Intelligent Energy Optimization in Smart Homes Using Cubic Fuzzy Frank Aggregation Operators

Intelligent Energy Optimization in Smart Homes

Résumé

Energy efficiency in smart homes is a complex challenge that requires intelligent decision-making under uncertainty. Fuzzy sets and interval-valued fuzzy sets (IFSs) provide effective mathematical frameworks for handling imprecise data, making them crucial for optimizing energy consumption. This paper introduces a novel Cubic Fuzzy Frank (CFF) methodology, integrating cubic fuzzy averaging and geometric aggregation operators to enhance decision-making for energy optimization in smart homes. We develop several new aggregation operators, including: Cubic Fuzzy Frank Weighted Averaging (CFFWA); Cubic Fuzzy Frank Ordered Weighted Averaging (CFFOWA); Cubic Fuzzy Frank Hybrid Averaging (CFFHA); Cubic Fuzzy Frank Weighted Geometric (CFFWG); Cubic Fuzzy Frank Ordered Weighted Geometric (CFFOWG) and Cubic Fuzzy Frank Hybrid Geometric (CFFHG). These operators, based on Frank t-norm and Frank t-conorm, enable more accurate and adaptive energy optimization by considering varying levels of uncertainty. Additionally, we introduce new score and precision functions to refine the decision-making process. A systematic step-by-step methodology is presented for applying the CFF approach to smart home energy management. To validate its effectiveness, we provide a numerical case study demonstrating its superior performance compared to existing techniques. The results highlight the efficiency, adaptability, and practicality of the proposed method, making it a powerful tool for optimizing energy consumption in intelligent home environments.