution of a non-linear optimization problem.