Development of Fuzzy Logic-based Arithmetic and Visual Representations for systems' modelling and optimization of interconnected networks

The foundation of new Fuzzy Logic Level Arithmetic and Visual representations, normalized fuzzy matrices, and the principle of fuzzy logic-based level tracking were developed by Gabr and Dorrah for systems modelling and optimization during all stages of formulation and solution. This new concept has an unlimited scope of generalizations and extensions to many classes of problems and systems in various disciplines. In this paper, further development of the above concept to the modelling and multi-objective linear optimization of multi-stations operating interconnected network in a fully fuzzy environment is presented. The development approach is based on a fuzzy logic-based arithmetic or visual representation incorporated in spreadsheet form with built-in using macros normal Visual Basic Application (VBA) Language. The approach is capable of accommodating an unlimited number of parameters and variables with open scales of fuzzy levels. These fuzzy levels can then be transferred at the end of solution to actual uncertainties. The approach is applied to a Case Study of 8 (eight) interconnected electric operated pump stations irrigation network of El Nasr Region at West of Delta (Egypt). The results demonstrated strongly the applicability and efficacy of the developed techniques to handle medium and large scale interconnected networks operating in a fully fuzzy environment.