Interpolative picture fuzzy rules A novel forecast method for weather nowcasting

Interpolative picture fuzzy rules: A novel forecast method for weather nowcasting Pham Huy Thong Le Hoang Son Hamido Fujita VNU University of Science Vietnam National University, Vietnam thongph@vnu.edu.vn VNU University of Science Vietnam National University, Vietnam sonlh@vnu.edu.vn Intelligent Software Laboratory Iwate Prefectural University, Japan HFujita-799@acm.org A Previous works Abstract— Weather nowcasting is a short-range forecasting that maps current weather, then uses an estimation of its speed and direction of movement to forecast weather in a short period ahead — assuming the weather will move without significant changes It operates through latest radar, satellite or observational data However, Àawed characterization of transitions between different meteorological structures is its main challenges In this paper, an innovative method for weather nowcasting from satellite image sequences using the combination of picture fuzzy clustering and interpolative fuzzy rules is proposed Firstly, picture fuzzy clustering algorithm, a fuzzy clustering method based on the theory of picture fuzzy set, is used to partition the satellite image pixels into clusters Secondly, the interpolative trapezoidal picture fuzzy rules are created from the clusters Finally, particle swarm optimization is employed to train the defuzzified parameter from the rules to enhance the accuracy of the predicted satellite images in sequence The experimental results indicate that the proposed method is better than the relevant ones for weather nowcasting Zhou et al [20] used wind and temperature information of AMDAR data to the analysis of severe weather nowcasting of airport Although weather nowcasting based on radar measurements results in better than other data, there are many regions, particularly in developing countries, that are away from radar coverage [4, 18] Appropriate alternative data used to forecast the weather in these areas are satellite observations [10 - 11] There are some researches based on the observations of satellite images to develop methods to track and nowcast meteorological parameters such as in Evans [1], Shukla and Pal [5], and Melgani [9] Melgani [9] reconstructed cloudcontaminated multi-temporal and multispectral images Evans [1] used multi-channel correlation-relaxation labeling to analyze cloud motion Shukla and Pal [5] proposed an approach to study the evolution of convective cells Another method for predicting satellite image sequences combining spatiotemporal autoregressive (STAR) model with fuzzy clustering to increase the forecast accuracy was presented by Shukla, Kishtawal and Pal [6] Recently, Hoa, Thong and Son [14] proposed a method using picture fuzzy clustering and STAR for weather nowcasting from satellite image sequences Although this technique resulted in better prediction accuracy than those in [1, 5-6, 8], the forecasting result could be enhanced by an advanced forecast method such as picture fuzzy rules Keywords—Interpolative picture fuzzy rules; picture fuzzy clustering; picture fuzzy sets; satellite images; weather nowcasting; I INTRODUCTION According to Mass [7], weather nowcasting combines a description of current state of the atmosphere and a short-term forecast of how the atmosphere will evolve during the next several hours It is possible to forecast small features of the weather such as rainfall, clouds and individual storms with reasonable accuracy based on its speed and direction of movement in this time range — assuming that the weather will move without significant changes [7] Therefore, weather nowcasting plays an important role to warning public of hazardous, high-impact weather including tropical cyclones, thunderstorms and tornadoes that cause flash floods, lightning strikes and destructive winds It contributed to the: i) reduction of fatalities and injuries due to weather hazards; ii) reduction of private, public, and industrial property damage; iii) improvement of efficiency and saving for industry, transportation and agriculture [2] Latest radar, satellite images and observational data are often used to make analysis of the small-scale features present in a small area such as a city, an airport, etc and make an accurate forecast for the following few hours [2] 978-1-5090-0626-7/16/$31.00 c 2016 IEEE B This work In this paper, we propose a novel forecast method (IPFR) for weather nowcasting combining picture fuzzy clustering (FC-PFS) with interpolative picture fuzzy rule technique Picture fuzzy clustering [16], a fuzzy clustering method on picture fuzzy set, was shown to have better quality than other fuzzy clustering algorithms Interpolative picture fuzzy rule, the novel part of this paper, is a generalization of triangular picture fuzzy rule [15] Comparing with the method in [14], STAR is replaced with the interpolative picture fuzzy rule Using fuzzy rule would make better accuracy [15] so that the new method can obtain high forecasting results The proposed method consists of three steps Firstly, FCPFS is used to partition the satellite image pixels into clusters Secondly, interpolative trapezoidal picture fuzzy rules are generated based on these clusters to form the next predicted output Finally, Particle Swarm Optimization (PSO) [17] is 86 employed to train the parameters of defuzzified function to archive forecasted images of weather nowcasting in sequences Experimental validation on the satellite image sequences of Southeast Asia will be performed C Organization of the paper The rest of the paper is organized as follows Section reviews the preliminaries containing picture fuzzy clustering algorithm and Interpolative picture fuzzy rules Section presents the proposed method for weather nowcasting problem Section shows the experimental results on satellite image sequences of Southeast Asia Finally, conclusions and further works are covered in Section In this section, we briefly review the Picture fuzzy Clustering algorithm [16] and the Interpolative picture fuzzy rules [13] A Picture fuzzy clustering Picture fuzzy clustering (FC-PFS) [16] based on Picture fuzzy set (PFS) [3] and Fuzzy C-means algorithm [12] partitions dataset into predefined number of clusters Using PFS, FC-PFS results in better clustering quality [16] The FCPFS merges data points xk , k = 1, N into cluster C j , j = 1, C with the objective function: J = ¦ ¦ (μ kj (2 − ξ kj )) xk − V j N C m k =1 j =1 + ¦¦η kj (logη kj + ξ kj ) → , N C (1) k =1 j =1 where μ kj ( x ) , η kj (x ) , ξ kj ( x ) are the positive, the neutral and the refusal degrees of each element x ∈ X , respectively; Vj is the center of cluster j FC-PFS is summarized as follow I: Data X whose number of elements ( N ); Number of clusters ( C ); the fuzzifier m ; exponent α ∈ (0,1] ; Threshold ε ; the maximum iteration max Steps > O: Matrices u , η , 1: 2: t=0 (t ) (t ) (t ) u kj ← random ; η kj ← random ; ξ kj ← random ξ and centers V ; ( k = 1, N , j = 1, C ) satisfy μ A ( x ),η A ( x ), γ A ( x ) ∈ [0,1] and ≤ μ A ( x ) + η A (x ) + γ A ( x ) ≤ , ∀x ∈ X 3: 4: 5: Repeat t=t+1 Calculate V j (t ) ¦ (μ (2 − ξ )) n m kj Vj = from u kj kj k =1 n and ξ kj (t −1) as follow, m where j = 1, C (2) kj k =1 6: Calculate u kj (t ) from V j (t ) and ξ kj (t −1) m −1 (3) , ki 7: Calculate η kj (t ) from u kj η kj = e −ξ kj c ¦ e −ξki (t ) and ξ kj ( t −1) as follow, Đ c ã ă1 Ư ki , â c i =1 (4) i =1 where ( k = 1, N , j = 1, C ) Calculate ξ kj (t ) from u kj (t ) and η kj (t ) ( ξ kj = − (μ kj + η kj ) − − (μ kj + η kj )α 9: as follow ) α (5) Until u (t ) − u (t −1) + η (t ) − η (t −1) + ξ (t ) − ξ (t −1) ≤ ε or max Steps has reached B Interpolative picture fuzzy rules Picture fuzzy rule using triangular picture fuzzy numbers [13] is developed based on fuzzy rule, an IF-THEN rule involving linguistic terms proposed by Zadeh [13] In this paper, each rule is equivalent to each cluster then the number of rules is equal to number of clusters We update the rule by using trapezoidal picture fuzzy numbers (TpPFN) for picture fuzzy rule TpPFN is described by six real numbers (a′, a, b′, b, c, c′) with (a′ ≤ a ≤ b′ ≤ b ≤ c ≤ c′) and two trapezoidal functions shown in equations (6-7) and Fig as follow ­x − a ° b'− a , for a ≤ x ≤ b' ° ° c − x , for b ≤ x ≤ c , u=® °c − b for b' ≤ x ≤ b °1, °0, otherwise ¯ (6) ­ b'− x ° b'− a′ , for a′ ≤ x ≤ b' ° ° x − b , for b ≤ x ≤ c′ η +ξ = ® ′ °c − b , ° for b' ≤ x ≤ b °1, otherwise ¯ (7) Denote that L = η + ξ and combining with equation (5), value of the neutral membership is calculated as in (8) ( η = − (1 − u − L )α Xk ¦ (μ (2 − ξ )) kj ( t 1) Đ X k Vj ã X k Vi i =1 â where ( k = 1, N , j = 1, C ) c Ư (2 )ăă 8: II PRELIMINARIES μ kj = ) α −u (8) DEF ( A) is the defuzzified value of the TpPFN A (in equation and Fig 1) as follow, 2016 IEEE International Conference on Fuzzy Systems (FUZZ) 87 DEF ( A) = h1a′ + h2 a + h3b'+ h4b + h5c + h6 c′ (9) ¦h i i =1 where hi ≥ , i = 1,6 , is the weight of TpPFN of defuzzified value A Ș+ȟ hour, every 30 minutes, etc These images are firstly preprocessed by calculating the different pixel matrices from the current image to the next image in sequence Suppose that there is an input with m sequent images, and then m − different pixel matrices are created after preprocessing The first ( m − ) matrices are partitioned by FC-PFS into clusters in order to generate interpolative picture fuzzy rules using trapezoidal picture fuzzy numbers The last one is utilized to train the defuzzified parameter of picture fuzzy rules by PSO algorithm and to predict the next different matrix after the rules have been established Image input u Different matrix 1, split into sub-matrices a’ a b’ b c c’ Image input Different matrix 2, split into sub-matrices Fig A trapezoidal picture fuzzy set A The closest fuzzy rules with respect to the input observation are utilized to produce an interpolated conclusion for sparse fuzzy rule-based systems The following picture fuzzy rules interpolation scheme illustrates that: and x2 = A2,1 and … and xk = Ad ,1 Rule 1: If x1 = A1,1 Partition different matrices using Picture Fuzzy Clustering Then y = B1 … … Different matrix m - 2, split into sub-matrices Image input m - Generate Interpolative Picture Fuzzy Rules from clusters using trapezoidal picture fuzzy numbers Different matrix m – 1, split into sub-matrices … Rule j: If x1 = A1, j and x2 = A2, j and … and xk = Ad , j Image input m Output predicted image Then y = B j Train defuzzified parameters using PSO algorithm to increase predicted accuracy … Rule q: If x1 = A1, p and x2 = A2, p and … and xk = Ad , p Then y = B p Observations: x1 = A and x2 = A and … and x1 = A * * * d Conclusion: y = B* where Rule j ( j = 1, q ) is the jth fuzzy rule in the sparse fuzzy rule base, xk denotes the k th antecedent variable, y denotes the consequence variable, Ak , j denotes the k th antecedent fuzzy set of Rule j , B j denotes the consequence fuzzy set of * k Rule j , A denotes the k antecedent variable th observation fuzzy set for the k th xk , B denotes the interpolated * consequence fuzzy set, d is the number of variables appearing in the antecedents of fuzzy rules, q is the number of fuzzy rules, k = 1, d , and j = 1, q III THE PROPOSED METHOD A The proposed method The proposed method uses satellite image sequences as the inputs for weather nowcasting Each image is collected from the same region in a constant interval time, for instance every 88 Fig The new algorithm’s schema Each different matrix is split into small-sized sub-matrices to keep the topology of the predicted image This means that the change of a region in an image is not affected by others through the sequent images Then, the algorithm processes each sub-matrix of the matrices to generate the region respectively in the predicted matrix Finally, the forecasted image is constituted by the combination of the last image in the sequent images with the predicted matrix The proposed algorithm is illustrated in Fig Suppose that we have a data set with d input time series and one output time series M (t ) , {T1 (t ), T2 (t ), , Td (t )} , t = 0, N Each element in different matrix is calculated by equation (10) based on the variation rates Rk (i ) , i = 1, N of the k th input time series Tk (i ) at time i , where k = 1, d Rk (i ) = Tk (i ) − Tk (i − 1) × 100% Tk (i − 1) (10) The variation rates {R1 (i ), R2 (i ), , Rd (i )} of the input time series {T1(t ), T2 (t ), ,Td (t )} , t = 0, N at time i are determined based on equation (10) N training samples {X , X , , X N } , 2016 IEEE International Conference on Fuzzy Systems (FUZZ) {R1 (i ), R2 (i ), , Rd (i ), R0 (i )} , where X i is represented by { i = 1, N are constructed Denote X i = I i(1) , I i( ) , , I i( d ) , Oi {R1 (i ), R2 (i ), , Rd (i ), R0 (i )}, where c′j = max i =1, 2, ,n Oi , }= ( ( aj = The picture fuzzy rules using TpPFN are constructed based on the clusters {P1 , P2 , , PC } , where rule j corresponds to Pj , ( j = 1, q ), shown as follows cj = Rule j: If x1 = A1, j and x2 = A2, j and … and xk = Ad , j where Rule j is the fuzzy rule corresponding to the cluster Pj , xk is the k th antecedent variable, Ak , j is the k th antecedent fuzzy set of Rule j , y is the consequence variable, B j is the ¦ ¦ ¦ ¦ (22) ( ) calculate the inferred output O in equation (23) * i O ¦ = q j =1 ( ) min1≤k ≤d U Ak , j I i( k ) × DEF (B j ) ¦ q ( ) min1≤k ≤d U Ak , j I i( k ) j =1 , (23) ( ) U Ak , j I i( k ) denotes as the membership value of the input (k ) i I ck′ , j = max i =1, 2, , n I i( k ) , (12) ( (13) j = 1, q and k = 1, d It is calculated based on the trapezoidal picture fuzzy function in equations (5-8) with q being denoted the number of activated picture fuzzy rules and DEF B j ( (k ) t ,V (k ) j ), where U ) tj = max (U ti ) , 1≤ i ≤ n th is the center of cluster j with k element ¦ i =1, , ,n and I i( k ) ≤bk′ , j ¦ ¦ i =1, , ,n and ¦ Ii( k ) ≥bk , j (14) U i , j × I i( k ) i =1, , ,n and I i( k ) ≤bk′ , j ck , j = U i, j i =1, , , n and I i( k ) ≥ b j (11) bk , j = max I ak , j = U i , j × Oi ak′ , j = i=1, 2, ,n I i( k ) , bk′ , j = I t( k ) ,V j( k ) V (21) * i ij (k ) j , If some picture fuzzy rules are activated by the inputs of the i th sample X i that means min1≤ k ≤ d U Ak , j I i( k ) > then (1 + ξ ) U i, j where Oi is the desired output of X i and j = 1, C Based on equations (11–22), TpPFN of the fuzzy rules are constructed k consequence fuzzy set of Rule j , j = 1, C , k = 1, d , and the real numbers (a′, a, b′, b, c, c′) of TpPFN Ak , j are uij + ηij i =1, , , n and I i( k ) ≤ b ′j i =1, , , n and I i( k ) ≥ b j (20) U i , j × Oi i =1, , , n and I i( k ) ≤ b ′j th calculated in (11-16) with U ij = 1≤ i ≤ n V j(k ) is the center of cluster j with k th element uij , the neutral degree ηij and Then y = B j ) (19) b j = max Ot( k ) ,V j( k ) , where U tj = max (U ti ) , ξij of X i the refusal degree ) b′j = Ot( k ) ,V j( k ) , I i(k ) ( Oi ) is the k th input (output) of X i , k = 1, d Then FC-PFS algorithm is used to partition the training sample into an appropriate number of clusters ( C ) {P1 , P2 , , PC } and calculate the center V j of cluster Pj , the positive degree (18) U i, j , (15) U i, j (16) where I i(k ) is the k th input of the training sample X i , j = 1, C , k = 1, d The real numbers (a′, a, b, c, c′) of TpPFN B j of Rule j are described in equations (17-22) a′j = i =1, 2, , n Oi , (17) picture fuzzy set Ak , j , ( ) being the defuzzified value of the consequence picture fuzzy set B j of the activated picture fuzzy rule j , j = 1, q , i = 1, N Otherwise, if there is not exist any activated picture fuzzy rule, calculate weight W j of Rule j with respect to the input observations x1 = I i1 , x2 = I i2 , , xd = I id by equation (24) and compute the inferred output Oi* by equation (25) Wj = U i , j × I i( k ) i =1, , ,n and Ii( k ) ≥bk , j belonging to the trapezoidal § r * rj Ưh=1 ăă r * r h â C ã á Oi* = ƯW j × DEF (B j ) , (24) C (25) j =1 r * denotes the input vectors {I i(1) , I i( 2) , , I i( d ) }, rj denotes the vector of the defuzzified values of the antecedent fuzzy sets of Rule j - {DEF (A1, j ), DEF (A2, j ), , DEF (Ad , j )} r * − r j is the 2016 IEEE International Conference on Fuzzy Systems (FUZZ) 89 r * and rj The Euclidean distance between the vectors (i ) δ (j i ) ← random , h j ← random , Pbesti = , Gbest = 1: ( i = 1, popsize ), t = Repeat t=t+1 For each particle i Calculate fitness function by equation (23) or (25) Generate a new different matrix Calculate diff i value of the particle i following constraints of the weights are: ≤ W j ≤ , j = 1, C and C ¦ j =1 W j = DEF (B j ) is the defuzzified value of consequence picture fuzzy sets B j The training defuzzified parameters process is conducted using the two last different matrices (m − 1) th and (m − ) th with roles as testing sample and input sample ( X ) respectively In order to determine the optimal defuzzified parameters for each rule, PSO algorithm [17] which is representation of the movement of organisms in a bird flock or fish school is used Suppose that we have popsize particles, each of them is encoded with six parameters (h1 , h2 , h3 , h4 , h5 , h6 ) corresponding to the weight for calculating defuzzified value for TpPFN as a solution For each particle i , if the achieved solutions are better than the previous ones, we record them in the local optimal solutions Pbest ( h (i ) , j = 1,6 ) of this particle Denote a new δ (ij ) is the Pbest j velocity for changing of parameter h j of particle i , j = 1,6 The evolution of all particles is continued until a number of iterations are reached The final solutions comprising the most suitable of the six parameters are then determined from all particles through the best values of particles ( Pbesti ) and the swarm ( Gbest ) Gbest includes hGbest j (the parameter for defuzzified value that make the rules have best accuracy) and Gbest value, the best quality value that all particles achieve – fitness value The fitness function is computed as the difference between the generated pixel matrix from Gbest parameters and the ( m − )th different pixel matrices The difference can be calculated as below N diff = ¦ pix i( n −1) − pix i( new) , 2: 3: 4: 5: 6: 7: equation (26) If( diffi < Pbesti or Pbesti =0) Pbesti = diff i 8: 9: 10: 11: 12: 13: 14: 15: Save best solution of particle If( Gbest < Pbesti or Gbest =0) Gbest = Pbesti Save best solution of swarm Update particle i by equations (27-28) Until ( Gbest > ε or t > maxSteps) Finally, we calculate the forecasted value M Forecasted (i ) at time i based on the predicted variation rate Oi* , where M (i − 1) is the actual value at time i − as in equation (29) ( where pix B Remark The proposed method uses interpolative picture fuzzy rules with training defuzzified parameter process then it can result in more accurate predicted images than those of STAR technique The STAR technique only employs autoregressive method, which affects more than one sets of parameters leading to the output, and may be over fitted or inaccurate in case of inappropriate candidate set of parameters IV EXPERIMENTS th th (new ) pixel matrices; pixi is the i pixel value of the new different pixel matrices generated from Gbest parameters Each particle i is updated by equations (27-28) as below ( ) ( ) δ (j i ) = δ (j i ) + c1 hPbest − h (j i ) + c hGbest − h (j i ) , (i) j j h (j i ) = h (j i ) + δ (j i ) , (27) (28) where c1 , c2 ≥ are PSO’s parameters Generally, c1 , c often are set to be Details of this method are described as follow I: O: Data X ; Maximum number of clusters ( Cmax ); exponent α ; threshold ε , maximum iteration maxSteps, the number of particles in PSO- popsize The optimal parameter defuzzified function 90 (29) (26) is the i pixel value of the ( m − ) different th ) M Forecasted (i ) = M (i − 1)× + Oi* i =1 ( n −1) i i (h1 , h2 , h3 , h4 , h5 , h6 ) for A Materials and system configuration The datasets for experiments include four sets of image: Malaysian, Luzon – Philippines, Jakarta – Indonesia and the Eastern Pacific [8, 19] Each set contains seven images consecutively from 7.30 am to 13.30 pm The first four images are used as training dataset and the last one are testing dataset All images have the same size (100x100 pixels) Figures 3-6 show the first, second, third and forth dataset respectively In order to evaluate the accuracy of weather nowcasting, Root mean square error (RMSE) is used as in equation (30) ¦ (M n RMSE = i =1 (i ) − M predicted (i ) ) corrected , (30) n where M corrected (i ) and M predicted (i ) denotes the real image pixels and the predicted image pixels in time i of the total number times ( n ) The experiments are run on the system with configuration of 2G RAM, 2.13 GHz core Duo 2016 IEEE International Conference on Fuzzy Systems (FUZZ) • PFC-STAR method of Hoa, Thong and Son [13] Experiments are conducted with parameters of PSO: c1 = c2 = , popsize = 10 [16] The proposed algorithms are run with different number of clusters from to 16 equivalents to from 16 rules The experimental results are taken in average of 50 times 7h 30 (1) 8h 30 (2) 9h 30 (3) 10h 30 (4) 11h 30 (5) 12h 30 (6) 7h 30 (1) 8h 30 (2) 9h 30 (3) 10h 30 (4) 11h 30 (5) 12h 30 (6) 13h 30 (7) Fig Satellite images of Data – Malaysian 13h 30 (7) Fig Satellite images of Data – Jakarta (Indonesia ) 7h 30 (1) 8h 30 (2) 9h 30 (3) 10h 30 (4) 11h 30 (5) 12h 30 (6) 7h 30 (1) 8h 30 (2) 9h 30 (3) 10h 30 (4) 11h 30 (5) 12h 30 (6) 13h 30 (7) Fig Satellite images of Data – Luzon (Philippines) In the experiment, three algorithms are implemented in Java including: • The proposed method (IPFR), • FCM-STAR method of Shukla, Kishtawal and Pal [5], 13h 30 (7) Fig Satellite images of Data – Eastern Pacific 2016 IEEE International Conference on Fuzzy Systems (FUZZ) 91 B Results and discussions Table I indicates the RMSE value of all three algorithms It is obvious that IPFR algorithm produces predicted image with smaller RMSE values than other methods in most of cases The bold number denotes the smallest value for a given predicted image and data TABLE I AVERAGE OF RMSE (STD) VALUES OF ALGORITHMS Algorithms Predicted image IPFR Predicted image Predicted image Predicted image PFCSTAR Predicted image Predicted image Predicted image FCMSTAR Predicted image Predicted image TABLE II IPFR PFCSTAR FCMSTAR Data Data Data Data 4.141 (0.076) 6.749 (0.505) 9.619 (1.013) 6.33 (0.424) 11.418 (0.458) 12.482 (3.463) 6.314 (0.479) 9.995 (0.468) 10.468 (1.911) 3.832 (0.302) 7.626 (1.559) 7.93 (1.715) 6.893 8.704 (0.103) 7.738 (0.634) 9.646 (1.241) (0.612) 10.324 (0.731) 12.422 (2.451) 9.549 (0.426) 5.234 (0.421) 10.42 (0.702) 11.309 (2.234) 8.451 (1.817) 10.356 (2.428) 8.661 (0.11) 8.865 (0.651) 9.828 (1.113) 11.158 (0.662) 11.809 (0.701) 12.546 (2.703) 12.955 (0.568) 13.209 (0.893) 13.772 (2.416) 5.892 (0.308) 9.065 (2.105) 10.872 (2.523) THE RATES OF AVERAGE RMSE VALUES OF ALGORITHMS Algorithms Predicted image Predicted image Predicted image Predicted image Predicted image Predicted image Predicted image Predicted image Predicted image Data 1 1 1.664 1.146 1.003 1.328 1.313 2.091 Data 1.106 1.005 1.375 1 1.763 1.144 1.009 Data 1 1.512 1.042 1.080 2.052 1.321 1.315 Fig RMSE values with different number of clusters in Data Fig RMSE values with different number of clusters in Data Data 1 1.366 1.108 1.306 1.537 1.188 1.371 The results of all algorithms in the case of Data with all three predicted images showed that IPFR has better accuracy than other algorithms with the RMSE value being (6.517, 6.749, 9.619), less than those of PFC-STAR (6.893, 7.738, 9.646) and FCM-STAR (8.661, 8.865, 9.828) Similarly, the results of all three predicted images of Data and Data also showed the advantage of IPFR over other algorithms Only in Data 2, IPFR has the last two predicted images with larger RMSE values (11.418, 12.482) compared to PFC-STAR (10.324, 12.422) However, these values of the proposed method are still less than those of FCM-STAR and especially, the first predicted image of the algorithm has the smallest RMSE value of all methods Besides, the std values of the proposed algorithm are mostly less than those of other algorithms; this indicates that IPFR produces more sustainable results than the others Details more about the rates of average RMSE values are established in Table II In this table, 92 RMSE values of PFC-STAR and FCM-STAR are mostly higher than IPFR about 1.5 times on predicted image 1, about 1.2 and 1.5 on predicted image and respectively Fig RMSE values with different number of clusters in Data Fig 10 RMSE values with different number of clusters in Data 2016 IEEE International Conference on Fuzzy Systems (FUZZ) RMSE values of IPFR are less than those of others although these are the average values of the proposed algorithm with different number of clusters Figures 7–10 show the appropriate number of clusters for each dataset [5] In those figures, RMSE values with different numbers of clusters of predicted image are always less than of the other For Data 1, RMSE values for predicted image and predicted image change significantly but not trivially for predicted image When the number of clusters is 9, IPFR have the best RMSE value for Data Analogously to Data 2, Data and Data 4, the best number of clusters are 12, 13 and 14 respectively [6] [7] [8] [9] TABLE III AVERAGE COMPUTATIONAL TIME OF DIFFERENT ALGORITHM (SEC) Algorithms IPFR PFC-STAR FCM-STAR Data 109.04 49.35 37.25 Data 118.434 51.235 39.363 Data 207.504 53.23 45.234 Data 169.725 46.463 41.42 Table III shows the average computational time for the experiments It is obviously that IPFR run slower than the two others are because it employed PSO algorithm to choose the best defuzzified parameters V CONCLUSION The paper proposed a hybrid method combining interpolative picture fuzzy rule technique and particle swarm optimization for the weather nowcasting problem The experimental results indicated that the proposed methods produce better RMSE value of predicted images than others although it needed more time to run In the future, we will improve the algorithm to run faster and practice with large datasets [10] [11] [12] [13] [14] [15] [16] ACKNOWLEDGEMENT This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 102.05-2014.01 [17] [18] APPENDIX Source codes and experimental datasets of this paper can be retrieved at this link: https://sourceforge.net/p/ipfrproject/code/ci/master/tree/ REFERENCES [1] [2] [3] [4] A N Evans, “Cloud motion analysis using multichannel correlationrelaxation labeling,” Geoscience and Remote Sensing Letters, IEEE, 3(3), 2006, pp 392-396 A V Kumar and H Rahman, Mobile Computing Techniques in Emerging Markets: Systems, Applications and Services, IGI Global, 2012 B C Cuong, Picture fuzzy sets, Journal of Computer Science and Cybernetics, 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the satellite image sequences of Southeast Asia will