Z-Harmonic Mean

Dual hesitant fuzzy set (DHFS) consists of two parts: membership hesitant function and non-membership hesitant function. This set supports more exemplary and flexible access to set degrees for each element in the domain and can address two types of hesitant in this situation. It can be considered a powerful tool for expressing uncertain information in the decision-making process. The function of z-score, namely z-arithmetic mean, z-geometric mean, and z-harmonic mean, has been proposed with five important bases, these bases are hesitant degree for dual hesitant fuzzy element (DHFE), DHFE deviation degree, parameter , (the importance of the hesitant degree), parameter  , (the importance of the deviation degree) and parameter , (the importance of membership (positive view) or non-membership (negative view). A comparison of the z-score with the existing score function was made to show some of their drawbacks. Next, the z-score function is then applied to solve multi-criteria decision making (MCDM) problems. To illustrate the proposed method's effectiveness, an example of MCDM specifically in pattern recognition has been shown.