Distance and similarity measures of Hesitant bi-fuzzy set and its applications in renewable energy systems

The concept of Hesitant bi-fuzzy set (HBFS) is an extension of dual hesitant fuzzy set, which play an important role in minimizing uncertainty in an efficient way. Distance and Similarity measures are an important tool for illustrating and integrating the differences between elements and its class and have a great importance in decision making, medical diagnosis and pattern recognition. To enhance and expand the applicability of HBFS, in this study, we have defined a series of distance and similarity measures of HBFS in both continuous and discrete environments. Since the information in day-to-day life may be biased, therefore, to show the importance of each factor/ criterion weighted measures are also defined. Due to global warming and climate change, the utilization of renewable energy systems not only plays a significant role but also decreases greenhouse gas emissions. Choosing the right energy system affects each nation's economic, social, and environmental development. To show the efficiency of proposed measures, these measures are implemented in renewable energy systems. An algorithm for hesitant bi-fuzzy TOPSIS has also been developed to demonstrate the application of these measures in decision- making. Finally, a comparative study is done in pattern recognition problem, to show the supremacy and efficiency of the proposed measures.