In this paper, a two-stage pattern classification and rule extraction system is proposed. The first stage consists of a modified fuzzy min-max (FMM) neural-network-based pattern classifier, while the second stage consists of a genetic-algorithm (GA)-based rule extractor. Fuzzy if-then rules are extracted from the modified FMM classifier, and a ¿don't care¿ approach is adopted by the GA rule extractor to minimize the number of features in the extracted rules. Five benchmark problems and a real medical diagnosis task are used to empirically evaluate the effectiveness of the proposed FMM-GA system. The results are analyzed and compared with other published results. In addition, the bootstrap hypothesis analysis is conducted to quantify the results of the medical diagnosis task statistically. The outcomes reveal the efficacy of FMM-GA in extracting a set of compact and yet easily comprehensible rules while maintaining a high classification performance for tackling pattern classification tasks.

Dealing with multi-objective problems has several interesting benefits, one of which is that it supplies the decision-maker with complete information regarding the Pareto front, as well as a clear overview of the various trade-offs that are involved in the problem. The selection of such a representative set is, in and of itself, a multi-objective problem that must take into consideration the number of choices to show the uniformity of the representation and/or the coverage of the representation in order to ensure the quality of the solution. In this study, day-ahead scheduling has been transformed into a multi-objective optimization problem due to the inclusion of objectives, such as the operating cost of multi-energy multi-microgrids (MMGs) and the profit of the Distribution Company (DISCO). The purpose of the proposed system is to determine the best day-ahead operation of a combined heat and power (CHP) unit, gas boiler, energy storage, and demand response program, as well as the transaction of electricity and natural gas (NG). Electricity and gas are traded by MGs with DISCO at prices that are dynamic and fixed, respectively. Through scenario generation and probability density functions, the uncertainties of wind speed, solar irradiation, electrical, and heat demands have been considered. By using mixed-integer linear programming (MILP) for scenario reduction, the high number of generated scenarios has been significantly reduced. The ɛ-constraint approach was used and solved as mixed-integer nonlinear programming (MINLP) to obtain a solution that meets the needs of both of these nonlinear objective functions.