Fully hesitant parametric fuzzy equation.

Linear equations are commonly used in various fields of science such as engineering, physics, computer science, technology, business, and economics. A recent and promising extension of fuzzy set theory is represented by hesitant fuzzy sets (HFSs). The promising characteristic of HFSs is that they permit to model a type of imprecise human knowledge that cannot be captured by classical fuzzy sets. As no research has been performed in the field of hesitant fuzzy equations, in this paper, hesitant parametric fuzzy set (HPFS) is introduced and operations on this set are investigated. Also, fully hesitant parametric fuzzy equation (FHPFE) in form of a x = b is solved for the first time in which a and b are known HPFS and x is an unknown HPFS. Then, the existence of different approximate solutions of FHPFE is investigated and proved. Finally, some numerical examples are presented that verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]