Assessing sustainable effectiveness of the adjustment mechanism of a ubiquitous clinic recommendation system

Abstract

Advances in computer and communication technologies have engendered opportunities for developing an improved ubiquitous health care environment. One of the crucial applications is a ubiquitous clinic recommendation system, which entails recommending a suitable clinic to a mobile patient based on his/her location, hospital department, and preferences. However, patients may not be willing or able to express their preferences. To overcome this problem, some ubiquitous clinic recommendation systems mine the historical data of patients to learn their preferences, and they apply an algorithm to adjust the recommendation algorithm after receiving more patient data. Such an adjustment mechanism may operate for several periods; however, this raises a question regarding the sustainability (i.e., long-term effectiveness) of such an adjustment mechanism. To address this question, this study modeled the improvement in the successful recommendation rate of a ubiquitous clinic recommendation system that adopts an adjustment mechanism as a learning process. Both the asymptotic value and learning speed of the learning process provide valuable information regarding the long-term effectiveness of the adjustment mechanism. The proposed methodology was applied in a regional study to a ubiquitous clinic recommendation system that adjusts the recommendation mechanism by solving an integer nonlinear programming problem on a rolling basis. The experimental results revealed that the proposed method exhibited a considerably higher level of accuracy in forecasting the successful recommendation rate compared with several existing methods. Although the adjustment mechanism exhibits long-term effectiveness, the learning speed requires improvement.

Appendices

Appendix 1

1.1 (PP Problem I)

$$ \operatorname{Min}\kern0.24em {Z}_1=\sum \limits_{t=1}^T\left({S}_{t3}-{S}_{t1}\right) $$

(22)

subject to

$$ {S}_t\ge {S}_{t1}+s\left({S}_{t2}-{S}_{t1}\right) $$

(23)

$$ {S}_t\le {S}_{t3}+s\left({S}_{t2}-{S}_{t3}\right) $$

(24)

$$ {S}_{t1}\cong 0.9957{S}_{01}-\frac{0.9555{b}_3{S}_{01}}{t}+\frac{0.3909{b}_3^2{S}_{01}}{t^2}-\frac{0.0645{b}_3^3{S}_{01}}{t^3} $$

(25)

$$ {S}_{t2}\cong 0.9957{S}_{02}-\frac{0.9555{b}_2{S}_{02}}{t}+\frac{0.3909{b}_2^2{S}_{02}}{t^2}-\frac{0.0645{b}_2^3{S}_{02}}{t^3} $$

(26)

$$ {S}_{t3}\cong 0.9957{S}_{03}-\frac{0.9555{b}_1{S}_{03}}{t}+\frac{0.3909{b}_1^2{S}_{03}}{t^2}-\frac{0.0645{b}_1^3{S}_{03}}{t^3} $$

(27)

$$ 0\le {S}_{01}\le {S}_{02}\le {S}_{03} $$

(28)

$$ {\displaystyle \begin{array}{l}0\le {b}_1\le {b}_2\le {b}_3\\ {}t=1\sim T\end{array}} $$

(29)

The objective function of PP Problem I is to minimize the sum of ranges of fuzzy successful recommendation rate forecasts. Constraints (23) and (24) demand that the membership of the actual value in the corresponding forecast must be greater than s, which is a prespecified threshold. Constraints (28)–(29) define the sequence of the three corners of the corresponding TFN.

1.2 (PP Problem II)

$$ \operatorname{Min}\kern0.24em {Z}_2=\frac{1}{T}\sum \limits_{t=1}^T\frac{\mid {S}_t-\frac{S_{t1}+{S}_{t2}+{S}_{t3}}{3}\mid }{S_t} $$

(30)

subject to

$$ \sum \limits_{t=1}^T\left({S}_{t3}-{S}_{t1}\right)\le Td $$

(31)

$$ {S}_t\ge {S}_{t1}+{s}_t\left({S}_{t2}-{S}_{t1}\right) $$

(32)

$$ {S}_t\le {S}_{t3}+{s}_t\left({S}_{t2}-{S}_{t3}\right) $$

(33)

$$ {S}_{t1}\cong 0.9957{S}_{01}-\frac{0.9555{b}_3{S}_{01}}{t}+\frac{0.3909{b}_3^2{S}_{01}}{t^2}-\frac{0.0645{b}_3^3{S}_{01}}{t^3} $$

(34)

$$ {S}_{t2}\cong 0.9957{S}_{02}-\frac{0.9555{b}_2{S}_{02}}{t}+\frac{0.3909{b}_2^2{S}_{02}}{t^2}-\frac{0.0645{b}_2^3{S}_{02}}{t^3} $$

(35)

$$ {S}_{t3}\cong 0.9957{S}_{03}-\frac{0.9555{b}_1{S}_{03}}{t}+\frac{0.3909{b}_1^2{S}_{03}}{t^2}-\frac{0.0645{b}_1^3{S}_{03}}{t^3} $$

(36)

$$ 0\le {s}_t\le 1 $$

(37)

$$ 0\le {S}_{01}\le {S}_{02}\le {S}_{03} $$

(38)

$$ {\displaystyle \begin{array}{l}0\le {b}_1\le {b}_2\le {b}_3\\ {}t=1\sim T\end{array}} $$

(39)

d is the threshold for the average range of fuzzy successful recommendation rate forecasts. The objective function of PP Problem II is to minimize the MAPE, for which each fuzzy successful recommendation rate forecast is defuzzified using the center-of-gravity method. Constraints (32) and (33) request that the membership of the actual value in the corresponding forecast must be greater than s_t, which can be different from period to period.

The objective function can be replaced by the following objective function and constraints:

$$ \operatorname{Min}\kern0.24em {Z}_2=\frac{1}{T}\sum \limits_{t=1}^T{A}_t $$

(40)

$$ {A}_t\ge 1-\frac{S_{t1}+{S}_{t2}+{S}_{t3}}{3{S}_t} $$

(41)

$$ {A}_t\ge -1+\frac{S_{t1}+{S}_{t2}+{S}_{t3}}{3{S}_t} $$

(42)

Appendix 2

1.1 (INLP problem)

$$ \operatorname{Max}\kern0.24em s=\frac{1}{n}\sum \limits_{i=1}^n{I}_i, $$

(43)

where

$$ {I}_i\left(\frac{\sum \limits_{j\ne {\alpha}_i}{X}_{i{\alpha}_ij}}{m_i-1}-1\right)\ge 0;i=1\hbox{--} n $$

(44)

$$ \sum \limits_{q=1}^Q{w}_q{\xi}_{i{\alpha}_iq}\ge {X}_{i{\alpha}_ij}\sum \limits_{q=1}^Q{w}_q{\xi}_{ijq};j\ne {\alpha}_i;i=1\hbox{--} n $$

(45)

$$ \sum \limits_{q=1}^Q{w}_q=1 $$

(46)

$$ {X}_{i{\alpha}_ij}\in \left\{0,1\right\};j\ne {\alpha}_i;i=1\hbox{--} n $$

(47)

$$ {I}_i\in \left\{0,1\right\};i=1\hbox{--} n $$

(48)

$$ {w}_q\in \left[0,1\right];q=1\hbox{--} Q $$

(49)

in a rolling manner:

$$ \mathrm{new}\kern0.24em {w}_q=\left(1\hbox{--} \eta \right)\cdot old\;{w}_q+\eta {w}_q^{\ast } $$

(50)