Pythagorean Fuzzy Sets to Solve Z-Numbers in Decision-Making Model

Abstract

Since the concept of Z-numbers was proposed, it has attracted the attention of scholars. In this article, we are committed to solving Z-numbers from the perspective of coordinate system and q-rung orthopedic fuzzy sets (q-ROFSs). First, a new layout coordinate system is defined to map Z-numbers to q-ROFSs. For convenience, Pythagorean fuzzy set (PFS), a special form of q-ROFSs, is employed in this article. In this way, the parameters <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$A$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$B$</tex-math></inline-formula> in Z-numbers are transformed into the corresponding membership and nonmembership. At the same time, the genetic algorithm is adopted to derive the potential probability distribution. Next, an approach for calculating the weighted information entropy of Z-numbers is proposed, and the theorem proves the rationality. To integrate multiple Z-information, the linguistic Z-PFS weighted aggregation operator ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$LZPFSPWAO$</tex-math></inline-formula> ) is presented. Also, a score function is defined with the help of curve length calculation formula in the coordinate system. Finally, a decision-making model is constructed based on the new solution. Two examples, UAV firefighting and energy investment selection, are adopted to demonstrate the validity. The comparison results show that the proposed method is effective and beneficial in solving Z-information.