FUZZY FINITE-ELEMENT APPROACH FOR THE ANALYSIS OF IMPRECISELY DEFINEDSYSTEMS

Many engineering systems are too complex to be defined in precise math ematical terms. They often contain information and features that are v ague, imprecise, qualitative, linguistic, or incomplete. The tradition al deterministic and probabilistic techniques are not adequate to anal yze such systems. This paper aims at developing a fuzzy finite element approach for the analysis of imprecisely defined systems. The develop ment of the methodology starts from the basic concepts of fuzzy number s of fuzzy arithmetic and implements suitably defined fuzzy calculus c oncepts such as differentiation and integration for the derivation, ma nipulation, and solution of the finite element equations. Simple stres s analysis problems involving vaguely defined geometry, material prope rties, external loads, and boundary conditions are solved to establish and to illustrate the new procedure. The approach developed is applic able to systems that are described in linguistic terms as well as thos e that are described by incomplete information. If complete data are k nown, the method handles the information similar to that of a probabil istic approach. The present approach represents a unique methodology t hat enables us to handle certain types of imprecisely known data more realistically compared with the existing procedures.