Nullnorms and Uninorms as Generators of Unions and Intersections Operations of Balanced Fuzzy Sets

In everyday life, we collect large amounts of data that describe different states: positive, neutral or negative. This data can describe redundancies, uncertain information and deficiencies. So, gathering, analysing, and processing data have three-state forms, e.i.: true, false, and no information, which requires developing extensions of fuzzy sets that allow their description and processing. One such extension is balanced fuzzy sets. Their development resulted in studying the concept of new fuzzy operators and their various properties. Nevertheless, many operators that have been described for classical fuzzy sets can indeed be extended to the range $[-1,1]$. To support fuzzy operations' bipolarity, we propose using extended to interval $[-1, 1]$ uninorms as unions and nullnorms as intersections. The work also presents the relationships between these operations and fuzzy balanced norms and conorms.