Study On Watter Pollution Control Based On Fuzzy Cognitive Maps (FCM)

Transcription

1 Global Journal of Pure and Applied Mathematis. ISSN Volume 13, Number 9 (2017), pp Researh India Publiations Study On Watter Pollution Control Based On Fuzzy Cognitive Maps (FCM) 1 G.Jenitha 2 Dr. Shenbaga Ezhil 3 Dr. A. Kumaravel 1,2 Department of Mathematis, AMET University, Kanathur, Chennai, India. 3 Dean, Shool of omputing, Bharath University, Chennai, India. Abstrat In this artile, we study the Fuzzy ognitive map an Eologial onept. Here we take the first omponent is Wetlands then we relate this omponent into others are like fish,lake pollution and Law enforement.sine there are different types of relationship between the omponents when the wetland goes up it has a strong positive relationship an the number of fish. so there is a positive. Next when the Lake pollution inreases the amount of wetland dereases, we an also think about law enforement as it inreases then Lake Pollution will derease. So In this artile we obtained some relationship between them and how one parameter influene the other through the mathematial onept of FCM. Key words: FCMs, Hidden pattern, fixed point, aversion. 1. INTRODUCTION Pollution is a essential evil of all development. Due to lak of development of a ulture of pollution ontrol, there has effeted a heavy baklog of gaseous, liquid and solid pollution in environment. It has to be leaned. Pollution ontrol is a reent environmental onern. Pollution is a man-made problem, mainly of effluent ountries. Pollution is an undesirable hange in the physial, hemial or biologial harateristis of air, water and soil that may harmfully affet the life or reate potential health hazard of any living organism. Pollution is thus diret or indiret hange in any omponent of the biosphere that is harmful to the living omponents and in partiular undesirable for man, affeting adversely the industrial progress,

2 5300 G.Jenitha, Dr. Shenbaga Ezhil & Dr. A. Kumaravel ultural and natural assets or general environment of living soiety. Types of pollutions are lassified in different ways. On the basis of the type of environmental being polluted, we may reognize air pollution, water pollution, and land (soil) pollution, marine pollution et. 1.1 Issues involved in enforement of laws: In today s time, everyone wants to fulfill his selfish desires and for this we are ontinuously exploiting our natural resoures. This is posing a great threat to our future generation. Keeping this in view, various laws and ats have been framed like the Environment Protetion At (EPA), Wildlife Protetion At, Water Pollution At, et. Whih are disussed above. But atual diffiulty lies in implementation of these laws. Even if they are implemented,they are generally violated. Fruitful results an be obtained only by effetive implementation of these laws.if a law is violated (by person, industry or institute), punishment should be given and desirable penalty must be harged through legal proess. Mass eletroni media an play an instrumental role in eduating publi about various laws and their provisions.every itizen must be responsible for his ations and one should at as a wathdog over other people who are violating the laws. 2. FUZZY COGNITIVE MAP (FCM): In 1965, L.A. Zadeh has introdued a mathematial model alled Fuzzy Cognitive Maps. After a deade in the year 1976, Politial sientist R. Axelord used this fuzzy model to study deision making in soial and politial systems.then B. Kosko enhaned the power of ognitive maps onsidering fuzzy values for the onepts of the ognitive map and fuzzy degrees of interrelationships between onepts. FCMs an suessfully represent knowledge and human experiene, introdued onepts to represent the essential elements and the ause and effet relationships among the onepts to model the behavior of any system. It is a very onvenient simple and powerful tool, whih is used in numerous fields suh as soial, eonomial and medial et. illustrated by W.B.Vasantha Kandasamy in her book, Appliation of Fuzzy Models in Soial Sienes. In this paper we reall the notion of Fuzzy Cognitive Maps (FCMs), whih was introdued by Bart Kosko in the year 1986.This work is based on expert opinion olleted throughout Chennai. The data was olleted and assimilated from the people using a linguisti questionnaire and this linguisti responses were transformed into fuzzy data. It is important to note that, while doing fuzzy mathematial models, the fuzzy matrix make take its entries from the interval [- 1.1]. Even then, they are known as fuzzy matries. Therefore, it is understood that Fuzzy tools alone have the apaity to analyze these onepts further substantiating the hoie of this method. In this setion we reall the notion of Fuzzy Cognitive Maps (FCMs), whih was introdued by Bart Kosko in the year 1986.We also give several of its interrelated

3 Study On Watter Pollution Control Based On Fuzzy Cognitive Maps (FCM) 5301 definitions. FCMs have a major role to play mainly when the data onerned is an unsupervised one. Further this method is most simple and an effetive one as it an analyze the data by direted graphs and onnetion matries. 2.1 Definition: An FCM is a direted graph with onepts like poliies, events, et. as nodes. and ausalities as edges. It represents ausal relationship between onepts. Let C1, C2,,Cn be the nodes of an FCM. A = (a1,a2,,an) where ai {0, 1}. A is alled instantaneous state vetor and it denotes the on-off position of the node at an instant. 2.2 Definition: Let C1, C2,,Cn be the nodes of an FCM. Let C1C2, C2C3, C3C4,, CiCj be the edges of the FCM (i j). Then the edges form a direted yle. An FCM is said to be yli if it possesses a direted yle. An FCM is said to be ayli if it does not possess any direted yle. 2.3 Definition: An FCM with yles is said to have a feedbak. 2.4 Definition: Let C1C2, C2C3, C3C4,, CiCj be a yle. When Ci is swithed on and if the ausality flows through the edges of a yle and if it again auses Ci, we say that the dynamial system goes round and round. This is true for any node Ci, for i = 1, 2,,n. The equilibrium state for this dynamial system is alled the hidden pattern. 2.5 Definition: If the equilibrium state of a dynamial system is a unique state vetor, then it is alled a fixes point. 2.6 Example: Consider a FCM with C1, C2,,Cn as nodes. For example let us start the dynamial system by swithing onc1. Let us assume that the FCM settles down with C1 and Cn on i.e. the state vetor remains as (1, 0, 0,, 0, 1) this state vetor(1, 0, 0,, 0, 1) is alled the fixed point. In the Next setion,we analyze Fuzzy ognitive map an Eologial onept. 3. ANALYSIS OF THE PROBLEM 3.1 Method of Determining Hidden Pattern Let C2, C2 Cn be the nodes of an FCM, with feedbak. Let E be the assoiated adjaeny matrix. Let us find the hidden pattern when C1 is swithed on. When an input is given as the vetor A1= (1, 0, 0 0), the data should pass through the relation matrix E. this is done by multiplying A1 by the matrix E. Let A1 E= (a1 an)with the threshold operation that is by replaing ai by 1 if ai > k and ai by 0 if ai < k (k is a suitable positive integer). We update the resulting onept. The onept C1 is inluded in the updated vetor by making the first oordinate as 1 in the resulting vetor. Suppose A1 E A2 then onsider A2 E and repeat the same proedure. This proedure is repeated till we get a limit yle or a fixed point.

4 5302 G.Jenitha, Dr. Shenbaga Ezhil & Dr. A. Kumaravel Using the linguisti questionnaire and the expert s opinion we have taken the onepts {C1, C2,..., C10} as nodes C1 Wetlands C2 Fish C3 C4 C5 Lake pollution Inome Law enforement The direted graph is drawn with the expert opinion where C1, C2, C3, C4, C5, are taken as nodes and ausalities as edges. C _ + C 5 _ + _ C 2 _ C 4 C 3 + Fig. 1: Relational direted graph A Assoiated Matrix

5 Study On Watter Pollution Control Based On Fuzzy Cognitive Maps (FCM) 5303 Now using the matrix A of the Fuzzy Cognitive Map (FCM) the on state, we determine the hidden pattern. Suppose the onept C1 is in the on state and another node are in the off sate. (i) Let the initial input vetor be X0 = { }. X0 A = { } { } = X1 X1 A = { } { } = X2 = X1 X1 is the hidden pattern whih is the fixed point. (ii) Let the initial input vetor be X0 = { }. X0 A = { } { } = X1 X1 A = { } = X2 = X1 X1 is the hidden pattern whih is the fixed point. (iii) Let the initial input vetor be X0 = { }. X0 A = { } { } = X1 X1 A = { } { } = X2 X2 A = { } { } = X3 = X2 (iv) X2 is the hidden pattern whih is the fixed point. Let the initial input vetor be X0 = { }. X0 A = { } { } = X1 X1 A = { } = X2 = X1 X1 is the hidden pattern whih is the fixed point

6 5304 G.Jenitha, Dr. Shenbaga Ezhil & Dr. A. Kumaravel (v) Let the initial input vetor be X0 = { }. X0 A = { } { } = X1 X1 A = { } { } = X2= X1 X1 is the hidden pattern whih is the fixed point 4. CONCLUSION As the amount of wetlands inreases, the number of fish inreases lot.as lake pollution inreases, the amount of wetlands dereases slightly. As law enforement inreases, lake pollution dereases a medium amount. So we know that beause it s parameterized in an FCM wetlands an go up or down and all of these various ovals an go up or down. We have got the relationship between these omponents and those are parameterized between positive one and negative one. Whether, if it s positive one it s got a high positive influene and if it s negative one it s got a high negative influene in the ourse of it 0.It doesn t have an influene so when thinking about these relationships. we an begin to model systems by using these different values and we an look at the different types of relationships that are represented and say well in this first one as the amount of wetlands goes up it has a strong positive relationship on the number of fish. So that s why there s a positive one then in this example as lake pollution inreases the amount of wetland dereases. We an also think about law enforement as it inreases. Lake pollution dereases about a medium amount. REFERENCE [1] Axelrod,R, Struture of deision. The ognitive maps of politial elites. Prineton University (1976). [2] Gonzalez, J., Castillo, O., Aguilar, L., Performane Analysis ofcognitive Map-Fuzzy Logi Controller Model for Adaptive Control Appliation, Proeedings of the 2008 IEEE World Congress onomputational Intelligene, WCCI2008, Hong Kong, 2008, pp [3] George J. klir/bo Yuan, Fuzzy Sets and Fuzzy logi(theory and appliation),phi Learning Private limited [4] Kosko,B. Fuzzy Cognitive Maps, International Journal of man-mahine studies, Jan (1986).

7 Study On Watter Pollution Control Based On Fuzzy Cognitive Maps (FCM) 5305 [5] Kosko B, Neural Networks and Fuzzy System, Prentie Hall of India (1997). [6] Kosko,B. Hidden patterns in Combined and adaptive Knowledge Networks, International Conferene of Neural Networks(ICNN-86) ,(1988). [7] Kaufman. A; Theory of Fuzzy Subsets,volume -1,1973 [8] Praveen Prakash.A,Esther Jerlin J, Bennilo Fernande, A Study on the auses for aversion to mathematis by engineering students using Fuzzy Cognitive Maps (FCMs), International Journal of Innovative Researh in Siene, Engineering and Tehnology, ISSN: , Vol. 3, Issue 3, Marh 2014 [9] Sagaya Bavia.M, J. Maria Roy Felix, K. Ponnivalavan, Study on Disappearane of House Sparrow Using Indued Fuzzy Cognitive Maps (IFCMs), International Journal of Computing Algorithm, Volume: 03, May 2014, Pages: [10] Vasantha Kandasamy.W.B and Smarandahe Florentin, Analysis of soial aspets of migrant laborers living with HIV/AIDs using Fuzzy Theory and Neutrosophi Cognitive Maps,Xiquan Phoenix.(2004). [11] Vasantha Kandasamy W.B and Smarandahe Florentin Fuzzy Cognitive Maps and Neutrosophi Cognitive Maps, Xiquan, Phoenix (2003). [12] VasanthaKandasamy.W.B and S.Uma, Combined Fuzzy Cognitive Maps of Soio EonomiModel Appl.Si.Periodial,225-27(2000) [13] Vasantha KandasamyW.B, Florentin Smarandahe; Fuzzy and Neutrosophi Analysis of women with HIV/AIDS,2005 [14] Vasantha Kandasamy W.B, Florentin Smarandahe and K. Ilanthenral; Elementrary Fuzzy matrix theory and Fuzzy Model for Soial Sientists, 2007.

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