4. A new parametric measure of fuzzy information measure involving three parameters α, β and γ

Further, a new generalised fuzzy information measure involving three parameters α, β and γ has been suggested and their necessary and required properties are examined. Thereafter, its validity is also verified. Also, the monotonic behaviour of fuzzy information measure of order α, β and γ has been introduced.

The generalised measure of fuzzy information involving three parameters α, β and γ is given by,

$$\begin{aligned} H\_{a,\beta,\gamma}(A) &= \frac{1}{1-a} \sum\_{i=1}^{n} \left[ \left( \mu\_A^{\{a+\beta\}\mu\_A(\mathbf{x}\_i)} + \left(1-\mu\_A(\mathbf{x}\_i)\right)^{\{a+\beta\}\{1-\mu\_A(\mathbf{x})\}} \right)^{\gamma} - 2^{\gamma} \right], \\\\ &a > 0, a \neq 1, \beta \neq 0, \gamma \neq 0 \end{aligned} \tag{27}$$
