Park and Park [70] extend the works Sun and Sun [61] by considering the interactions of any three aggregated arguments instead of any two to develop generalized fuzzy weighted Bonferroni

harmonic mean (GFWBHM) operator and generalized fuzzy ordered weighted Bonferroni

harmonic mean (GFOWBHM) operator.

In this paper, it was shown that, due to the choice of generator function, [A.sub.p], [G.sub.p], and [H.sub.p] means are reduced to ordinary arithmetic, geometric, and

harmonic mean, respectively.

While the arithmetic and geometric means are ill-suited--mathematically undefined--to the kind of change in prices suggested by these scenarios, the

harmonic mean converges to 2[p.sub.L] .

Name Notation Definition Arithmetic Mean A(a, b) [a + b]/2 Geometric mean G(a, b) [square root of [ab]]

Harmonic Mean H(a, b) [2ab]/[a + b] Logarithmic Mean L(a, b) [[a - b]/[In a - In b]] when a [not equal to] b a when a [not equal to] b Heron Mean [H.sub.e](a, b) [a + [square root of [ab]] + b]/3 Identric Mean I(a, b) [1/e][([a.sup.a]/[b.sup.b]) .sup.[1/[a - b]]] Power Mean [M.sub.r](a, b) a when r[not equal to] 0 and a = b[[([[a.sup.r] + [b.sup.r]]/2)].sup.[1/r]] when r[not equal to] 0 [square root of [ab]] when r = 0 Now, we define the homogeneous function N [a, b; p, q; r, [alpha], [mu]] = [[{[[[a.sup.p] + [mu][M.sub.r]([a.sup.p], [b.sup.p]) + [alpha][b.sup.p]]/[[a.sup.q] + [mu][M.sub.r]([a.sup.q], [b.sup.q]) + [alpha][b.sup.p]]]}].sup.[1/[p - q]]].

The respiratory surface density was [RS.sub.d] = 122.99 [+ or -] 35.84 [mm.sup.-1] and the

harmonic mean thickness of the air-hemolymph barrier was [tau]h = 0.14 [+ or -] 0.03 [micro]m (Fig.

To validate the superiority of the CSE based on the weighted

harmonic mean of COPs in comparison to the IPLV index, three types of SCOPs are compared for a specified building (building A shown in Figure 1).

The asymptotic analysis of the Poisson expectation departs from the usual paradigm of analysis exemplified by [10, 14, 23] because of the coupling introduced by the

harmonic mean, namely, the factor ([summation] [2.sup.-kj])-1.

The arithmetic and

harmonic mean models correspond to parallel and perpendicular components and thus, as mentioned above, to upper [[lambda].sub.U] and lower [[lambda].sub.L] thermal conductivity limits of the layered media.

- Seasonal home and core ranges and maximum home ranges (Kaufman, 1962) were estimated using minimum convex polygon (home range) (Mohr, 1947) and

harmonic mean (core range) (Dixon and Chapman, 1980).

Equation (1) is closely approximated by the

harmonic mean (Wright 1938):