Using Fuzzy Analytic Hierarchy Process for Southern River Ranking

Mohamad Ashari Alias Siti Zaiton Mohd Hashim Supiah Samsudin Faculty of Computer Science Faculty of Computer Science Faculty of Civil Engineering, and Information Systems, and Information Systems, University Teknologi , University Teknologi Malaysia. University Teknologi Malaysia. Malaysia Malaysia Malaysia 607-5531581 607-5532458 607-5532458 [email protected] [email protected] [email protected]

ABSTRACT rivers into Class I, II, III, IV or V based on Water Quality This paper presents the application of fuzzy set theory in Index (WQI) and Interim National Water Quality multi criteria decision making (MCDM). Fuzzy Analytic Standards for Malaysia (INWQS) respectively. However, Hierarchy Process (FAHP) technique will be used to rank these classification schemes did not consider other alternatives to find the most reasonable and efficient use aspects such as water quantity, land use and economy of river system. The overall aspects of river system which directly influence the final result in finding the including both qualitative and quantitative are most appropriate use of water system. Therefore, this emphasized. Four criteria and 20 sub-criteria have been study included water quantity, land use and economy identified and compared. Fuzzy numbers and linguistic aspect in the decision making. variables are presented to address inherently uncertain or imprecise data. The technique is tested to real rivers data. Previous study on river ranking ([1], [30]) had used point A comparison between the proposed technique and the value to represent the subjective data. This approach is previous results obtained using conventional techniques found to be adequate when the absolute point value can is presented. exactly represent the DMs preferences. However, this point value cannot represent the degree of preference of the DMs and also the degree of risk tolerance that the Categories and Subject Descriptors DMs are ready to take. Also, in real situation, the I.2.1. [Computing Methodologies] : Artificial absolute point value is not always adequate to represent Intelligence: Applications and Expert Systems the DMs preference naturally. Decision makers usually find it more convenient to express interval judgments General Terms than fixed value judgments due to the fuzzy nature of the Algorithms comparison process [2]. Therefore, this paper proposed fuzzy set defuzzification technique to address vague data Keywords using triangular fuzzy number (TFN) and to represent MCDM, Fuzzy AHP, fuzzy logic DMs degree of confidence and degree of risk that the DMs are ready to take.

1. INTRODUCTION The purpose of this study are threefold; 1. To construct Nowadays, water resource management should be structural hierarchy that considers various aspects of river managed in integrated manner including water quality, basins, 2. To rank rivers for Southern Johor to find the water quantity, land use and economy, especially when most appropriate used of water system and 3. To compare we wanted to find the highest potential river to be the result with the previous work using water quality developed for efficient use of water systems. Water Index (WQI) and Hipre 3+. resources planning and management should consider various aspects of river basins.. Current river ranking 2. LITERATURE REVIEW techniques namely, Water Quality Index (WQI) and There a numerous multi criteria decision making National Water Quality Standard (INWQS) were found to (MCDM) techniques had been developed to date. One of only consider water quality aspects. Other important the most common MCDM techniques is AHP ([3]-[8]). water related aspects were neglected. Furthermore, the The use of AHP will keep increasing because of the more the aspects are to be considered, the more difficult AHP’s advantages such as ease of use, great flexibility, to obtain exact preference value when multiple units of and wide applicability [3]. In this study, AHP will be data are used. The difficulties also faced by the decision used together with fuzzy set to solve river ranking maker (DM) when there exist qualitative data in the problem. decision making process. In this study, a special focus is given on the method that deals with vague qualitative Numerous authors have presented different ranking data which the DMs accounted during data acquisition. methods to rank alternatives under fuzzy environment during the last two decades [8]. Bottani and Rizzi [9] had Currently, in Malaysia, water quality data were used to used fuzzy logic to deal with vagueness of human thought determine the water quality status weather in clean, and AHP to make a selection the most suitable dyad slightly polluted or polluted category and to classify the

105 supplier/purchased item. Buyukozkan et al. [10] had used extensively dealing with such problems [32]. proposed fuzzy AHP method to evaluate e-logistics-based Problems such as ranking, evaluation and comparing strategic alliance partners. Efendigil et al. [2] proposed river to find the best management strategies is considered two-phase model based on artificial neural networks and as multiple criteria decision making. Ranking, comparing fuzzy AHP to select a third-party reverse logistics and evaluating existing river basin to find the most provider. Cascales and Lamata [11], proposed fuzzy AHP efficient and reasonable use of water system need a for management maintenance processes where only proper algorithm. linguistic information was available. Pan [12] used fuzzy AHP for selecting the suitable bridge construction The challenge is when the data consist of vague data method. Sheu [13], proposed a hybrid neuro-fuzzy besides exact data values. Fuzzy logic has been the most methodology to identify appropriate global logistics widely used AI technique used in MCDM ([8], [34], [35], operational modes used for global supply chain [36]). Fuzzy logic also had been widely used to represent management. Tsai et al. [14] used fuzzy AHP for market data that cannot be given by exact (crisp) value. positioning and developing strategy in order to improve Therefore, the present of variety of units involved in the service quality in department stores. Wu et al. [15], evaluation process has motivated this work in handling proposed fuzzy AHP for measurement non-profit vague data involving qualitative data. organizational performance. Huang et al. [16] had applied fuzzy AHP to represent subjective expert judgements in 4. FUZZY AHP APPROACH government-sponsored R&D project selection. Lee et al. The propose approach consists of 3 stages: Data [17] had constructed fuzzy AHP to evaluate performance gathering, Fuzzy-AHP calculation and Decision making. of IT department in the manufacturing industry in Steps taken in each stage are described as follows: Taiwan. Chang C W et al. [18, 19], used fuzzy AHP to evaluate and controlling silicon wafer slicing quality. Chang and Wang [20] had proposed consistent fuzzy Stage 1: Data Gathering. preference relation in a comparison matrix. Chen et al. Step 1: Determine objective and choosing alternatives. [21], proposed combination of fuzzy AHP with multi This is done through literature survey and discussion with dimensional scaling in identifying the preference knowledgeable experts. During this step, we do the similarity of alternatives. following: • Define the problem clearly with specifications Chen and Qu [22], had proposed fuzzy AHP to evaluate on its multi-criteria aspects. the selection of logistics centre location. Dagdeviren and • Determine the overall goal and sub-goals, Yuksel [23], developed fuzzy AHP for behavior-based identifying the evaluation criteria. safety management. Nagahanumaiah et al. [24], using fuzzy AHP to identify problem features for injection Step 2: Determines criteria to be used in the ranking mold development. Duran and Aguilo [25], used fuzzy process. AHP for machine-tool selection. Onut et al. [26], In this step, we identified the candidate alternatives. This proposed a combined fuzzy AHP and fuzzy TOPSIS is also done with the confirmation from the knowledge approach for machine tool selection problem. Yang et al. experts. 4 criteria namely water quality, water quantity, [27], proposed fuzzy AHP for Vendor selection by land use and economy have been identified. 20 sub- integrated fuzzy MCDM techniques with independence criteria namely biochemical oxygen demand (BOD), and interdependence. suspended solid (SS), pH, dissolve oxygen (DO), chemical oxygen demand (COD), ammonia nitrogen A significant finding from all the researchers is they used (AN), temperature, iron, flow rate, length of river, width triangular fuzzy number (TFN) to represent vague data or of river, residential, industry, agriculture, forest, fishery, linguistic variables. It is important to note that the extent industry, recreation and reservoir have been chosen. analysis method used by [23] and [26] was found cannot estimate the true weights from a fuzzy comparison matrix Step 3: Structuring decision hierarchy. [28]. In this step, the decision problem is structured into a hierarchical model, in which the overall goal (usually the selection of the best alternative) is situated at the highest 3. MOTIVATION level; elements with similar features (usually evaluation Water is the most vital resource for all living things on criteria) are grouped at the same interim level and earth. River is one of the main sources of fresh water on decision variables (usually alternatives) are situated at the earth besides lake and wetlands. Excessive use and lowest level misuse of surface and groundwater and pollution of these vital resources by residential, agricultural, and industrial Step 4: Approved decision hierarchy. wastewater has threatened our well-being. Integrated Decision hierarchy is analysed in detail. This study water resources management (IWRM) has been gaining defined the evaluation criteria and sub-criteria using momentum in the last few years. “Planning for water quality index, quantity of water, land use and sustainable development of water resources means water economical activity. The 4 criteria and 20 sub-criteria conservation, waste and leakage prevention, improved proposed were structured in a hierarchy and final decision efficiency of water systems, improved water quality, is made. The top level in the hierarchy is our goal to find water withdrawal and usage within the limits of the the highest rank river for efficient use of water system. system, a level of water pollution within the carrying Second level in the hierarchy is the four criteria which are capacity of the streams, and water discharge from identified as water quality, water quantity, land use and groundwater within the safe yield of the system.” [31]. economy. Third level in the hierarchy is the 20 sub-

criteria identified in step 2. At the lowest level in the A common problem faced by decision makers is choosing hierarchy are alternatives which present the six rivers in the best alternative from among many. MCDM has been the comparison namely Layang river, Segget river,

106 , Tukang Batu river, Kempas river and Buloh previous work ([1], [30]) used in this study is shown in river. The structured hierarchy used in this study is Table 4.1. presented in Figure 4. Table 4.1 Sample of Triangular Fuzzy numbers for fishery

Fishery Point TFN Linguistic value variables Kempas 4 (3,4,5) Less important

Layang 4 (3,4,5) Less important

Tebrau 3 (2,3,4) Weak important

Segget 3 (2,3,4) Weak important

Buloh 2 (1,2,3) Weaker important Tukang Batu 1 (1,1,1) Weakest important

Step 6: Approving weights used. Weights were approved by knowledge experts through a construction of judgement matrix as well as weight vector W for the hierarchical structure. The comparisons are Figure 4 The structured hierarchy used in this study used to form a matrix of pair-wise comparisons called the judgement matrix A. Stage 2: Fuzzy AHP Calculation. Step 5: Assigning weights to criteria and alternatives via fuzzy AHP. In this study, all criteria in the judgement matrix are given equal important weights and all sub criteria (alternatives) weight vectors are represented using objective value, which were obtained from real data collection. These data cannot be used directly into AHP since they are in different unit, therefore data Each entry a of the judgements matrix are governed by normalization must be done in advanced. Some bigger ij the three rules: a > 0 ; a = 1/a ; a = 1 for all i. The values might be preferred and therefore have higher ij ij ji ii resulting weights of the elements may be called the local priority in AHP but for certain sub-criteria, smaller values weights. are preferred than bigger values. For water quality, the lowest value for BOD, COD, AN, SS, temperature and After a judgement matrix has been built, any fuzzy data is iron, the highest value of DO and the nearest value for pH then defuzzified and is performed using a method used by were the highest priority in AHP. For water quantity, the Chang [18, 19] as follows, highest value for flow rate, the longest and the widest rivers were the highest priority value in AHP. For land use, the highest percentage of forest and the lowest percentage of resident, industry and agriculture were the highest priority value in AHP. For economy, the highest value is the highest priority value in AHP. In the case where Lij = (Mij – Lij) * α + Lij and Uij= Uij – (Uij – Mij) * α when smaller values are preferred, for normalized values and its reciprocal value can be calculated as below. aj, the values of 1/aj will be used and therefore higher value can be obtained and hence higher priority in AHP.

Vague data were presented by triangular fuzzy numbers (TFN). Each membership function is defined by three where α display a decision maker’s preference and λ is parameters (L, M, U), where L is the lowest possible risk tolerance. Initial value for both α and λ is 0.5 to value, M is the middle possible value and U is the upper reflect normal preference and risk tolerance respectively. possible value in the DMs interval judgements. The value When α = 1, the uncertainty range is lowest and when λ = of L, M and U can also be determined by the DMs 1, the DMs are pessimistic. Based on Table 4.1, when α themselves. In this study we proposed the three fuzzy and λ is 0.5, defuzzification is performed as follows: parameters to represent conventional Saaty’s AHP 1 – 9 relative importance scale [29], given by means of the L11 = 0.5 * (4 – 3) + 3 = 3.5, U11 = 5 – (5-4) * 0.5 = 4.5. following equations ≡ (1,1,1), ≡ (x-1, x, x+1) ∀ x = a11 = [0.5 * 3.5 + (1 – 0.5) * 4.5 = 4. 2,3,..,8 and ≡ (9, 9, 9).

Eigenvalue and eigenvector were calculated and a The TFN can express subjective pair wise comparison or consistency check is performed using Saaty and Kearns’s presents certain degree of vagueness. The example of the conventional AHP method [29]. Saaty and Kearns [29] TFN and linguistic variables to represent vague data from

107 proposed consistency index (C.I.) and consistency ratio data which were used in this method. There are other (C.R.) to verify the consistency of the comparison matrix. ways, such as least value method and best value method C.I. and C.R. are defined as follows: that can be used in this work but it is beyond the focus of this study.

Table 4.2 Data for water quality

BOD COD AN SS DO Where is the largest eigenvalue of the judgement *Kem 0.87 5.66 1.34 1.43 0.26 matrix and n is the number of elements and R.I is the *Lay 31.85 119.05 123.46 23.47 0.29 random index for consistency for different order of *Teb 4.08 12.14 18.18 27.86 0.16 random matrix. The value of C.R. should be around 10% *Seg 2.39 8.81 18.87 13.16 0.13 11.20 8.27 21.28 15.82 0.08 or less to be accepted. According to Saaty and Kearns *Bul *Tuk 13.87 2.01 11.03 12.41 0.09 [29], in some cases, 20% of C.R can be tolerated but cannot more than that. pH Temp Iron

*Kem 4 1.09 1.00 Step 7: Ranking the alternatives. *Lay 2 1.14 1.42 Calculate the relative weight of element for each level. *Teb 1 1.05 1.28 The composite priorities of the alternatives will be *Seg 3 1.07 1.96 determined by aggregating the weights throughout the *Bul 6 1.06 7.28 hierarchy. Set the weight vector W made up of evaluation *Tuk 5 1.00 2.62 T criteria as [wi]nx1. W is the transpose of the weight vector W and it can be shown as [wi]nx1. The judgement matrix A *Kem = Kempas, *Lay = Layang, *Teb = Tebrau, *Seg = is made up of candidate alternatives [A1, A2, …,Am] and Segget, *Bul = Buloh, *Tuk = Tukang Batu. the evaluation criteria is given as Si, then the final score S of alternatives can be calculated as follows: Table 4.3 Data for water quantity

Length Flow Width Kempas 0.11 0.07 0.03 Layang 0.10 0.18 0.02

Then, Tebrau 1.00 0.00 1.00

Segget 0.11 0.32 0.07 Buloh 0.09 1.00 0.05 Tukang B 0.06 0.26 0.01

where aij is the relative importance of the jth evaluation wj Table 4.4 Data for land use criteria. aij is the relative importance of the ith alternative Ai corresponding to the jth evaluation criterion Resident Industry Agri Forest and is the final score of candidate alternative Ai. Operator Kempas 20.12 5.52 0.00 0.63 ⊗ represents multiplication and is an addition operator. Layang 129.87 12.71 212.77 1.00 Stage 3: Decision Making Tebrau 1.00 1.05 1.00 0.00 Step 8: Choosing the highest ranking from the set of Segget 8.36 1.00 0.00 0.00 alternatives. Alternative with the highest priority value will be the Buloh 36.23 1.16 0.00 0.00 chosen one. Tukang B 0.00 2.35 0.00 0.00

4.1 Case study The ranking method proposed is tested on ranking six rivers for Southern Johor namely, Layang River, Tebrau Table 4.5 Data for economy River, Buloh River, Kempas River, Segget River and Fish Recre Ind Agric Reserv Tukang Batu River. Kempas 1.00 0.50 1.00 0.20 0.40 Data set used in this study consists of the following: Layang 1.00 1.00 0.60 0.60 1.00 • For Water quality: SS, DO, BOD, AN, COD, pH, temperature and Iron. Tebrau 0.75 0.50 0.60 1.00 0.40 • For Water quantity: Flow rate, length of river Segget 0.75 1.00 1.00 0.20 0.40 and width of river. Buloh 0.50 0.50 1.00 0.20 0.20 • For Land use: Residential, industry, agricultural and forest. Tukang B 0.25 0.50 1.00 0.20 0.20 • For Economy: Fishery, industry, recreation, reservoir and agriculture.

For all data used in this study, average value method is used. Table 4.2 – Table 4.5 present normalized (average)

108 5. RESULT need to be considered is the difficulty in formulating the Table 5.1 shows the composite priorities for the 6 rivers problem. using fuzzy AHP method. Based on the overall composite value, Layang River is the best-ranked river followed by It is important to focus effort on structuring the decision Tebrau River, Buloh River, Kempas River, Segget River problem and the support of problem definition and and Tukang Batu River. design. There is little guidance available to help a decision analyst structure an MCDM problem ([33], Table 5.1 Composite Priorities using Fuzzy AHP. [37]). Based on review on peer reviewed papers and also review papers by other researchers had shown that until Kem Lay Teb Seg Bul Tuk now, there is still little efforts in building a knowledge ______base that stored most if not all design and definition previously used and/or published which can be used to Water qual 0.063 0.173 0.081 0.070 0.110 0.082 assist DM in structuring MCDM problem. Therefore, a Water quan 0.017 0.024 0.167 0.041 0.095 0.027 work to assist DMs to structure their problem is needed. Landuse 0.076 0.248 0.006 0.009 0.023 0.011 Economy 0.155 0.210 0.163 0.168 0.120 0.108 7. CONCLUSION AND FURTHER Overall 0.311 0.655 0.416 0.288 0.348 0.229 WORK Rank 4 1 2 5 3 6 Various aspects of river basins to find the most efficient use of water system had been proposed in this study. The Figure 5 shows comparison result of priority index proposed fuzzy AHP approach is found to be able to deal between WQI and HIPRE 3+ ([1], [30]) and fuzzy AHP with vague data using fuzzy triangular numbers. The final methods used in this study. ranking result is similar to previous HIPRE 3+ technique and slight different when compared to WQI technique. It is claimed that the proposed technique not only can be used to represent vague data but it can also represent the relative level of risk and level of confidence that the DMs may given. The TFN used in this study can also be used to represent linguistic variables should the DMs feel uncomfortable to use interval judgements. Layang River is found to be the best river to be chosen should a development project is to be made which emphasize on efficient use of river system.

Further work will focus on assisting DMs to structure the problem in a hierarchical structure. An internet-based knowledge-base will be developed. A ‘point and click’ method will be developed to make the searching faster and easier. Figure 5 Comparison results between WQI, HIPRE 3+ and Fuzzy AHP.

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Developing a Fuzzy Analytic Hierarchy Process (AHP) Model for

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