ABSTRACT
This chapter focuses on the investigation of the stability of the equilibrium state of Fuzzy Relational Models. It presents a new approach for linguistic fuzzy system’s modeling, which is also suitable for stability analysis of linguistic models. The chapter examines the two models using some definitions and stating a necessary and a sufficient condition for stability of a class of linguistic fuzzy systems. It explores the stability analysis method to fuzzy linguistic systems associated with a class of applied nonlinear systems. The chapter reviews some definitions about the potential energy and conservative forces in pure mechanical systems. It discusses a motivating and inspiring preparatory study, which leads to the approaches of stability analysis taken in the sequel. The chapter considers fuzzy relational dynamic system based on sum-prod fuzzy composition. The concepts of fuzzy intra-planarity and unit-row matrix are introduced to obtain the proposed conditions.
