Double Fuzzy Number and its Application in Risk Analysis in a Production System using Fuzzy Cognitive Map

Abstract

Any production system consist of different factors and they are interrelated to each other. Corresponding to each factor there also exist some risk in continuation or failure of that production system due to the lack of sufficiency of any factor. since there are interrelationship between the factors a fuzzy cognitive map (FCM)has been considered in this present model. The factors values are taken in linguistic form i.e., fuzzy form. Now the risk is associated with each factor so to relate the risk with the factors a new fuzzy number has been introduced in this paper which is named as "double fuzzy number". Some properties corresponding to this double fuzzy number also has been introduced. To analyze the total risk of the system, the application of this double fuzzy number has been considered. The proposed production system has been analyzed with a numerical example.