A Case Study on the Commercial House in Kunming (China)

Note that for some special purposes, we may use the Weighted Mean Absolute Error of interval, .

Example 4.2 Let X=[4,7]=(5.5;1.5) be the real interval,Yˆ=[1,8]=(4.5;3.5) and Zˆ=[6,8]=(7;1) be the forecasting intervals obtained by two different forecasting methods. It is easy to calculate MAEL of Yˆ= 1, MRES of Yˆ=2, MAEI of Yˆ=3, and

MREL of Zˆ= 1.5, MRES of Zˆ= 1.5, MAEI of Zˆ=3

That is Yˆhas more efficient forecasting location thanZˆ. While Zˆhas more efficient forecasting interval scale thanYˆ. However they have the same MAEI.

Example 4.3 Let the interval time series beX₁=[4,6]=(5;1), X₂=[5,8]=(6.5;1.5), the predicted intervals are X^ˆ₁=[2.8,5.4]=(4.1;1.3) and X^ˆ₂=[3.8,7.8]=(5.8;2). Then

MAEL=(|5−4.1|+|6.5−5.8|)/2=0.8. MRES = (|1−1.3|+|1.5−2|)/2= 0.4 MAEI = 0.8+0.4=1.2

5. A Case Study on the Commercial House in Kunming (China)

In this section we present a case which shows how to valuate the price of real estate in Kunming by fuzzy estimation method. The fuzzy valuation process is as follows:

(1) Decide the influence factors which are of importance for the valuation price of commercial house.

(2) Apply the fuzzy ordering method to calculate the weights{ ,w w_{1 2},...,w_k}.

(3) Collect information of the similar property case and then use the Marketing Comparison Approach to modify the value of location, house type, community and quality of the cases.

(4) Investigate the transaction price of commercial house which located in different district. In generally, five cases are possible.

(5) Compute the fuzzy mode and fuzzy mean in order to get the valuation price of our subject property.

As is mentioned before, the most important effective factors of the commercial house valuation price are location, house type, community and quality.

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The weights of location, house type, community and quality have been calculated in the section of 3.3.

Table 5.1 is the result of the surveys for weights with respect to the effective factors Table 5.1 the weights of Commercial house

factors location house type community quality

w 0.3 0.2 0.3 0.2

We use the Marketing Comparison Approach to choose some of the similar cases which depend on the most important effective factors which we will show later. Then the fuzzy estimation method will be applied to obtain the predicted value of our subject property. In this paper we suppose the appraisal purpose is to get the current market price of our subject property for the trader.

Generally, the effective factors of estimated value of a commercial home include: location, house type, community and quality. Take the commercial house in Panlong District as our subject property, so the value of location, house type, community and quality of the subject property can be standardized as 1. By using the Marketing Comparison Approach, we need to choose other similar cases as the reference object to compare. Here we take the district of Kaiyue Times, ShiGuangJunYuan, PropertyCenter, HeTangYueSe and JiangDongWorld as our comparable market cases, which are quite similar in the effective factors.

Take the district of Kaiyue Times for an example then modify the location effective factor. The standard value of location of our subject property is 1 and the evaluating rule of the location is that the less far from the center of the city the more valuable it is. Since the location of the district of Kaiyue Times is much a little far away from the center of the city than our subject property, so we can modify the location effective factor by 0.9.

Modify the house type. Our subject property in Panlong District is with one living room, two bed rooms, two bath rooms, one study room, one kitchen and twobalconies which is a quite normal type whose area is 120.5 square meters. The case in the district of Kaiyue Times is also designed similar as our subject property, but be decorated much more reasonable, easier living and with more bright sun shines. The area is 135 square meters. So we can modify the house type effective factor by 1.3.

Modify the community. The community of our subject property in Panlong District is like the other excellent districts in Kunming. It is covered with green grass and trees in the forest belt.

There are some body building equipments and entertainment facilities for the residents.

The nearest bus station is about one kilometer away and it is convenient to go to the urban centre.

There are many restaurants nearby that can supply lots of delicious dishes. However, the community in the case of the district of Kaiyue Times has more advantages. Besides, there is a modern shopping mall surrounding it and a hospital not far away. So we can modify the community effective factor by 1.1.

Modify the quality. The quality of our subject property in Panlong District is a common level and has 7 years history. However, the quality of the case in the district of Kaiyue Times has higher quality since the building only have been finished 2 years. So we can modify the quality effective

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factor by 1.2.

In order to get a more appropriate price we evaluate the price of our subject property by fuzzy estimation method.

The detailed valuation steps are as follows. The valuation price of commercial house is:

Valuation Price :{ price, location, house type, community, quality}

The price initially used to get the valuation price is the transaction price of the cases. In this paper, we investigated the transaction price under the help of one real estate business agency which located in Kunming. We get the transaction price in the first market case of Kaiyue Times district is form 5151 to 6255 yuan per square meters. As is known to all, some of the commercial houses are decorated in a high grade level, some of them are of common level and some even are blank housing. Therefore, three typical cases in the district of Kaiyue Times are selected by the rank of decoration, and the interval is from 5151 to 6522 yuan per square meter.

Let for the multiplicative weight.

The Table 5.2 showed how we get the fuzzy valuation price of our subject property.

Table 5.2 the Valuation Price of The Commercial House in Pan long DistrictUnit =RMB / m²

Factors Cases

Pricet Location House type

Fuzzy Mode [5398,5773]

Fuzzy Mean [4864,6483]

From Table 5.2 we can find that the fuzzy mode and fuzzy mean of the valuation price. Take the first case as an example, from Definition 3.2, we can find that the [5151, 6522] is the transaction price of the market case of Kaiyue Times district. Finally computed with the weight and the modified value of location, house type, community and quality, we can get the fuzzy mean of the subject property, which is

]

As is shown in the Table 5.2 we get the fuzzy mode is [5398, 5773] and the fuzzy mean is [4864, 6483]. It is not difficult to find that the interval of fuzzy mode is short than the fuzzy mean. It implies that the probabilities of the valuation price of our subject property are more likely in the

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fuzzy mode interval. However, the fuzzy mean interval implies the lowest price which the seller can accept and the highest price which the buyer can supply.

According to section 4.3we can calculate the MAEL, MAES and MAEI. The Table 5.3 shows them.

Table 5.3 the MAEL, MAES and MAEI of the valuation price, Unit =RMB / m² Fuzzy Mode

(5585;187)

Fuzzy Mean (5673;809) factors

cases

Pricet+1

( c; r)

MAEL MAES MAEI MAEL MAES MAEI Kaiyue Times （6360;747） 775 560 1335 687 62 749 ShiGuangJunYuan (5278;1493) 307 1306 1613 395 684 1079 PropertyCenter (6140;742) 555 555 1110 467 67 534 HeTangYueSe (5205;568) 380 381 761 468 241 709 JiangDongWorld (5384;496) 201 309 510 289 313 602

Result 444 622 1066 461 273 735

It is easy for us seeing the result from table 5.3 that the fuzzy mode has more efficient forecasting location than fuzzy mean, since 444 is smaller than 461. While fuzzy mean has more efficient forecasting interval scale than fuzzy mode, since 273 is smaller than 622.

6. Conclusion

Estimating the value of real estate is a wide-ranging and complex area and its evaluation involves much dispute. The advantage of the fuzzy statistical analyzing techniques proposed in this article lies in the way it handles human thought and recognition, improving on vague measurement. The presented integrated procedure differs from the traditional assessment method, and establishes the membership grade of evaluator’s weight to better capture real values. Moreover, suppose we are surveying real estate. No matter how carefully we read the measuring process, we can never be certain of the exact value, but we can answer with more confidence that the appropriate area lies within certain bounds. Though interval analysis and fuzzy set theory are areas of active research in mathematics, numerical analysis and computer science began in the late 1950s and early 1960s.

The application to statistical evaluations in real estate is just beginning.

Using fuzzy statistical analysis we can get fuzzy data which can be applied in different areas. The methodology which integrates the traditional valuation approach with fuzzy logic shows us how the appraisals can valuate a commercial house in the form of a fuzzy interval which satisfies different components of real transactions.

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