Research evaluation on impact of mobile phone information technology on the urban public space development under the internet background

Abstract

In recent years, construction of urban space in China likes a ranging fire, which effectively improves urban habitats. However, serious problems appear incessantly among decisions, layout, designs, development and management of public space in China. In terms of urban common space in individual city, it exits quality decline, structure illegibility and regression of functions and artistic appearances, which are what we need to keep away and improve on. In this paper, we study the problem of multiple attribute decision making for evaluating the impact of mobile phone information technology on the urban public space development under the internet background in which the decision making information values are interval number, a new decision making method is proposed. Then, according to the concept of the cross entropy, the relative closeness degree is defined to determine the ranking order of all alternatives by calculating the cross entropy to both the interval positive-ideal solution (IPIS) and interval negative-ideal solution (INIS) simultaneously. At last, a numerical example for evaluating the impact of mobile phone information technology on the urban public space development under the internet background is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.

Keywords

Multiple attribute decision making interval number cross entropy impact of mobile phone information technology urban public space development internet background

1 Introduction

Multiple attribute decision making (MADM) problem is to find a desirable solution from a finite number of feasible alternatives assessed on multiple attributes, both quantitative and qualitative. In the recent years, MADM has received a great deal of attention from researchers in many disciplines [1 –4]. Up to now, many operators have been proposed for aggregating information. Two of the most common operators for aggregating arguments are the weighted averaging operator [5] and the ordered weighted averaging operators [6]. The ordered weighted geometric (OWG) operator [7] is an aggregation operator based on the ordered weighted averaging (OWA) operator(Yager,1988) and on the geometric mean. Xu [8] proposed the uncertain OWA operator and Xu and Da [9] proposed the Uncertain ordered weighted geometric averaging (UOWGA) operator. Xu [10] investigated the dynamic multiple attribute decision making problems with uncertain information. Two new operators called dynamic weighted averaging (DWA) operator and uncertain dynamic weighted averaging (UDWA) operator operator are presented. Xu [11] proposed the dynamic weighted geometric averaging (DWGA) operator. In recent years, aggregating operators have been extended to many domains [12 –36].

Public service facilities are the spatial carrier of public service. The spatial distribution of public service facilities is related to the quality of life and social justice, which is an important research field in urban geography. Our country is now moving from survival society to development society, while the needs of residents is moving from basic survival data to development and enjoyment data, which is bound to put forward higher, more diversified demands of public service supply in terms of quality and quantity. However, the different class groups can not enjoy equal access to limited public resources because of the residential spatial differentiation and concentrated public resources. How to provide effective public resources to ensure each stratum can enjoy equal public service is the necessary requirement of the service-oriented government. Most domestic studies are qualitative study based on regional macro scale from the perspective of public policy, public management and so on, which ignore the distribution of urban space and social space. Therefore, it is necessary to draw lessons from foreign related theory to carry out the research of spatial equity of urban public facilities, which will enrich the equity theory about public service and look for the breakthrough point to resolve the contradiction between supply and demand of public service.

With the development of economic globalization and new media, more and more cities are facing with the problems of convergences on urban public spaces, loss of landscapes characteristics, landscapes out of fashion, defficiency of funds and so on. As an important way to show the city itself, urban public-spaces not only supply an entertainment place for people, but also it is an important carrier to show urban characteristics. Public-spaces landscapes with cultural characteristics could be of great significance in the formation process of urban culture. The soul of the landscapes lies in the contents of the culture. Thus, the establishment of urban public spaces relies on the study on the culture. It is hard to study precisely culture from certain aspects at certain time for its dynamic development process. Study on landscapes planning in urban public spaces involves in series of complicated subjects and systematic contents, such as urban planning science, planning and designing science on landscapes, urban cultural science, sociology and so on. For a long time, to seek for a suitable way on the research of urban cultural characteristics and urban public spaces is of great difficulties. It might be the key to know the loss reasons of urban landscapes characteristics and the methods to solve it. Cultural ecology supplies a new way for us to know the urban public spaces landscapes and urban culture. Only through it could we deeply understand the soul of the city and people living in it, and the necessity of urban public spaces as well. According to different functions, urban public spaces could be divided into several parts as urban parks, urban streets, urban squares, pedestrain streets for shopping and waterways. They are the windows to the outside, the main ways to reveal the urban cultures, and the places residents and travellers facing most frequently. Their development process is most representative in urban landscapes in future.

LBS provide location-based information service for mobile objects, meeting the needs of people on spatial information of 4A (anytime, anywhere, anybody, anything). As the important component and basic spatial information platform of LBS, mobile spatial information services facilitate users with different resolutions, different spatial resources, real-time dynamically changed, and large amount of spatial information. It will become an important source and approach of service for people’s daily life, and will become an important component of future information services. With the development of GIS technology, wireless positioning technology of mobile terminals, wireless transmission technology of spatial information and mobile representation technology of spatial information, there is a new opportunity for the development of mobile spatial information services. However, poor performance hardware of mobile terminals, narrow bandwidth of wireless networks and slow transmission of spatial data make enormous challenge for the application of mobile spatial information services. In this paper, we study the problem of multiple attribute decision making for evaluating the impact of mobile phone information technology on the urban public space development under the internet background in which the decision making information values are interval number, a new decision making method is proposed. Then, according to the concept of the cross entropy, the relative closeness degree is defined to determine the ranking order of all alternatives by calculating the cross entropy to both the interval positive-ideal solution (IPIS) and interval negative-ideal solution (INIS) simultaneously. At last, a numerical example for evaluating the impact of mobile phone information technology on the urban public space development under the internet background is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.

2 Preliminaries

2.1 Interval numbers

In this section, we briefly describe some basic concepts and basic operational laws related to interval numbers.

Let $\tilde{a} = [a^{L}, a^{U}] = {x | a^{L} \leq x \leq a^{U}}$ , then $\tilde{a}$ is called an interval number. If 0 ≤ a^L ≤ a^U, then $\tilde{a}$ is called a positive interval number[4].

Consider any two positive interval number $\tilde{a} = [a^{L}, a^{U}]$ and $\tilde{b} = [b^{L}, b^{U}]$ λ ∈ [0, 1], we define their operational laws as follows [4]:

$\tilde{a} + \tilde{b} = [a^{L}, a^{U}] + [b^{L}, b^{U}] = [a^{L} + b^{L}, a^{U} + b^{U}]$ ;

$λ \tilde{a} = [λ a^{L}, λ a^{U}]$ ;

${\tilde{a}}^{k} = [{(a^{L})}^{k}, {(a^{U})}^{k}]$ ;

$\tilde{a} \cdot \tilde{b} = [a^{L} \cdot b^{L}, a^{U} \cdot b^{U}]$ ;

$\frac{\tilde{a}}{\tilde{b}} = [\frac{a^{L}}{b^{U}}, \frac{a^{U}}{b^{L}}]$ .

2.2 Cross entropy

Based the entropy developed by Shannon [37], Kullback and Leibler[38] proposed a measure of the “cross entropy distance” between two probability distributions.

Definition 1. [38]. Let x_j, y_j ≥ 0 (j = 1, 2 ⋯ , n) two discrete probability measure, and $1 = \sum_{j = 1}^{n} x_{j} \geq \sum_{j = 1}^{n} y_{j}$ , then $h (X, Y) = \sum_{j = 1}^{n} x_{j} ln \frac{x_{j}}{y_{j}} \geq 0$ (1) is called the cross entropy of X with respect to Y, where X = (x₁, x₂, ⋯ , x_n) , Y = (y₁, y₂, ⋯ , y_n).

According to the definition of cross entropy, we have h (X, Y) = 0 if and only if x_j = y_j (j = 1, 2, ⋯ , n). Cross entropy is a measurement to measure the variation degree between X and Y. The larger the difference between X and Y, the larger h (X, Y); vice versa.

3 Cross entropy method for uncertain multiple attribute decision making

In this section, we shall utilize the cross entropy to solve the uncertain multiple attribute decision making problems for evaluating the impact of mobile phone information technology on the urban public space development under the internet background.

For a multiple attribute decision making problems with interval information, let A ={ A₁, A₂, ⋯ , A_m } be a discrete set of alternatives, G ={ G₁, G₂, ⋯ , G_n } be the set of attributes, whose weight vector is ω = (ω₁, ω₂, ⋯ , ω_n), with ω_j ≥ 0, j = 1, 2, ⋯ , n, $\sum_{j = 1}^{n} ω_{j} = 1$ . Suppose that $A = {({\tilde{a}}_{ij})}_{m \times n} = {[a_{ij}^{L}, a_{ij}^{U}]}_{m \times n}$ is the multiple attribute decision making matrix, where ${\tilde{a}}_{ij} = [a_{ij}^{L}, a_{ij}^{U}]$ is a preference value, which take the form of interval numbers, given by the decision maker, for the alternative A_i ∈ A with respect to the attribute G_j ∈ G.

Then, we utilize the cross entropy method to develop an approach to multiple attribute decision making problems with interval numbers, which can be described as following:

Step 1. Normalize each attribute value ${\tilde{a}}_{ij}$ in the matrix A into a corresponding element in the matrix $R = {({\tilde{r}}_{ij})}_{m \times n} = {[r_{ij}^{L}, r_{ij}^{U}]}_{m \times n}$ using the following formulas: ${\begin{matrix} r_{ij}^{L} = a_{ij}^{L} / - \sum_{j = 1}^{m} a_{ij}^{U} \\ r_{ij}^{U} = a_{ij}^{U} / - \sum_{j = 1}^{m} a_{ij}^{L} \end{matrix}, j \in I_{1};$

${\begin{matrix} r_{ij}^{L} = (1 / - a_{ij}^{U}) / - \sum_{j = 1}^{m} (1 / - a_{ij}^{L}) \\ r_{ij}^{U} = (1 / - a_{ij}^{L}) / - \sum_{j = 1}^{m} (1 / - a_{ij}^{U}) \end{matrix}, j \in I_{2} .$ (2) where I₁ and I₂ are the set of benefit attribute and cost attribute, respectively.

Step 2. Determine the interval positive-ideal solution (IPIS) and interval negative-ideal solution (INIS). ${\tilde{r}}^{+} = ({\tilde{r}}_{1}^{+}, {\tilde{r}}_{2}^{+}, \dots, {\tilde{r}}_{n}^{+}), {\tilde{r}}^{-} = ({\tilde{r}}_{1}^{-}, {\tilde{r}}_{2}^{-}, \dots, {\tilde{r}}_{n}^{-})$ (3) where ${\tilde{r}}_{j}^{+} = [max_{i} r_{ij}^{L}, max_{i} r_{ij}^{U}], {\tilde{r}}_{j}^{-} = [min_{i} r_{ij}^{L}, min_{i} r_{ij}^{U}]$

Step 3. Calculate the expected value $E ({\tilde{r}}_{ij})$ , $E ({\tilde{r}}_{j}^{+})$ and $E ({\tilde{r}}_{j}^{-})$ . $E ({\tilde{r}}_{ij}) = \frac{r_{ij}^{L} + r_{ij}^{U}}{2}$ (4) $E ({\tilde{r}}_{j}^{+}) = \frac{max_{i} r_{ij}^{L} + max_{i} r_{ij}^{U}}{2}$ (5) $E ({\tilde{r}}_{j}^{-}) = \frac{min_{i} r_{ij}^{L} + min_{i} r_{ij}^{U}}{2}$ (6)

Step 4. Calculate the cross entropy of ${\tilde{r}}_{i} = ({\tilde{r}}_{i 1}, {\tilde{r}}_{i 2}, \dots, {\tilde{r}}_{in})$ with respect to interval positive-ideal solution (IPIS) ${\tilde{r}}^{+}$ . $\begin{matrix} h ({\tilde{r}}_{i}, {\tilde{r}}^{+}) = \sum_{j = 1}^{n} ω_{j} (E ({\tilde{r}}_{ij}) ln \frac{E ({\tilde{r}}_{ij})}{E ({\tilde{r}}_{j}^{+})} + \\ (1 - E ({\tilde{r}}_{ij})) ln \frac{1 - E ({\tilde{r}}_{ij})}{1 - E ({\tilde{r}}_{j}^{+})}) \end{matrix}$ (7)

Step 5. Calculate the cross entropy of ${\tilde{r}}_{i} = ({\tilde{r}}_{i 1}, {\tilde{r}}_{i 2}, \dots, {\tilde{r}}_{in})$ with respect to interval negative-ideal solution (INIS) ${\tilde{r}}^{-}$ . $\begin{matrix} h ({\tilde{r}}_{i}, {\tilde{r}}^{-}) = \sum_{j = 1}^{n} ω_{j} (E ({\tilde{r}}_{ij}) ln \frac{E ({\tilde{r}}_{ij})}{E ({\tilde{r}}_{j}^{-})} + \\ (1 - E ({\tilde{r}}_{ij})) ln \frac{1 - E ({\tilde{r}}_{ij})}{1 - E ({\tilde{r}}_{j}^{-})}) \end{matrix}$ (8)

Step 6. Calculate the relative closeness degree of each alternative from IPIS using the following equation $c ({\tilde{r}}_{i}, {\tilde{r}}^{+}) = \frac{h ({\tilde{r}}_{i}, {\tilde{r}}^{-})}{h ({\tilde{r}}_{i}, {\tilde{r}}^{-}) + h ({\tilde{r}}_{i}, {\tilde{r}}^{+})}$ (9)

Step 7. According to the relative closeness degree, the ranking order of all alternatives can be determined. If any alternative has the highest value $c ({\tilde{r}}_{i}, {\tilde{r}}^{+})$ , then, it is the most important alternative.

4 Numerical example

At present, the Chinese urban public space construction has already gotten the certain achievement, which is being carried on with the high speed and large scale, causing the urban appearance environment greatly changed beyond recognition. But in the transformation process of urban public space construction in many areas, the construction activities of big dismantle and build greatly has brought for the environment of urban public space the enormous impact, because it is influenced by various factors, such as the idea cognition, the management operation and the market economy law and so on, causing the drop of the environment quality of urban life and the separation between urban public space and people. In order to solve the relationship between public space and masses well, we first should be in light of the people-oriented design idea, considering the crowd’s need at any time, but the most direct also is the most basic contradiction between the people and the urban public space is the problem of easy access. This section presents a numerical example for evaluating the impact of mobile phone information technology on the urban public space development under the internet background to illustrate the method proposed in this paper. Suppose an expert group plans to evaluate the impact of mobile phone information technology on the urban public space development under the internet background. There is a panel with five possible cities A_i (i = 1, 2, 3, 4, 5) to select. The expert group school selects four attribute to evaluate the five possible cities: ding172G₁ is the cultural value; ding173G₂ is the landscape value; ding174G₃ is the economical value; ding175G₄ is the the combination of both social and economical benefit. The five possible citiesA_i (i = 1, 2, ⋯ , 5) are to be evaluated using the 0-100 scale by the decision maker under the above four attributes, as listed in the following matrix. $\begin{matrix} \begin{matrix} G_{1} & G_{2} & G_{3} & G_{4} \end{matrix} \\ \tilde{A} = \begin{matrix} A_{1} \\ A_{2} \\ A_{3} \\ A_{4} \\ A_{5} \end{matrix} (\begin{matrix} [37, 47] & [60, 70] & [30, 40] & [80, 90] \\ [50, 60] & [70, 80] & [65, 75] & [40, 60] \\ [30, 40] & [42, 52] & [60, 70] & [50, 65] \\ [35, 45] & [45, 55] & [35, 45] & [70, 90] \\ [90, 100] & [60, 70] & [70, 90] & [80, 90] \end{matrix}) \end{matrix}$ (10)

Then, we utilize the proposed approach to get the most desirable city.

Step 1. Construct the normalized interval decision matrix as $\tilde{R}$ . $\tilde{R} = [\begin{matrix} [0 . 127, 0 . 194] [0 . 183, 0.253] [0 . 094, 0.154] [0 . 203, 0.281] \\ [0 . 171, 0 . 248] [0 . 214, 0.289] [0 . 203, 0.288] [0 . 101, 0.188] \\ [0 . 103, 0.165] [0 . 128, 0.188] [0 . 188, 0.269] [0 . 127, 0.203] \\ [0 . 120, 0.186] [0 . 138, 0.199] [0 . 109, 0.173] [0 . 177, 0.281] \\ [0 . 308, 0.413] [0 . 183, 0.253] [0 . 219, 0 . 346] [0 . 203, 0.281] \end{matrix}]$

Step 2. Determine IPIS and INIS as: $\begin{matrix} {\tilde{r}}^{+} = & [[0 . 308, 0 . 413] [0 . 214, 0 . 289] [0 . 219, 0 . 346] \\ [0 . 203, 0 . 281]] {\tilde{r}}^{-} = [[0 . 103, 0 . 165] \\ [0 . 128, 0 . 188] [0 . 094, 0 . 154] [0 . 101, 0 . 188]] \end{matrix}$

Step 3. Calculate the expected value $E ({\tilde{r}}_{ij})$ , $E ({\tilde{r}}_{j}^{+})$ and $E ({\tilde{r}}_{j}^{-})$ . $E (\tilde{R}) = (\begin{matrix} 0 . 160 & 0 . 218 & 0 . 124 & 0 . 242 \\ 0 . 210 & 0 . 251 & 0 . 246 & 0 . 144 \\ 0 . 134 & 0 . 158 & 0 . 228 & 0 . 165 \\ 0 . 153 & 0 . 168 & 0 . 141 & 0 . 229 \\ 0 . 361 & 0 . 218 & 0 . 282 & 0 . 242 \end{matrix})$ $E ({\tilde{r}}^{+}) = (0 . 361, 0 . 251, 0 . 282, 0 . 242)$ $E ({\tilde{r}}^{-}) = (0 . 134, 0 . 158, 0 . 124, 0 . 144)$

Step 4. Calculate the cross entropy $h ({\tilde{r}}_{i}, {\tilde{r}}^{+})$ of ${\tilde{r}}_{i} = ({\tilde{r}}_{i 1}, {\tilde{r}}_{i 2}, \dots, {\tilde{r}}_{in})$ with respect to interval positive-ideal solution (IPIS) ${\tilde{r}}^{+}$ (ω = (0.2, 0.1, 0.3, 0.4)). $\begin{matrix} h ({\tilde{r}}_{1}, {\tilde{r}}^{+}) = 0.042, h ({\tilde{r}}_{2}, {\tilde{r}}^{+}) = 0.023 \\ h ({\tilde{r}}_{3}, {\tilde{r}}^{+}) = 0.038, h ({\tilde{r}}_{4}, {\tilde{r}}^{+}) = 0.041 \\ h ({\tilde{r}}_{5}, {\tilde{r}}^{+}) = 0.000 \end{matrix}$

Step 5. Calculate the cross entropy $h ({\tilde{r}}_{i}, {\tilde{r}}^{-})$ of ${\tilde{r}}_{i} = ({\tilde{r}}_{i 1}, {\tilde{r}}_{i 2}, \dots, {\tilde{r}}_{in})$ with respect to interval negative-ideal solution (INIS) ${\tilde{r}}^{-}$ (ω = (0.2, 0.1, 0.3, 0.4)). $\begin{matrix} h ({\tilde{r}}_{1}, {\tilde{r}}^{-}) = 0.015, h ({\tilde{r}}_{2}, {\tilde{r}}^{-}) = 0.024 \\ h ({\tilde{r}}_{3}, {\tilde{r}}^{-}) = 0.013, h ({\tilde{r}}_{4}, {\tilde{r}}^{-}) = 0.011 \\ h ({\tilde{r}}_{5}, {\tilde{r}}^{-}) = 0.074 \end{matrix}$

Step 6. Calculate the relative closeness degree of each city from IPIS $\begin{matrix} c ({\tilde{r}}_{1}, {\tilde{r}}^{+}) = 0.264, c ({\tilde{r}}_{2}, {\tilde{r}}^{+}) = 0.504 \\ c ({\tilde{r}}_{3}, {\tilde{r}}^{+}) = 0.258, c ({\tilde{r}}_{4}, {\tilde{r}}^{+}) = 0.212 \\ c ({\tilde{r}}_{5}, {\tilde{r}}^{+}) = 0.996 \end{matrix}$

Step 7. According to the relative closeness degree, the ranking order of the five cities is: A₅ ≻ A₂ ≻ A₁ ≻ A₃ ≻ A₄, and thus the most desirable city is A₅.

5 Conclusion

Modern City designing is a synthesis regular design on type of city environment; peoples’ life environment and city’s public space. Recently, some cities public space building has kinds of more and more serious problems. These problems are about policy decision, planning, designing, developing, managing and so on. The most crucial reason is city’s public space developing attach impotence to building’s build only, hut less to outside landscape. For giving wide expression to city designing but building designing aim decide the direction of environment and development; search positively for the way of sustainable development on social, economy and environment; research and make interrelated field of sustainable development program and operate some large ecology programs by the aim of positive circulation of ecology environment. In this paper, we have developed the cross entropy with interval information. It can measure the discrimination information of two interval numbers. Therefore, it can be applied to multiple attribute decision making problems. An optimal decision making method based on the weights of alternatives has been established by means of the interval numbers cross entropy. Through the relative closeness degree, the best alternative can be easily identified and the ranking order of all alternatives can be determined as well. Finally, an illustrative example for evaluating the impact of mobile phone information technology on the urban public space development under the internet background illustrated the efficiency of the developed approach. In the future, we shall continue working in the application of the cross entropy to other domains [39 –50].

Footnotes

Acknowledgment

The paper is supported by the Public Space in Jiangsu since the Modern China,(13LSC011), Jiangsu Philosophy and social science project funding, 2013 and the product innovation and culture study center of Jiangnan University, China central university basic research special project funding, (2015JDZD03).

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