KR20130124691A - Fuzzy Topsis Approach for Flood Vulnerability Assessment - Google Patents

Abstract

)을 산출하는 단계와; (f) 중앙처리장치는 표준화된 퍼지 행렬

과 일정한 수학식이 포함된 메인 메모리 내의 프로그램을 이용해 퍼지 양의 이상적인 해(A+)와 퍼지 부의 이상적인 해(A-)를 산출하는 단계, 및 (g) 중앙처리장치는 근접도 계수(C_i+)를 구하는 일정한 수학식이 포함된 메인 메모리 내의 프로그램을 이용해 각 광역시도별 근접도 계수를 산정하고 상기 근접도 계수가 클수록 홍수 취약성의 순위가 높은 것으로 판단하는 단계로 이루어짐으로써, 불확실성을 고려하여 홍수 취약성을 정량화하기 위해 퍼지(Fuzzy) 개념을 반영하여 지역별 취약성을 산정하면서 신뢰성 있는 방법을 제시하는 효과가 있다.The present invention relates to a fuzzy topless approach for flood vulnerability assessment, wherein (a) the value of sub-substitute variables for each municipality and the weight of each surrogate variable given by a certain number of experts and the sub-substitute weight for each surrogate variable are inputted. It is stored in the main memory by the device, and the central processing unit writes a histogram for each detailed surrogate value by using a program in the main memory including the value of the detailed surrogate variable and logs an uneven distribution of the histogram. Converting to a form; (b) standardizing and storing the value of each substitute variable using a constant equation for obtaining a standardized value and a program in the main memory including the value of the substitute variable; (c) The central processing unit selects the minimum value and the mode and maximum value through the histogram for each standardized subvariable value stored in the main memory, and each surrogate variable assigned by a certain number of experts stored in the main memory. By selecting the minimum and maximum values through the histogram and the minimum and maximum values for each weighted variable and each weighted subvariable, it converts each standardized subsurface variable value and each weighted value into a triangular fuzzy index in the form of (minimum, mode, maximum). Making a step; (d) The central processing unit is weighted using a program in the main memory that includes a constant equation that calculates the value of each sub-substitute variable for each broad perspective converted to trigonometric index, the weight of each sub-substitute variable, and the product of two trigonometric indexes. Calculating a weighted fuzzy matrix for each surrogate variable and each wide view by obtaining a triangular fuzzy index of each detailed surrogate variable value and adding the triangular fuzzy index of each detailed surrogate variable weighted by the surrogate variable; (e) The central processing unit uses a program in main memory that includes a weighted fuzzy matrix and certain equations,

); (f) The central processing unit has a standardized fuzzy matrix

And calculating an ideal solution of the fuzzy amount (A +) and an ideal solution of the fuzzy portion (A-) using a program in the main memory including the equation and (g) the central processing unit having a proximity coefficient (C _i +). Using the program in the main memory including a constant equation to calculate the proximity coefficient for each wide-spectrum trial, and the larger the proximity coefficient is determined to rank higher flood vulnerability, considering the flood vulnerability in consideration of uncertainty In order to quantify, it is effective to suggest a reliable method while calculating regional vulnerabilities by reflecting the concept of fuzzy.

Description

Fuzzy TopSIS Approach method to Flood Vulnerability Assessment

The present invention relates to a fuzzy topless approach for flood vulnerability assessment, and more particularly, to provide a reliable method for estimating regional vulnerability by reflecting fuzzy concept to quantify flood vulnerability in consideration of uncertainty. And fuzzy topless approaches for flood vulnerability assessment.

Since the assessment of watershed management status is difficult to evaluate with only a single indicator such as quantity and water quality, an integrated index and various indicators are needed to comprehensively evaluate the components of the watershed system. Are being done.

In Korea, Kang Min-gu and Lee Kwang-man (2006) developed the Water Resources Sustainability Idex (WRSI), while Jeong Eun-sung and Lee Gil-sung (2007) developed the Potential Flood Damage (PFD), Watershed Evaluation Index (WEI) to quantify the overall hydrologic vulnerability of the watershed after calculating the Potential Streamflow Depletion (PSD) and Potential Water Quality Deterioration (PWQD). Has developed. (2009) developed a Flood Risk Index (FRI) based on pressure, state, and response schemes to compare and analyze vulnerability to floods between basins. Furthermore, researches considering climate change, which is becoming a big issue recently in conjunction with global warming, have developed a Vulnerability-Resilience Indicator (VRI) that can assess the regional climate change vulnerability in Korea. The direction of its use was presented. Koh and Kyung Hee-sun (2010) reviewed the climate change vulnerability assessment methodology and developed basic vulnerability assessment indicators for each local government. Min-Woo Son et al. (2011) developed the Flood Vulnerability Index (FVI), which can quantitatively indicate the increase in flood damage due to climate change, and the National Institute of Environmental Research (2012) considers future climate change. We calculated the vulnerability index of 232 metropolitan municipalities in Korea in terms of water quality, completion and water quality.

However, studies to date have not taken into account the uncertainties of hydrologic and humanities and social data input to estimate the index. In other words, the causal relationship between the natural and social systems and their components is very complex and it is difficult to obtain data that can reflect the characteristics of the system. This is inherent. In addition, the weights for indicators can vary from one expert to the next, and research on the use of scientific approaches to weighting is required.

Furthermore, uncertainty may exist in the selection of indicators used to calculate the vulnerability index.

Min-woo Son, Jin-Young Sung, Eun-Sung Jung, Jeon Soo Soo (2011). "Development of Flood Vulnerability Indicators Considering Climate Change." Proceedings of the Korea Water Resources Association Conference, Korea Water Resources Association, Vol. 44, No. 3, pp. 231-248.

The present invention has been devised to solve the above problems, and an object of the present invention is that a lot of information obtained from the real world has an uncertainty to reflect the uncertainty to reflect the concept of fuzzy to quantify flood vulnerability It is to provide a fuzzy topsis approach for flood vulnerability assessment that provides a reliable method for estimating regional vulnerabilities.

In order to achieve the above object, the present invention is (a) the value of the sub-substitute variable for each municipality and the weight of each surrogate variable given by a certain number of experts and the weight of the sub-substitute variable for each surrogate variable by the input device to the main memory Stored in the central processing unit, using the program in the main memory including the value of the detailed surrogate variable, creating a histogram for the detailed surrogate value for each substitutive variable, and converting an uneven distribution of the histogram into a log form. Wow;

(b) standardizing and storing the value of each substitute variable using a constant equation for obtaining a standardized value and a program in the main memory including the value of the substitute variable;

(c) The central processing unit selects the minimum value and the mode and maximum value through the histogram for each standardized subvariable value stored in the main memory, and each surrogate variable assigned by a certain number of experts stored in the main memory. By selecting the minimum and maximum values through the histogram and the minimum and maximum values for each weighted variable and each weighted subvariable, it converts each standardized subsurface variable value and each weighted value into a triangular fuzzy index in the form of (minimum, mode, maximum). Making a step;

(d) The central processing unit is weighted using a program in the main memory including the following equation for calculating the value of each sub-substitute variable for each broad perspective converted to trigonometric index, the weight of each sub-substitute variable, and the product of two trigonometric indexes: Calculating a triangular fuzzy index of each substituted subsurface variable value and adding the triangular exponent index of each substituted variable value weighted by each surrogate variable to calculate a weighted fuzzy matrix for each surrogate variable and each wide view; ;

,

는 각각 세부 대용변수 값과 세부 대용변수별 가중치 삼각퍼지수)(here,

,

Are the trigonometric index values for each detailed surrogate variable and each substitutive variable)

)을 산출하는 단계와;(e) The central processing unit uses a program in main memory that includes a weighted fuzzy matrix and certain equations,

);

과 일정한 수학식이 포함된 메인 메모리 내의 프로그램을 이용해 퍼지 양의 이상적인 해(A+)와 퍼지 부의 이상적인 해(A-)를 산출하는 단계, 및(f) The central processing unit has a standardized fuzzy matrix

Calculating an ideal solution of the fuzzy amount (A +) and an ideal solution of the fuzzy part (A−) by using a program in main memory including a constant equation and

(g) The central processing unit calculates the proximity coefficient for each wide-spectrum trial using a program in the main memory including a constant equation for calculating the proximity coefficient (C _i +), and the higher the proximity coefficient, the higher the ranking of flood vulnerability. The basic feature is that the step is determined to be.

Further, in the step (b) of the present invention, the equation for obtaining the normalized value I _qc is

는 세부 대용변수 q의 전체 지역(모든지자체)

에 대한 세부 대용변수 값 중 최소값을 의미하며

는 세부 대용변수 q의 전체 지역(모든지자체)

에 대한 세부 대용변수 값 중 최대값) 인 것을 특징으로 한다.Where x _qc is the value of sub-substitution of sub-sub q in region c (specific area _itself ),

Is the total region (all municipalities) of the detailed surrogate variable q

The minimum of the detailed surrogate values for

Is the total region (all municipalities) of the detailed surrogate variable q

The maximum value of the detailed substitution variable value for).

)을 산출하는 수학식은

Further, the fuzzy matrix (normalized in step (e) of the present invention)

) ≪ / RTI >

은 표준화된 삼각퍼지수, i는 광역시도의 갯수, j는 대용변수의 갯수,

(

),

(

),

,

,

는 각각 삼각퍼지수로 변환된 대용변수 값의 최소값, 최빈값과 최대값,

는 대용변수가 편익기준(B)일 경우 각 광역시도별로 삼각퍼지수로 변환된 대용변수 값의 최대값 중에서 최대값,

는 대용변수가 비용기준(C)일 경우 각 광역시도별로 삼각퍼지수로 변환된 대용변수 값의 최소값 중에서 최소값) 인 것을 특징으로 한다.(here,

Is the standardized triangular index, i is the number of global trials, j is the number of surrogate variables,

(

),

(

),

,

,

Are the minimum, mode, and maximum values of the surrogate variable converted into trigonometric indexes,

If the surrogate variable is the benefit criterion (B), the maximum value of the surrogate variable value converted into the triangular fuzzy index for each regional trial,

If the surrogate variable is the cost criterion (C), it is characterized in that the minimum value of the minimum value of the surrogate variable converted into a triangular fuzzy index for each regional attempt.

Further, in the step (f) of the present invention, the equation for calculating the ideal solution of the purge amount (A +) and the ideal solution of the purge part (A−) is

라 할때

,

이고,

,

이며, i는 광역시도의 갯수, j는 대용변수의 갯수) 인 것을 특징으로 한다.(here,

When

,

ego,

,

I is the number of global trials, and j is the number of surrogate variables).

Further, in the step (g) of the present invention, the equation for obtaining the proximity coefficient (C _i +) is

와

는 각각 A+(FPIS)와 A-(FNIS)로부터 각 광역시도의 대용변수 값과의 간격(

,

,

와

는 A+(FPIS)와 A-(FNIS)로부터 각 광역시도의 대용변수 값과의 거리로

라 할때

) 인 것을 특징으로 한다.
(here,

Wow

Is the distance from the surrogate value of each global trial from A + (FPIS) and A- (FNIS), respectively.

,

,

Wow

Is the distance from A + (FPIS) and A- (FNIS) to the surrogate variable value for each global trial.

When

It is characterized by that).

As mentioned above, the inventors of the fuzzy topsis approach for flood vulnerability assessment have a lot of information from the real world, so in order to quantify the flood vulnerability in consideration of such uncertainty, the vulnerability concept is applied to reflect the regional vulnerability. It is effective to suggest a reliable method while calculating.

1 is a flow diagram of a fuzzy topsis approach for flood vulnerability assessment in accordance with the present invention.
2 is a diagram showing the concept of a triangular purge index.
3 is a diagram showing an example of a histogram converted into log form and histogram for substitutive substitute data.
4 is a diagram showing the distance between each surrogate variable of the sixteen wide field trials and each surrogate variable of FPIS and FNIS.
FIG. 5 shows the results of a fuzzy top shepherd (TOPSIS) and the results of a top sheath (TOPSIS) and weighted sum method; FIG.
FIG. 6 is a comparison of sensitivity, adaptability, climate exposure, triangular fuzzy index (TFN) and topsis (TOPSIS) sensitivity, adaptability, and climate exposure values.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings.

The process of the present invention can be largely divided into several steps as shown in FIG. First, we define vulnerabilities that take into account climate change, and then determine proxy variables and weights through Delphi investigation. After that, the histogram distribution of the input data (substitute variable values) is checked to confirm the discrimination of the evaluation criteria, and the insufficient variables are converted into a log form and reviewed again. It is also noncommensurable because the unit of measure for each surrogate variable varies. Next, the input data (substitute variable values) and weights are converted into triangular fuzzy numbers (TFNs), followed by normalization of triangular fuzzy indexes (TFNs) of different scales. Finally, the vulnerability is assessed using the Fuzzy Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) technique.

Meanwhile, in the present invention, the values of the surrogate variables and the weights in the surrogate variable and the weight determination step among these stages are determined by the National Institute of Environmental Research (2012, Vulnerability Map by Climate Change, NIER 2011-04-1290, pp. 5-19). .) Results were used.

Vulnerability Concept

The concept of vulnerabilities is used in many different fields, and definitions are not defined in one. UNDP (2005) defines vulnerabilities as sensitivity to exposure to climate variability or stress and the risks of exposure units due to their ability to cope, recover, and adapt, and to adapt to climate change stimuli with climate change vulnerabilities. Expressed as a function of ability. IPCC (2007) understands climate change vulnerabilities as a function of the nature, scale and rate of climate change, sensitivity to climate change, and adaptability to which the system is exposed, and external factors such as system exposure to climate change and these stressors. They should include internal factors such as sensitivity to and adaptability. Climate change adaptation is also defined as the activity that mitigates damages, or further promotes beneficial opportunities, through natural and anthropogenic system adjustments to the impacts and effects of climate change now and in the future.

In the present invention, when a system that is vulnerable to climate change is exposed to various effects of climate change, it is defined as exposure, sensitivity, and adaptability to the effects, where exposure and sensitivity are determined by potential effects, Defined as a combination of capabilities.

Substitute Variables and Weights

As a method for objectively determining surrogate variables and weights, there are techniques such as Delphi. The Delphi technique is conducted by guaranteeing anonymity to experts in each field and predicts the phenomenon through repeated collection and exchange of opinions. The feedback from the experts will be reflected in the next questionnaire and the feedback will go through. Through this, exchange of opinions is made, and based on this, feedback process of revising and supplementing one's opinion is repeated and consensus of opinion is achieved. Therefore, it is a suitable technique for collecting various opinions of various experts.

The general procedure of the Delphi technique is to prepare in advance, then to conduct a real survey, and finally to analyze and conclude several surveys. Also, in the Delphi technique, the right area and the right number of experts are important. Existing studies have argued that the larger the number of experts, the better, and that the 15 groups of experts, in terms of cost and efficiency, have shown little difference.

Histogram and Standardization of Substitute Variable Data

The data of each substitutive variable is checked through the histogram to determine the distribution of the data, and the data with low discrimination due to the uneven distribution are converted into a log form. Because the rank value is determined by the researcher's subjective judgment, it can be an obstacle to obtaining an appropriate histogram. Therefore, in the present invention, the following equation 1 is generally used to determine the number of rank sections, but the present invention is not limited thereto.

Where k is the number of class intervals and n is the number of data points.

Also, since each surrogate variable has different units, it is necessary to standardize various values in order to create an integrated index. In the present invention, as shown in Equation 2 (standardized value), the re-scaling method of standardizing the data within the entire data range to have a value of 0 to 1 is used.

는 대용변수 q의 전체 지역

에 대한 대용변수 값 중 최소값을 의미하며

는 대용변수 q의 전체 지역

에 대한 대용변수 값 중 최대값을 의미한다.
Where x _qc is the substitution variable value of substitution variable q in region c.

Is the total area of substitution variable q

Quot; means a minimum value among substitution variable values for "

Is the total area of substitution variable q

Quot; means the maximum value among substitution variable values for "

Trigonometric Index ( TFN )

The basic definition of fuzzy set and fuzzy number theory is as follows.

A fuzzy set is a set with elements that have ambiguous boundaries and whose boundaries belong to a particular subset and whose boundaries change gradually, rather than being clear. All elements included in the fuzzy set are represented by membership function. A membership degree of 1 means completely belonging to the fuzzy set, and a boundary region has a value between 1 and 0.

The fuzzy number means "usually 10" or "about 10". In other words, the fuzzy number is a number represented by the degree of belonging that is likely to be a value. For example, if the fuzzy numbers A = [a ₁ , a ₃ ], (a ₁ , a ₃ ∈R (real), a ₁ <a ₃ ), this interval can be considered a set. Therefore, the membership function μ _A (x) of the interval set is expressed by Equation 3 below.

There are many forms of fuzzy numbers that represent these membership functions. Of these many types of fuzzy numbers, the triangular fuzzy index (TFN) can be represented by three points, making it easy to use. For example, if the triangular purge number (TFN) A is defined as (a ₁ , a ₂ , a ₃ ) ∈ R (real), the following equation (4) may be expressed as shown in FIG. 2.

,

의 곱셈은 다음의 수학식 5와 같다.Also, two triangular indexes (TFNs)

,

Is multiplied by Equation 5 below.

In the present invention, when using a simple average value of the sub-substitute variables of 232 city and districts for each of the 16 metropolitan cities as shown in Table 1 below, uncertainty may occur in this process, The weight value assigned by 11 people is converted into trigonometric index (TFN) and used.

Fuzzy Top Sheath TOPSIS)

TOPSIS is a concept that allows you to select the alternative that is the closest to the Positive Ideal Solution (PIS) and the farthest from the Negative Ideal Solution (NIS). It is a technique that induces rational selection of human beings by considering alternatives simultaneously. In addition, the evaluation results of all the alternatives can be easily calculated and displayed in terms of multi-attributes.

은 다음의 수학식 6과 같이 나타낼 수 있다.In order to apply the triangular index (TFN) to TOPSIS, different scales of the triangular index (TFN) should be standardized to comparable scales while maintaining the characteristics of the triangle index (TFN). Standardized fuzzy matrix

May be expressed as in Equation 6 below.

은 표준화된 삼각퍼지수(TFN)를 의미하며, i는 각 지자체(광역시도)의 갯수, j는 각 속성(대용변수)의 갯수를 의미한다. 또한, 다음의 수학식 7 내지 10의 B와 C는 각 편익기준(측정치가 클수록 더 선호되는 기준, 예를 들어 민감도와 기후노출)과 비용기준(측정치가 작을수록 더 선호되는 기준, 예를 들어 적응능력)의 집합이다.here,

Is the standardized triangular exponent (TFN), i is the number of municipalities, and j is the number of each property (substitute variable). In addition, B and C in the following Equations 7 to 10 are each benefit criterion (the larger the measurement, the more preferable criteria, such as sensitivity and climate exposure) and the cost criterion (the smaller the measurement, the more preferred criteria, for example Adaptability).

,

,

는 각각 삼각퍼지수로 변환된 대용변수 값의 최소값, 최빈값과 최대값이고,

는 대용변수가 편익기준일 경우 각 광역시도별로 삼각퍼지수로 변환된 대용변수 값의 최대값 중에서 최대값이고,

는 대용변수가 비용기준일 경우 각 광역시도별로 삼각퍼지수로 변환된 대용변수 값의 최소값 중에서 최소값이다.here,

,

,

Are the minimum, mode, and maximum values of the surrogate variable converted into trigonometric indexes, respectively.

Is the maximum value of the maximum value of the surrogate variable converted into triangular fuzzy index for each metrology when the surrogate variable is a benefit criterion.

Is the smallest value among the minimum values of the surrogate variable converted into triangular purge index for each regional trial when the surrogate variable is a cost basis.

라 할 때 표준화된 퍼지 행렬

로부터 퍼지 양의 이상적인 해(Fuzzy Positive Ideal Solution, FPIS)와 퍼지 부의 이상적인 해(Fuzzy Negative Ideal Solution, FNIS)는 다음의 수학식 11과 같이 정의된다.Further, here

A standardized fuzzy matrix

From the Fuzzy Positive Ideal Solution (FPIS) and the Fuzzy Negative Ideal Solution (FNIS) is defined as in Equation 11 below.

,

이고,

,

이며, i는 각 지자체(광역시도)의 갯수, j는 각 속성(대용변수)의 갯수를 의미한다.here,

,

ego,

,

Where i is the number of municipalities and j is the number of each property.

과 TFN

의 거리를 구하는 방법으로 계산할 수 있다. 또한, A+(FPIS)와 A-(FNIS)로부터 각 지자체(i)인 광역시도의 대용변수 값과의 간격

와

은 다음의 수학식 13 과 14를 이용해 유도할 수 있으며 각 대안의 상대적 근접도 계수, C_i+는 다음의 수학식 15를 이용해서 도출할 수 있다. 여기서 1위는 가장 취약한 지역이며 16위는 가장 덜 취약한 지역을 의미한다.The distance between A + (FPIS), A- (FNIS) and the surrogate variable value of the metropolitan city, each municipality (i), is TFN as shown in Equation 12 below.

And TFN

Can be calculated by a method of finding the distance of the object. In addition, the distance from the surrogate variable values of the metropolitan city (i) of each municipality from A + (FPIS) and A- (FNIS)

Wow

Can be derived using the following equations (13) and (14), and the relative proximity coefficient of each alternative, C _i +, can be derived using the following equation (15). The first place is the most vulnerable area and the 16th place is the least vulnerable area.

Fudge( Fuzzy ) TOPSIS Application of

In the present invention, the results obtained through the Delphi survey from the National Institute of Environmental Research (2012) were used for proxy variable selection and weight selection. The National Institute of Environmental Research (2012) constructs a detailed list of surrogate variables and asks 11 experts to select a list of surrogate variables through the first Delphi survey. A total of 21 final surrogate variables were selected, including 7 (adaptive capacity), 5 climate exposures. Sensitivity is selected as a surrogate variable that can cause flood damage, flood damage, factors that induce flooding, and surrogate variables that can reflect past flood damage performance. In this case, surrogate variables were selected that reflect adaptable socio-economic factors and countermeasures installed for dimensions, and climate exposures were selected to show concentration of precipitation as surrogate variables that could reflect vulnerability in the flood sector. . In addition, the 2nd Delphi survey was conducted on the selected surrogate variable list, and the 3rd Delphi survey was conducted through the derived 2nd Delphi survey results, and the final weight was determined as shown in Table 2 below. On the other hand, the weight of the following Table 2 is an average of the values of 11 experts, the present invention uses a triangular fuzzy index.

In the present invention, the histogram of the detailed surrogate data of 232 municipalities is analyzed to confirm the distribution form of the selected detailed surrogate data. For example, as a result of checking the histogram of the detailed surrogate variable C3, the distribution of the data is not uniform as shown in FIG. 3 (a), and the distribution of the data is changed evenly when converted to the log form as shown in FIG. 3 (b). . Where the x-axis is the class interval and the y-axis is the frequency. As a result of histogram analysis of 232 municipalities of all substitutive variables, except for summer precipitation, maximum daily rainfall, and regional average slope, the remaining data were converted into log form because the data distribution was not uniform. In addition, each substitutive variable is standardized in the range of 0 to 1 because the unit of measurement is different.

Here, the number of rank sections is obtained through Equation 1, and standardization is obtained through Equation 2.

In other words, the value of the sub-substitute variable for each municipality, the weight of each surrogate variable given by a certain number of experts and the weight of the sub-substitute variable for each surrogate variable are stored in the main memory by the input device, the central processing unit is Using the program in the main memory including the value of the detailed surrogate variable, a histogram with the x-axis class interval and the y-axis frequency for the detailed surrogate variable value is created for each sub-substitute variable, and the uneven distribution of the histogram is in log form. To convert. In addition, the standardization of each substitute variable is obtained by the CPU using a program in the main memory including the value of Equation 2 and the substitute variable. Here, the execution of the above process is performed by a program that directly codes an algorithm through a commercial program such as Excel or a program language to perform the process with a computer.

In addition, as shown in Table 1 above, in order to quantify vulnerabilities of 232 municipalities in units of 16 wide city trials, triangular fuzzy index (TFN) of standardized substitutive variable data of 16 wide city trials (Minimum, Mode, Maximum) Convert to For example, Seoul Metropolitan Government is composed of 25 districts and draws histograms of the values of 25 districts for each sub-substitute variable and uses them as the triangular fuzzy index (TFN). At this time, the number of rank sections is calculated through the above equation (1). In the case of the remaining 15 broad-based trials, the value of each sub-substitute variable in the city and district is converted into a triangular fuzzy index (TFN). In the case of weights, triangular fuzzy numbers are calculated by deriving the minimum, mode, and maximum values using the histogram, and the weights of sensitivity, adaptability, and climate exposure converted to triangular fuzzy indexes (TFNs). In Table 3 below, the weight of each substitute variable is shown in Table 4 below. However, it is impossible to convert to trigonometric index (TFN). For example, in the case of the low-area of 10 m or less in Seoul, the values of 25 spheres are all the same, so all three fuzzy numbers use the same value.

In other words, the conversion of the standardized substitute variable value and the weight into triangular fuzzy index in the form of (minimum value, mode value, maximum value) means that the central processing unit has the minimum value for each standardized subvariable value for each global trial stored in the main memory. The mode and the maximum value are selected through the histogram and the minimum and the maximum value through the histogram are selected for the weight of each surrogate variable and the weight of each sub-substitute variable given by a certain number of experts stored in the main memory. Here, the above process is performed by a program that directly codes an algorithm through a commercial program such as Excel or a program language to perform the above process with a computer.

Each sub-substitute value converted into trigonometric index (TFN) and the corresponding weight are multiplied by a weight by the arithmetic calculation of the fuzzy number as shown in Equation 5 above, and the trigonometric index of each weighted sub-substitute value is 3 The weighted fuzzy matrix is obtained for each of three surrogate variables and for each global trial by adding them back into each surrogate variable. Since these weighted fuzzy matrices have different scales, they must be standardized at comparable scales. In the present invention, in order to represent the most vulnerable regions as the final calculated vulnerability index is larger, the standardized fuzzy matrix as shown in Equation 6 is given by using the sensitivity and climate exposure surrogate variables as a benefit criterion and the adaptability as a cost criterion. Table 5 shows.

That is, the CPU calculates a weighted fuzzy matrix by using each sub-substitute value converted into a triangular fuzzy index, a corresponding weight, and a program in the main memory including Equation 5, and the weighted fuzzy matrix And a standardized fuzzy matrix using a program in the main memory including Equations 6 to 10. Here, the above process is performed by a program that directly codes an algorithm through a commercial program such as Excel or a program language to perform the above process with a computer.

The fuzzy TOPSIS technique can be applied using the above results. The results of calculating the FPIS and the FNIS are shown in Table 6, and the distances between the surrogate variables (sensitivity, adaptability, climate exposure) and the surrogate variables of the FPIS and FNIS were calculated as shown in FIG. 4. In the case of FIG. 4 (a), the area located farther from the lower left side is relatively less vulnerable. In the case of FIG. Based on this, the proximity coefficients and rankings of flood vulnerabilities of 16 metropolitan cities were drawn and shown in Table 7. As a result, Jeollanam-do, Busan, and Gyeongsangnam-do were selected as the most vulnerable areas for flooding, and Seoul, Daejeon, and Chungcheongnam-do were the least vulnerable areas.

과 상기 수학식 11이 포함된 메인 메모리 내의 프로그램을 이용해 퍼지 양의 이상적인 해(FPIS)와 퍼지 부의 이상적인 해(FNIS)를 산출하고, 상기 수학식 12 내지 14이 포함된 메인 메모리 내의 프로그램을 이용해 각 광역시도별로 표준화된 퍼지 행렬에서의 각 대용변수 값(바람직하게는, 표준화된 퍼지 행렬(표 5)에 삼각퍼지수로 변환된 각 대용변수별 가중치(표 3)를 곱한 값)과 FPIS 및 FNIS의 각 대용변수 값 간의 거리를 산출하며, 상기 수학식 15가 포함된 메인 메모리 내의 프로그램을 이용해 각 광역시도별 근접도 계수를 산정하고 상기 근접도 계수가 클수록 홍수 취약성의 순위가 높은 것으로 판단한다. 여기서도, 상기 과정의 수행은 이를 컴퓨터로 수행하기 위해 엑셀(Excel)과 같은 상용 프로그램이나 프로그램 언어를 통해 직접 알고리즘을 코딩한 프로그램에 의해 이루어지게 된다.That is, the central processing unit is a standardized fuzzy matrix

And an ideal solution of the fuzzy amount (FPIS) and an ideal solution of the fuzzy part (FNIS) using a program in the main memory including Equation (11), and using a program in the main memory including Equations 12 to 14, respectively. The value of each surrogate variable in the fuzzy matrix normalized by the wide range of perspectives (preferably, multiplied by the standardized fuzzy matrix (Table 5) multiplied by the weight of each surrogate variable converted to the triangular fuzzy index (Table 3)) and FPIS and FNIS The distance between the values of the surrogate variables is calculated, and the proximity coefficient for each wide-area view is calculated using a program in the main memory including Equation 15, and it is determined that the flood vulnerability is higher as the proximity coefficient is larger. Here, the above process is performed by a program that directly codes an algorithm through a commercial program such as Excel or a program language to perform the above process with a computer.

The results of the fuzzy TOPSIS and the results of the TOPSIS and weighted sum method are shown in FIG. 5. Jeollanam-do, which was ranked first in the Fuzzy TOPSIS, ranked fourth in TOPSIS, while Jeju, which was fifth in the Fuzzy TOPSIS, ranked first in TOPSIS, and Gyeongsangbuk-do, which was ranked sixth and seventh in the Fuzzy TOPSIS. And Gangwon-do ranked 11th and 12th in TOPSIS, while Gwangju and Daejeon, which were 13th and 15th in Fuzzy TOPSIS, ranked 6th and 8th in TOPSIS. Other rankings were the same or showed slight fluctuations. As a result of comparing the fuzzy TOPSIS and the weighted sum method, Jeollanam-do and Jeju-do were ranked 4th and 1st in the weighted sum method. In addition, the 6th and 7th positions in the fuzzy TOPSIS shifted to 8th and 11th positions in the weighted sum method, and the 13th and 15th positions in the fuzzy TOPSIS shifted to 6th and 12th positions in the weighted sum method. The rest of the rankings were the same or fluctuated slightly.

To determine the cause of the ranking fluctuation, the sensitivity, adaptability, and triangular index (TFN) of fuzzy TOPSIS and TOPSIS sensitivity, adaptability, and climate exposure values for A5 and A14 with large ranking fluctuations were investigated. It was compared as shown in FIG. As a result, in case of A5, the sensitivity of Fuzzy TOPSIS and the TFN distribution reflect the distribution of values smaller than the value of TOPSIS, whereas the adaptability reflects the distribution of values larger than the average value. Appeared. As the sensitivity and climate exposure were defined earlier, the weaker the adaptation ability, the greater the vulnerability. Therefore, A5 is ranked 6th in TOPSIS and 13th in fuzzy TOPSIS. In the case of A14, the sensitivity reflects a distribution larger than the mean, and the adaptability reflects a distribution smaller than the mean. Therefore, we believe that the 11th place in TOPSIS shows a fluctuation in ranking, with the vulnerability rising to the 6th place in fuzzy TOPSIS. In other words, the results of the fuzzy TOPSIS using the triangular fuzzy index (TFN) reflecting the distribution of data are clearly different from those of TOPSIS, which uses a simple average of the values of 232 city and districts for each of 16 metropolitan cities. Could.

In other words, the results of common Multi Criteria Decision Making (MCDM) methods that do not combine the results of fuzzy TOPSIS with the concept of fuzzy using the same data and weighted results are due to data uncertainty. Since the present invention can vary greatly, it is necessary to use a triangular fuzzy index (TFN) to consider the uncertainty of data and weights of surrogate variables.

While specific preferred embodiments of the present invention have been illustrated and described above, the present invention is not limited to the above-described embodiments, and a person skilled in the art to which the present invention pertains has the technical gist of the present invention. Various changes can be made without departing.

Claims (8)

(a) The value of the detailed surrogate variable for each municipality, the weight of each surrogate variable assigned by a certain number of experts and the weight of the substitutive variable for each surrogate variable are stored in the main memory by the input device, and the central processing unit is stored in the main surrogate variable. Creating a histogram for each detailed surrogate variable using a program in main memory including a value of and converting the histogram having an uneven distribution into a log form;
(b) standardizing and storing the value of each substitute variable using a constant equation for obtaining a standardized value and a program in the main memory including the value of the substitute variable;
(c) The central processing unit selects the minimum value and the mode and maximum value through the histogram for each standardized subvariable value stored in the main memory, and each surrogate variable assigned by a certain number of experts stored in the main memory. By selecting the minimum and maximum values through the histogram and the minimum and maximum values for each weighted variable and each weighted subvariable, it converts each standardized subsurface variable value and each weighted value into a triangular fuzzy index in the form of (minimum, mode, maximum). Making a step;
(d) The central processing unit is weighted using a program in the main memory including the following equation for calculating the value of each sub-substitute variable for each broad perspective converted to trigonometric index, the weight of each sub-substitute variable, and the product of two trigonometric indexes: Calculating a triangular fuzzy index of each substituted subsurface variable value and adding the triangular exponent index of each substituted variable value weighted by each surrogate variable to calculate a weighted fuzzy matrix for each surrogate variable and each wide view; ;

(here,

,

Are the trigonometric index values for each detailed surrogate variable and each substitutive variable)
(e) The central processing unit uses a program in main memory that includes a weighted fuzzy matrix and certain equations,

);
(f) The central processing unit has a standardized fuzzy matrix

Calculating an ideal solution of the fuzzy amount (A +) and an ideal solution of the fuzzy part (A−) by using a program in main memory including a constant equation and
(g) The central processing unit calculates the proximity coefficient for each wide-spectrum trial using a program in the main memory including a constant equation for calculating the proximity coefficient (C _i +), and the higher the proximity coefficient, the higher the ranking of flood vulnerability. Fuzzy topless approach for flood vulnerability assessment, characterized in that it comprises the steps of determining.
The method of claim 1,
In the step (b), the equation for obtaining the normalized value I _qc is

Where x _qc is the value of sub-substitution of sub-sub q in region c (specific area _itself ),

Is the total region (all municipalities) of the detailed surrogate variable q

The minimum of the detailed surrogate values for

Is the total region (all municipalities) of the detailed surrogate variable q

Fuzzy topless approach for flood vulnerability assessment, characterized in that the maximum of the detailed surrogate values for.
The method of claim 1,
The fuzzy matrix normalized in step (e)

) &Lt; / RTI &gt;

(here,

Is the standardized triangular index, i is the number of global trials, j is the number of surrogate variables,

(

),

(

),

,

,

Are the minimum, mode, and maximum values of the surrogate variable converted into trigonometric indexes,

If the surrogate variable is the benefit criterion (B), the maximum value of the surrogate variable value converted into the triangular fuzzy index for each regional trial,

Fuzzy topless approach for flood vulnerability assessment, characterized in that when the surrogate variable is the cost criterion (C) is the minimum of the minimum value of the surrogate variable converted into a triangular fuzzy index for each regional trial.
The method of claim 1,
In the step (f), the equation for calculating the ideal solution of the purge amount (A +) and the ideal solution of the purge part (A−) is

(here,

When

,

ego,

,

And i is the number of global trials, and j is the number of surrogate variables).
The method of claim 1,
Equation for obtaining the proximity coefficient (C _i +) in the step (g)

(here,

Wow

Is the distance from the surrogate value of each global trial from A + (FPIS) and A- (FNIS), respectively.

,

,

Wow

Is the distance from A + (FPIS) and A- (FNIS) to the surrogate variable value for each global trial.

When

Fuzzy topsis approach for flood vulnerability assessment, characterized in that
The method of claim 1,
The surrogate variable in step (a) is a sensitivity, adaptability and climate exposure, fuzzy topsis approach for flood vulnerability assessment.
The method according to claim 6,
The detailed surrogate variable of sensitivity, which is the surrogate variable, includes the lowland area below 10m, lowland household below 10m, dike use area ratio, population density, total population, regional average slope, road area ratio, flood damage in the last three years and flood in the last three years Substitutive variables of adaptive capacity, which are the damage population and surrogate variables, are financial independence, number of civil servants per population, total output in the region, water management officials per area, river yield, domestic drainage capacity, and reservoir flood control capacity. The detailed surrogate variables for climatic exposure are fuzzy top-system approaches for flood vulnerability assessment, characterized in that the maximum daily precipitation, the number of days with more than 80 mm of daily precipitation, the maximum daily precipitation of five days, the ground runoff and the rainfall in summer.
The method of claim 5, wherein
In step (g), the surrogate variable value of each wide view is obtained using the normalized fuzzy matrix of step (e)

) Is a value obtained by multiplying the weight of each surrogate variable converted into the triangular fuzzy index of step (c), fuzzy topless approach for flood vulnerability assessment.

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