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. 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 the analysis and design of
various types of linear, nonlinear, multivariable, dynamic, etc., systems in real life in the fields of basic
sciences, evolutionary systems, engineering, biology, medicine, economics, finance, political and management
sciences, social sciences, humanities, and education. |
