Integrated Intelligent Research (IIR)
International Journal of Data Mining Techniques and Applications Volume: 02 Issue: 02 December 2013 Page No.64-66 ISSN: 2278-2419
An Interval Based Fuzzy Multiple Expert System to Analyze the Impacts of Climate Change on Indian Agriculture A.Victor Devadoss1 and D.Ajay2 1
Head & Associate Professor, Department of Mathematics, Loyola College, Chennai-34. 2 Ph.D Research Scholar, Department of Mathematics, Loyola College, Chennai-34. Email: hanivictor@ymail.com,dajaypravin@gmail.com
Abstract - Indian agriculture is completely dependent on the environment and any undesirable change in the environment has an adverse impact on agriculture. Climate change and pollution in India have caused great damage to the environment. In this paper we analyse the impact of climate change on Indian agriculture. The first section gives an introduction to the problem. In section two we introduce a new fuzzy tool called interval based fuzzy multiple expert system. Section three adapt the new fuzzy tool to analyse the problem of agricultural impacts of climate change and in section four we give the results and suggestions based on our analysis.
amount of uncertainty in each causal relationship. We propose an interval based multiple fuzzy experts system which can process any number of opinions of experts at the same time and whose matrix entries are fuzzy intervals. The theoretical framework for the model proposed is first explained and then we enumerate the opinion of the experts in matrices from which we arrive at the interval based multiple expert system matrixes. A fuzzy set is a map μ: X → [0, 1] where X is any set called the domain and [0, 1] the range. That is to every element x X, μ assigns membership value in the interval [0, 1]. Fuzzy theorists often picture membership functions as twodimensional graphs with the domain X represented as a onedimensional axis.
Keywords - Climate change, Fuzzy expert system, intervalbased expert system, Fuzzy associative memories, Indian agriculture, global warming, green house gas emission, farming system, biosecurity of crops. I.
The
fuzzy sets involves both domain X ( x 1 , x 2 , ... x n ) and the range [0, 1] of mappings μ: X →
INTRODUCTION
geometry
of
[0, 1]. A fuzzy subset equals the unit hyper cube I Indian agriculture is rich in diversity of soils, climate, farming systems, and resource endowments but at the same time it is vulnerable to many factors such as policies, trade, pollution and changes in the environment. Its vulnerability is more exposed by the number of crises it has undergone, and most parts of it are human-made. As the report M.S.Swaminathan committee states the growth rate of agriculture was about 2% during the IX Plan period and is slated to decline to 1.8% per annum during the X Plan. Climate change has also played a role in deepening the crisis. Adverse changes in the environment have affected the stability of the farming systems and biodiversity on which agriculture is dependent. A number of new diseases which affect crops have been observed which make seeds vulnerable to pests. Farmers are caught in a vicious circle between these diseases and the use of pesticides which affects the health of the soil of their farmland. Farming in India is supplemented by farm animals the farmers have. Research has shown that these animals suffer a genetic change and their resources and livelihood have also been affected by climate change. II.
n
[ 0 ,1] . n
n
The fuzzy set is a point in the cube I . Vertices of the cube I
n n
define a non-fuzzy set. Now within the unit hyper cube [ 0 ,1]
n
we are interested in distance between points, which led to measures of size and fuzziness of a fuzzy set and more fundamentally to a measure. Thus within cube theory directly extends to the continuous case when the space X is a I
n
subset of R . The next step is to consider mappings between fuzzy cubes. A fuzzy set defines a point in a cube. A fuzzy system defines a mapping between cubes. A fuzzy system S maps fuzzy sets to fuzzy sets. Thus a fuzzy system S is a transformation S : I I . The n-dimensional unit hyper cube In houses all the fuzzy subsets of the domain space or n
p
input universe of discourse X ( x 1 , x 2 , ... x n ) . I houses all the fuzzy subsets of the range space or output universe of discourse, Y ( y 1 , y 2 , ..., y p ) . X and Y can also denote p
subsets of R
n
p
and R . X
INTERVAL BASED MULTIPLE FUZZY EXPERT SYSTEM
Y
Then the fuzzy power sets F ( 2 ) and F ( 2 ) replace I
n
p
and I . In general a fuzzy system S maps families of fuzzy sets to families of fuzzy sets thus
Fuzzy expert systems work on the opinion of the experts which are expressed as fuzzy values ranging from 0 and 1. In neural networks based fuzzy expert systems, the expert opinion on the causal relationship between the neurons of a neuron field or between neurons of two different neuron fields are expressed as a matrix whose entries are fuzzy values representing the
I
... I
nr
n
I
that map balls of fuzzy sets in I
p1
... I
ps
n1
. Here too we can extend the definition of a fuzzy system to allow arbitrary products or arbitrary mathematical spaces to serve as the domain or range spaces of the fuzzy sets. We shall focus on fuzzy system S :I
S : I
64
p
n
to balls of
Integrated Intelligent Research (IIR)
International Journal of Data Mining Techniques and Applications Volume: 02 Issue: 02 December 2013 Page No.64-66 ISSN: 2278-2419 p fuzzy set in I .Consider a system of k matrices If y 1 j , it is ON state. where M a , M a , ..., M a , If y 1 j , it is in OFF state. i 1, 2 , ..., m and j 1, 2 , ..., n which represent opinions of k experts about causal relationship between nodes. Then the III. ADAPTATION OF CFAM TO THE PROBLEM combined interval based multiple expert system matrix is given by We take the following attributes given by the experts which J . . . J arerelated with the effects of climate change as nodes of the J domain space: J J . . . J (1 )
1
(2)
ij
2
M
where
I
11
, X
ij
12
1n
21
22
2 n
a
12
k
11
. . . J m1
J ij m i n
all i and j. Let X X
(k )
ij
J
(k ) ij
.
m 2
.
, m ax a
, ..., X
1 j
(k ) ij
.
J
mn
C1 -Migration of species C2 -Glacier and snowpack decline C3 -Sea level rise C4 -Species extinction C5 -Rise in average temperature C6 -Spread of new diseases C7 -Weather disasters such as floods and droughts C8 -Higher concentrations of ground level ozone C9 -Decrease in fresh water availability C10 -Failure of monsoon The following are the attributes related with agriculture which we take as nodes of the range space: G1 -Agricultural productivity G2 -Profitability G3 -Stability of farming systems G4 -Health of the farmers G5 -Nutrition content in agricultural produce G6 -Biosecurity of crops, farm animals, fish and forest trees G7 -Ground and surface water G8 -Making seeds vulnerable to pests G9 -Economic sustainability of farming systems G10 -Soil health G11 -Animal genetic
and J ij 0 ,1 for
be the initial input vector such
that each X 1 j 0,1 . Then XM
J
I
'
X M
T
ij
X
1 j
m i n ( a
m i n ( a
(l ) ji
(l )
), m a x (b
Now
(r )
) , m a x ( b ij
ij
)
(r ) ji
1 j
)
X
1 j
' 1 j
Y
a , b The fuzzy intervals in the resultant row matrix can be reduced to fuzzy values by finding the centres of each interval using the formula Y
(l )
(l )
C (I )
(r )
1 j
a1
j
1 j
b1
(r ) j
2
Therefore
C (Y )
y , 1 j
j 1, 2 , ..., m
.
Defuzzification of the resultant vector can be done by setting the threshold .
The interval based multiple expert matrix is obtained from the opinions of eight experts as explained above and is given by the following matrix:
M
[.5 , .6 ] [.3, .5 ] [.4 , .6 ] [.6 , .7 ] [.6 , .9 ] [.6 , .8 ] [.8 , .9 ] [.6 , .8 ] [.7 , .9 ] [ . 8 , . 9 ]
I
[.4 , .6 ]
[.3, .5 ]
[.5 , .8 ]
[.2 , .3 ]
[.4 , . 5 ]
[.2 , .3 ]
[.2 , .3 ]
[.5 , .8 ]
[.4 , .6 ]
[.3, .4 ]
[.5 , .7 ]
[ . 1, . 2 ]
[.2 , .3 ]
[.3, . 6 ]
[.6 , .8 ]
[.2 , .3 ]
[.5 , .7 ]
[.6 , .7 ]
[.4 , .6 ]
[.3, .7 ]
[.2 , .3 ]
[.3, .5 ]
[.3, . 7 ]
[ .7 , .9 ]
[.3, .5 ]
[.4 , .5 ]
[.4 , .7 ]
[.6 , .7 ]
[.5 , .8 ]
[.5 , .8 ]
[.3, .5 ]
[.4 , . 6 ]
[.2 , .3 ]
[.3, .5 ]
[.6 , .9 ]
[.4 , .5 ]
[.6 , .8 ]
[.6 , .9 ]
[.5 , .7 ]
[.3, .6 ]
[.3, . 7 ]
[.5 , .7 ]
[.3, .6 ]
[.4 , .7 ]
[.4 , .6 ]
[.6 , .8 ]
[.5 , .8 ]
[.7 , .9 ]
[.3, .5 ]
[.5 , .8 ]
[.4 , .6 ]
[.5 , .9 ]
[.5 , .8 ]
[.2 , .4 ]
[.7 , .9 ]
[.8 , .9 ]
[.3, .7 ]
[.4 , .6 ]
[.3, . 7 ]
[.4 , .8 ]
[.3, .5 ]
[.6 , .8 ]
[.5 , .7 ]
[.5 , .6 ]
[.4 , .6 ]
[.4 , .7 ]
[.3, .5 ]
[.3, . 5 ]
[.4 , .6 ]
[.3, .5 ]
[.5 , .7 ]
[.2 , .4 ]
[.6 , .9 ]
[.6 , .8 ]
[.7 , .9 ]
[.6 , .8 ]
[.6 , . 8 ]
[.8 , .9 ]
[.5 , .7 ]
[.5 , .7 ]
[.4 , .5 ]
[.7 , .9 ]
[.6 , .8 ]
[.3, .6 ]
[.4 , .7 ]
[.5 , . 7 ]
[.7 , .8 ]
[.6 , .8 ]
[.6 , .8 ]
[.4 , .7 ]
[.4 , .5 ] [.3, .6 ] [.2 , .4 ] [.3, .6 ] [.3, .7 ] [.4 , .7 ] [.2 , .5 ] [.3, .6 ] [.4 , .6 ] [ . 3 , . 5 ]
Let X be the initial input vector given by the experts. X
XM '
[ .3, .5 ]
[ .1, .3 ]
[.0 3, .7 2 ]
[.0 3, .7 2 ]
I
X M
T
[ .0 0 4 , .5 1 2 ]
.2 5 8
.2 5 7
[ .5 , .7 ]
[.0 5, .7 2 ]
[ .0 0 1, .5 1 2 ]
.2 8 9
[ .5 , .6 ]
[.0 1, .5 6 ]
[ .0 0 2 , .5 7 6 ]
.2 9 1
[ .6 , .8 ]
[.0 2 , .5 6 ] [ .0 0 5 , . 5 7 6 ]
.3 2 7
.2 9 1
[ .4 , . 6 ]
[.0 3, .5 6 ]
[ .0 0 5 , .6 4 8 ]
.3 2 6
[ .7 , .8 ]
[.0 6 , .6 4 ]
[ .0 0 6 , .5 7 6 ]
.2 9
[ .4 , .6 ]
[.0 2 , .6 4 ]
.3 2 8
[ .4 , .6 ]
[.0 5, .6 4 ]
.0 0 3, .6 4 8 .3 2 6
[ .6 , .8 ]
[.0 6 , .5 6 ]
[ .0 0 4 , .5 7 6 ]
[.0 3, .5 6 ] X [ .0 0 7 , .6 4 8 ]
'
[ .0 0 3, .6 4 8 ]
↪(0 0 0 0 1 0 1 0 1 1) It can be observed that for the given input vector four attributes namely, Rise in average temperature, Weather disasters, Decrease in fresh water availability and Failure of monsoon,
turn into ON state. These four attributes play pivotal role in destabilizing agriculture. In general it means that the effects of climate change do have an impact on agriculture. 65
Integrated Intelligent Research (IIR)
IV.
International Journal of Data Mining Techniques and Applications Volume: 02 Issue: 02 December 2013 Page No.64-66 ISSN: 2278-2419
CONCLUSION AND SUGGESTIONS
Rise in average temperature has an adverse impact on agriculture. Observations since 1961 show that the average temperature of the global ocean has increased to depths of at least 3000m and that the ocean has been taking up over 80% of the heat being added to the climate system. This is mainly due to emission of greenhouse gases (GHG). The government should take steps to curb emission of GHGs. Immediate steps should be taken to protect groundwater as the amount of fresh water available is finite and has seen a decline in the past decades. Industries which pollute ground water and surface water bodies should be stopped and should be under the maintenance of the government. Indian agriculture is completely dependent of monsoon; any failure in monsoon results in a loss for the farmers and an increase in hunger and poverty in the country. Effective and modern monsoon prediction technology should be adopted and the farmers should be informed of monsoon prior as there is lot of variation and uncertainty. Water survey should be conducted in all agricultural areas and government-owned public irrigation methods should be introduced. REFERENCES [1] Auffhammer Maximilian, et al., Clime Change, the Monsoon and rice yield in India, Climate Change, DOI 10.1007/s10584-011-0208-4, 02 September 2011. [02] Kosko B., Neural Networks and Fuzzy Systems, Prentice-Hall , Inc., New Jersey, USA, 1992. [03] Kosko B., Fuzzy cognitive maps, Int, J. Man-Machine studies (1986), 24, 65-75. [04] “Climate change 2007: synthesis report” a report by IPCC. [05] Deshpande R.S, et al (Ed)., Agrarian Crisis and Farmer Suicides., Sage Publications India Pvt Ltd, 2010. [06] Ghosh Prodipto., Equity in Climate Change: A suggested aapproach., Economic and Political Weekly, Vol XLVIII No.12., March 23, 2013. [07] Government of India (2007), Agricultural Statistics At A Glance-2006, Department of Agriculture and Cooperation, Ministry of Agriculture, New Delhi, 2006. [08] Gupta K.R., Climate Change: Meeting the Challenge, Vols I and II, Atlantic Publishers, New Delhi, 2010. [09] Hardy J T., Climate Change: Causes, Effects and Solutions, John Wiley & Sons Ltd, England, 2003. [10] Hung Wen-Liang., et al., Similarity Measures Between Type-2 Fuzzy Sets., International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol.12, No.6, (2004) 827-841. [11] Mall R.K., et al., Impact of Climate Change on Indian Agriculture: A Review, Climate Change (2006) 78: 445-478, 2006. [12] Mathur Archana S, et al., Status of Agriculture in India: Trends and Prospects, Economic and Political Weekly, Vol XLI, No.52, December 30, 2006. [13] McMichael. A.J., et al (Ed)., Climate and Human Health: Risks and Responses., WHO, Geneva, 2003. [14] Mendel Jerry M., Type-2 Fuzzy Sets Made Simple., IEEE Transactions on Fuzzy Systems, Vol.10, No.2, April 2002. [15] National Sample Survey Organisation (NSSO) (2006) ‘Some Aspects of Operational Land Holdings in India’, 2002-03, NSS 59th Round (JanuaryDecember 2003), NSS Report No.492 (59/18.1/3), Ministry of Statistics and Programme Implementation, Governament of India, New Delhi. [16] “Rio Political Declaration on Social Determinants of Health”, WHO, Rio de Janeiro, Brazil, 21 October 2011. [17] Roy Tirthankar., Roots of Agrarian Crisis in Interwar India: Retrieving a Narrative, Economic and Political Weekly, Vol XLI, No.52, December 30, 2006. [18] Vasantha Kandasamy W.B, et al., Fuzzy Interval Matrices, Neutrosophic Interval Matrices and their Applications, Hexis, Phoenix, Arizona 2006. [19] Zadeh L.A., Fuzzy Sets, Information and Control 8, 338-353, 1965. [20] Zimmermann H.J., Fuzzy Set theory and its Applicarions, Kluwer Academic, Dordrecht, 1991.
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