In the article, we provide new bounds for two Sándor–Yang means in terms of the arithmetic and contraharmonic means. Our results are the improvements of the previously known results.
On approximating the quasi-arithmetic mean Zhao, Tie-Hong; Zhou, Bu-Chuan; Wang, Miao-Kun ...
Journal of inequalities and applications,
02/2019, Letnik:
2019, Številka:
1
Journal Article
Recenzirano
Odprti dostop
In this article, we prove that the double inequalities
α
1
7
C
(
a
,
b
)
16
+
9
H
(
a
,
b
)
16
+
(
1
−
α
1
)
3
A
(
a
,
b
)
4
+
G
(
a
,
b
)
4
<
E
(
a
,
b
)
<
β
1
7
C
(
a
,
b
)
16
+
9
H
(
a
,
b
)
...16
+
(
1
−
β
1
)
3
A
(
a
,
b
)
4
+
G
(
a
,
b
)
4
,
7
C
(
a
,
b
)
16
+
9
H
(
a
,
b
)
16
α
2
3
A
(
a
,
b
)
4
+
G
(
a
,
b
)
4
1
−
α
2
<
E
(
a
,
b
)
<
7
C
(
a
,
b
)
16
+
9
H
(
a
,
b
)
16
β
2
3
A
(
a
,
b
)
4
+
G
(
a
,
b
)
4
1
−
β
2
hold for all
a
,
b
>
0
with
a
≠
b
if and only if
α
1
≤
3
/
16
=
0.1875
,
β
1
≥
64
/
π
2
−
6
=
0.484555
…
,
α
2
≤
3
/
16
=
0.1875
and
β
2
≥
(
5
log
2
−
log
3
−
2
log
π
)
/
(
log
7
−
log
6
)
=
0.503817
…
, where
E
(
a
,
b
)
=
(
2
π
∫
0
π
/
2
a
cos
2
θ
+
b
sin
2
θ
d
θ
)
2
,
H
(
a
,
b
)
=
2
a
b
/
(
a
+
b
)
,
G
(
a
,
b
)
=
a
b
,
A
(
a
,
b
)
=
(
a
+
b
)
/
2
and
C
(
a
,
b
)
=
(
a
2
+
b
2
)
/
(
a
+
b
)
are the quasi-arithmetic, harmonic, geometric, arithmetic and contra-harmonic means of
a
and
b
, respectively.
In the article, we present the best possible parameters
,
,
,
∈ ℝ and
,
∈ 1/2, 1 such that the double inequalities
hold for
,
> 0 with
≠
, and provide new bounds for the complete elliptic integral of ...the second kind, where
,
) = (
+
)/2 is the arithmetic mean,
is the quadratic mean,
,
) = (
+
)/(
+
) is the contra-harmonic mean,
;
,
) =
+ (1 –
,
+ (1 –
is the one-parameter contra-harmonic mean and
is the Toader mean of order 3.
In this study, several equations are employed to estimate monthly mean daily diffuse solar radiation for eight typical meteorological stations in China. Estimated values are compared with measured ...values in terms of statistical error tests such as mean percentage error (MPE), mean bias error (MBE), root mean square error (RMSE). All the models fit the data adequately and can be used to estimate monthly mean daily diffuse solar radiation from global solar radiation and sunshine hours. This study finds that the quadratic model performed better than the other models:
H
¯
d
H
¯
g
=
0.945
-
0.675
H
¯
g
H
¯
0
-
0.166
H
¯
g
H
¯
0
2
-
0.173
S
S
0
-
0.079
S
S
0
2
The measured values of monthly mean daily diffuse solar radiation for Kashi, Geermu, Shenyang, Chengdu and Zhengzhou stations are analyzed to test the generalization of the selected model. The model is found to be able to predict the measured data with good accuracy. Therefore, it is possible to estimate monthly mean daily diffuse solar radiation by using this equation.
In this paper, we introduce the Bonferroni geometric mean, which is a generalization of the Bonferroni mean and geometric mean and can reflect the correlations of the aggregated arguments. To ...describe the uncertainty and fuzziness more objectively, intutionistic fuzzy set could be used for considering the membership, non-membership and uncertainty information. To aggregate the Atanassov’s intuitionistic fuzzy information, we further develop the Atanassov’s intuitionistic fuzzy geometric Bonferroni mean describing the interrelationship between arguments, and some properties and special cases of them are also discussed. Moreover, considering the importance of each argument, the weighted Atanassov’s intuitionistic fuzzy geometric Bonferroni mean is proposed and applied to multi-criteria decision making. An example is given to compare the proposed method with the existing ones.
This paper is concerned with the open-loop linear-quadratic (LQ) Stackelberg game of the mean-field stochastic systems in finite horizon. By means of two generalized differential Riccati equations, ...the follower first solves a mean-field stochastic LQ optimal control problem. Then, the leader turns to solve an optimization problem for a linear mean-field forward-backward stochastic differential equation. By introducing new state and costate variables, we present a sufficient condition for the existence and uniqueness of the Stackelberg strategy in terms of the solvability of some Riccati equations and a convexity condition. Furthermore, it is shown that the open-loop Stackelberg equilibrium admits a feedback representation involving the new state and its mean. Finally, two examples are given to show the effectiveness of the proposed results.
In the article, we prove that
λ
1
=
1
/
2
+
(
2
+
log
(
1
+
2
)
)
/
2
1
/
ν
−
1
/
2
,
μ
1
=
1
/
2
+
6
ν
/
(
12
ν
)
,
λ
2
=
1
/
2
+
(
π
+
2
)
/
4
1
/
ν
−
1
/
2
and
μ
2
=
1
/
2
+
3
ν
/
(
6
ν
)
are ...the best possible parameters on the interval
1
/
2
,
1
such that the double inequalities
C
ν
λ
1
x
+
(
1
−
λ
1
)
y
,
λ
1
y
+
(
1
−
λ
1
)
x
A
1
−
ν
(
x
,
y
)
<
R
Q
A
(
x
,
y
)
<
C
ν
μ
1
x
+
(
1
−
μ
1
)
y
,
μ
1
y
+
(
1
−
μ
1
)
x
A
1
−
ν
(
x
,
y
)
,
C
ν
λ
2
x
+
(
1
−
λ
2
)
y
,
λ
2
y
+
(
1
−
λ
2
)
x
A
1
−
ν
(
x
,
y
)
<
R
A
Q
(
x
,
y
)
<
C
ν
μ
2
x
+
(
1
−
μ
2
)
y
,
μ
2
y
+
(
1
−
μ
2
)
x
A
1
−
ν
(
x
,
y
)
hold for all
x
,
y
>
0
with
x
≠
y
and
ν
∈
1
/
2
,
∞
)
, where
A
(
x
,
y
)
is the arithmetic mean,
C
(
x
,
y
)
is the contraharmonic mean, and
R
Q
A
(
x
,
y
)
and
R
A
Q
(
x
,
y
)
are two Neuman means.
Display omitted
► The intuitionistic fuzzy geometric Heronian mean (IFGHM) operator is proposed.► The intuitionistic fuzzy geometric weighed Heronian mean (IFGWHM) operator is proposed. ► The ...properties and special cases of the IFGHM operator is studied in detail. ► An approach to multi-criteria making problem is introduced based on the IFGWHM operator.
In this paper, the multi-criteria decision making problem with the assumption that the criteria are correlative is studied under intuitionistic fuzzy environment. Some new aggregation operators for intuitionistic fuzzy information are proposed, including the intuitionistic fuzzy geometric Heronian mean (IFGHM) operator and the intuitionistic fuzzy geometric weighed Heronian mean (IFGWHM) operator. We investigate the properties of the proposed operators, such as idempotency, monotonicity, permutation and boundary. Moreover, an approach is proposed for multi-criteria decision making based on IFGWHM operator. An example about talent introduction is given to illustrate the proposed method.
The generalized Heronian mean and geometric Heronian mean operators provide two aggregation operators that consider the interdependent phenomena among the aggregated arguments. In this paper, the ...generalized Heronian mean operator and geometric Heronian mean operator under the q‐rung orthopair fuzzy sets is studied. First, the q‐rung orthopair fuzzy generalized Heronian mean (q‐ROFGHM) operator, q‐rung orthopair fuzzy geometric Heronian mean (q‐ROFGHM) operator, q‐rung orthopair fuzzy generalized weighted Heronian mean (q‐ROFGWHM) operator, and q‐rung orthopair fuzzy weighted geometric Heronian mean (q‐ROFWGHM) operator are proposed, and some of their desirable properties are investigated in detail. Furthermore, we extend these operators to q‐rung orthopair 2‐tuple linguistic sets (q‐RO2TLSs). Then, an approach to multiple attribute decision making based on q‐ROFGWHM (q‐ROFWGHM) operator is proposed. Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.
PDF
