lectura nº 10 el uso de la lógica difusa en la eia

7/29/2019 Lectura N 10 El uso de la lgica difusa en la EIA

1/7

International Journal of Applied Environmental Sciences

ISSN 0973-6077 Volume 3 Number 3 (2008) pp. 265270

Research India Publications

http://www.ripublication.com/ijaes.htm

IWRM : An Application of Fuzzy Logic in

Environmental Impact Assessment

Srijit Biswas1, Pankaj Kr. Roy

2and Sekhar Datta

3

1Late Jagneswar Sarkar, Krishnanagar, Nutanpally,

(Near Chatrashangha Club), P.O : Agartala,Tripura - 799001, India

E-mail : [email protected] Engineer (PWD), Govt. of Tripura, India

Lecturer, School of Water resources Engineering,

Jadavpur University, Kolkata-700032, West Bengal,

India , Tel. NO : 91-9433106266(M)

E-mail :[email protected], Tripura Institute of Technology,

Agartala-799009, Tripura , India,

E-mail: [email protected]

Abstract

Environmental Impact Assessment(EIA) has been acknowledged as a

powerful planning and decision making tool to an integrated water resources

management (IWRM) [4]. It is most essential to an IWRM before taking

decision whether a new project will go ahead or not. Generally in EIA, local

public views and observation are collected as an important information in

addition of other observed data. But this kind of response may lead to an

unreasonable bias since the human thinking is full with fuzzy and uncertainty.

The parametric information or data so obtained from the various sources alongwith the Engineers perceptions are not always crisp or precise. Most of the

data are not numeric, rather linguistic viz. good, very good, less

turbidity, too much polluted, etc. to list a few only out of infinity. Such

type of imprecise data are fuzzy data[1,6]. In most cases of judgements,

evaluation is done by human beings (or by an intelligent agent) where there is

certainly a limitation of knowledge or intellectual functionaries. Naturally,

every decision-maker hesitates more or less, on every evaluation activity.

Because some part of the evaluation contribute to truthness, some part to

falseness[1,2,6]. So considerable uncertainty and impreciseness are involved

in the process of EIA which is the greatest problem of IWRM during its


2/7

266 Srijit Biswas et al

prediction. In this paper we study a methodology to find out the sanitary

condition of a catchment area. We use fuzzy logic[6] for such evaluation.

Keywords: EIA, fuzzy set, fuzzy weight, MCO, nlt, weighted average.

IntroductionIWRM is the process of promoting the coordinated development and management of

water, land and related resources, in order to maximize the resultant economic and

social welfare in an equitable manner without compromising the sustainability of vital

ecosystems[4,5]. Almost all activities which take place in a catchment area that could

adversely affect the conditions of aquatic ecosystems in terms of water quality and

quantity, biological communities and the integrity of aquatic ecosystems are subject toan environmental impact assessment (EIA). By EIA we do a systematic analysis using

information usually which focuses the public views and comments on the periphery of

the project. The general public attitude in a major project is often expressed as

concern about the existence of unknown or unforeseen effect. But there are two types

of uncertainty associated with EIA : that associated with the process and, that

associated with predictions. The accuracy of predictions is dependent on a variety of

factors such as lack of precise data or lack of precise knowledge[2,3]. So uncertainty

is a major factor in such evaluation of EIA which could be solved by using powerful

mathematical tool of fuzzy logic[6].

PreliminariesIn this section we present some preliminaries which will be useful to our main work

in the next section.

Fuzzy Set [6]

Prof. L. Zadeh , Dept. of Electrical Engineer and Computer Science, University of

California first laid the foundation of fuzzy logic i.e fuzzy set theory in 1965. He

initiated the notion of fuzzy set theory as a modification of the ordinary set theory and

at present day there is a tremendous application of fuzzy logic in various field of

technology. According to his concept, the membership function for fuzzy sets can

take any value form the closed interval [0,1] and thus it is also called infinite valued

fuzzy logic. Fuzzy set A is defined as the set of ordered pairs A = { x, A(x) },

where A(x) is the grade of membership of element x in set A. The greater value of

A(x), indicate the greater truthness of the statement that element x belongs to set A.

Concept of fuzzy numbers

Fuzzy numbers are fuzzy subsets of the real line. They have a peak or plateau with

membership grade 1, over which the members of the universe are completely in the

set. The membership function is increasing towards the peak and decreasing away

from it. It is a convex normalized fuzzy set M of the real lineR such that :

(i) It exists exactly one x0 R with M (x0) = 1


3/7

IWRM : An Application of Fuzzy Logic 267

12 14 16 18 20 22 24 26 28

1

.5

0

(x)

8:24 8:25 8:26 8:27 8:28 8:29 8:30 8:31

1

0.5

0.0

(x)

(x0 is calledthe mean value of M ).

(ii) M (x) is piecewise continuous.

The following fuzzy sets are fuzzy numbers:

(1) Approximately 5 = { (3,.2), (4,.6) (5, 1), (6,.7), (7,.1) }

(2) Approximately 12 = { (10,.3), (11,.8), (12,1), (13,.4), (14,.2) }

Clearly, {(6,.4), (7, 1), (8,1), (9,.2)} is not a fuzzy number because (7) and

(8) both are equal to 1 and thus it is not a convex normalized fuzzy set. The

figure-1, shows the graph of fuzzy number approximately 20.

Figure 1: The fuzzy number approximately 20 or approx.20

The Fuzzy Numbersnlt(x) and MCO(x)

Let x R, the set of real numbers. The fuzzy number not less than x, as defined

above is called nlt(x). It is to be noted that the membership value nlt(x) may or may

not be equal to unity. In figure-2, for the value of nlt(8:25), we see that nlt(x)(8:25)

1, but nlt(x)(8:27)=1. A real number x R is said to be most certain object in nlt(x)

denoted by MCO(x) if nlt(x)=1.

Figure 2: The fuzzy number not less than 8:25 or nlt(8:25)

MethodologyNow we will propose a method of fuzzy assessment for environmental impact. First

of all we present some definitions.

Attribute of the Assessment

The assessment is done by collecting information or values for certain attributes

which are called the attributes of the assessment. For example, consider a project of


4/7


SANITARY ASSESSMENT OF A CATCHMENT AREA, for which some

relevant attributes could be noisy surroundings, dirty place, etc.

Universe of the Assessment

Collection of all attributes of the assessment is called the Universe of the Assessment.

Weighted Average of a Fuzzy Set

Let be a fuzzy ser of a finite set X. Suppose that to each element x X, there is

an associated weight Wx R+ (set of all non-negative real numbers). Then the

weighted average of the fuzzy set is the non-negative number a() given by

(x) . Wx

a () =

Wx

Grading of Fuzzy Assessment Output

Depending upon the value of a (), the grading of overall output could be temporarily

proposed as below (which could be configured by the decision makers): -

grade = A, if .8 < a () 1

grade = B, if .6 < a () .8

grade = C, if .4 < a () .6

grade = D, if .2 < a () .4

grade = E, if 0 a () .2

Obviously, the best grade is E, and the worst grade is A here.In the next part we present the methodology of assessment by a hypothetical case

study for the sake of better understanding.

Case Study

Consider a project of SANITARY ASSESSMENT (DRAWBACK) of a catchment

area. To do the assessment let us consider the following attributes (for the sake of

simplicity in presenting the method we consider here only ten attributes) :-

x1 = bad approachable road.

x2 = unusual use of pesticides, insecticides in paddy land

x3 = dirty surroundings

x4 = unusual number of mosquito breedingx5 = unusual number of fly breeding

x6 = poor drainage system

x7 = insufficient medical facilities

x8 = shortage of drinking water

x9 = crude discharge of industrial waste effluent

x10 = poor solid waste management.

Now the job is to assign values to these attributes for each state. This can be done

either by direct observation or by collecting views and opinions from a good

number of experts in addition of the local inhabitants, in general..


5/7

IWRM : An Application of Fuzzy Logic 269

Let us suppose that the data collected from 100 people for an attribute xi reveals

that more or less 70 people are in support of the truthness of the attribute and the rest

30 are in support of falseness. We set for our fuzzy analysis that A(xi) = .7

and (xi) = . 3

Suppose that the data (hypothetical) are as shown in a tabular form (table-1).

Table 1

Attribute name in support of

truthness (x)

in support of

falseness

Fuzzy weight

fx

weight of the

attribute

wx = MCO (x)

x1x2

x3x4x5

x6x7x8x9x10

.75

.85

.5.6

.85

.8

.9

.45

.9

.75

.25

.15

.5.4

.15

.2

.1

.55

.1

.25

approx. 6

nlt(48)

approx. 10approx. 11

approx. 18

nlt(19)

approx. 10

approx. 9

approx. 42

nlt(19)

5

50

1010

20

20

10

10

40

20

These data leads to a fuzzy set X of the universe E, where

E = { x1, x2, x3, x4, x5, x6, x7, x8, x9, x10 },

and the fuzzy set X is given byx1 x2 x3 x4 x5 x6 x7 x8 x9 x10

X =, , , , , , , , ,

.75 .85 .5 .6 .85 .8 .9 .45 .9 .75

We can easily calculate that the weighted average a(X) of this fuzzy set which is

0.793, and consequently the grade to be awarded is B. Thus the assessment

reveals that the area is not in a good book of the authority as far as the sanitary

condition is concerned.

ConclusionEIA has a potential to play an important role at early stages of a IWRM-Project. In the

present study we see that for any such type of assessment and analysis fuzzy

technique can be suitably applied, because the data or information so available from

the experts perception are not always crisp rather fuzzy and vague. However, the

overall assessment or summarization of the environmental impact should only serve

as one of the parameters or criteria just to the decision makers. There could be other

parameters such as local politics, local constraints, etc which will influence the

decision makers of the project. To understand the methodology for evaluation of

environmental impact, a hypothetical case study is presented here.


6/7


References

[1] Atanassor, K.T. (1986); Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 ,

87-97.

[2] Biswas, Srijit. (2005); A fuzzy approach to Environmental Impact

Assessment, published in the Asian Journal. of Information Technology

, 4 (1) : 35-39, Grace Publication Network-2005.

[3] Carter, Larry W. (1977); Environmental Impact Assessment, M. Graw Hill,

New York.

[4] Dungumaro, Esther. W. (2006); Integrated water Resources Management in

Tanzania, AJEAM-RAGEE, Vol-11, April , pp-33-41

[5] Goldman, A. S.; and Edwards, A.K.(1992); Integrated water Resources

Planning, national Resources Forum, 16(1), 65-70.[6] Zadeh. L. (1965); Fuzzy sets, Infor: and Control , 8 , pp-338-353.


7/7

Copyright of International Journal of Applied Environmental Sciences is the property of Research India

Publications and its content may not be copied or emailed to multiple sites or posted to a listserv without the

copyright holder's express written permission. However, users may print, download, or email articles for

individual use.

lectura nº 10 el uso de la lógica difusa en la eia

Documents