Foundation of New Systems' Consolidity Theory Using Arithmetic Fuzzy Logic-Based Representation in Fully Fuzzy Environment

Abstract — This paper establishes the foundation of new systems’ consolidity theory using the Arithmetic Fuzzy Logic-based Representation approach for investigating the internal behavior of systems operating in fully fuzzy environment. Consolidated systems are defined as being stable at the original state, but due to fuzzy variations in their inputs or parameters tend to react accordingly in a manner leading to maintaining their consolidity and strength, or vice versa. Under the new theory, systems are classified into consolidated, neutrally consolidated or unconsolidated type based on their output fuzziness reaction to combined input and parameters fuzziness action. The systems’ consolidity theory is demonstrated by several examples of mathematical functions of different dimensionalities, control theory and Predator-Prey populations’ dynamics. The suggested consolidity theory is illustrated to be an effective tool for revealing the inner property of systems and predicting their hidden behavior when operating in fully fuzzy environment. Monitoring and control of systems’ consolidity through forward and backward fuzziness tracking are suggested during systems’ operation, for avoiding their drifting to possible unwanted unconsolidated domains. Finally, it is shown that the analysis will lead at the end to determining the System’s Consolidity Index that could be regarded as a general basic internal property of the system. Such Systems’ Consolidity concept can also be defined far from fuzzy logic, and is applicable to various types of linear, nonlinear, multivariable, dynamic, ...etc systems. Index Terms:- Fuzzy Theory, Fuzzy Dynamic Systems, Advanced Fuzzy Control Systems, and Systems’ Consolidity Theory.