Environmental Performance Evaluation Based on Fuzzy Logic

Transcription

1 20 Internatinal Cnference n Scial Science and Humanity IEDR vl5 (20) (20) IACSIT ress, Singapre Envirnmental erfrmance Evaluatin Based n Fuzzy Lgic Hasanali Aghajani, hd in Management Department f Management University f Mazandaran Bablsar, Iran aghajani@umzacir Abbas Namdar Aliabadi, MA Student f MBA Department f Management University f Mazandaran Bablsar, Iran anamdar@umzacir Hssein Nazktabar, HD student, Department f Sciall science, University f ayamenr Tehran, Iran hntabar@yahcm Abstract The envirnmental erfrmance Evaluatin (EE) f rganizatins is becming an independent and pwerful management tl In general, prs agree n the imprtance f measuring envirnmental perfrmance related t their main missins and activities The purpse f this paper is t describe the develpment f the fuzzy lgic apprach t decisin making and its usefulness fr managers by illustrating its applicatin t envirnmental perfrmance appraisals The literature is reviewed t prvide the framewrk fr the mdel develpment in this research Envirnmental perfrmance evaluatins represent a critically imprtant decisin that ften invlves subjective infrmatin There are mdels and heuristic techniques that fcus n the use f different types f infrmatin; hwever, with few exceptins, these mdels are nt rbust enugh t be applied in a practical, managerially useful manner Fuzzy lgic mdels prvide a reasnable slutin t these cmmn decisin situatins Fuzzy lgic can be a pwerful tl fr evaluating the envirnmental perfrmance in cmparisn with traditinal mdel In this article a mdel fr evaluating envirnmental perfrmance was presented Firstly thrugh library research and interviews with experts the evaluatin criteria are extracted and classified int 6 qualitative factrs f evaluatin criteria and then a fuzzy inference functin will be utilized t rank envirnmental perfrmances The flexibility f the mdel allws the decisin maker t intrduce vagueness, uncertainty, and subjectivity in the evaluatin system Cncerning the traditinal quantitative methds, this research intrduces an alternative methd f the envirnmental perfrmance evaluatin system Of curse, further research in this area is needed t develp a methd fr relating membership values t linguistic variables in envirnmental perfrmance evaluatin, as well as testing the sensitivity f membership values and their impact n the utcme This paper prvides a simple-t-use fuzzy lgic mdel fr establishing a mre meaningful envirnmental erfrmance evaluatin system Keywrds- Envirnmental erfrmance Evaluatin, Fuzzy Lgic, Decisin Making, Linguistics I INTRODUCTION The envirnmental perfrmance evaluatin (EE) f rganizatins is turning int an independent management tl Generally speaking, prs agree n the imprtance f measuring envirnmental perfrmance related t their main missins and activities Standard EE is defined as a prcess t facilitate management decisin making regarding an rganizatin s envirnmental perfrmance by selecting indicatrs, cllecting and analyzing data, assessing infrmatin against envirnmental perfrmance criteria, reprting and cmmunicating, and peridically reviewing and imprving this prcess [] In rder t make decisins, envirnmental mdels shuld cntain the best knwledge Als, they shuld be supprted by the necessary data t perfrm well against measuring issues This has led t the develpment f mre cmplex and fundamental mdels in recent years Anyway, even the mst advanced mdels are still assciated with large uncertainties [2] The alternative apprach is t cnsider bth the decisin bringing abut envirnmental imprvements and the techniques which allw decisins t make mdels These mdels may invlve greater uncertainty than mre cmplex mdels, but they facilitate mre readily the treatment f uncertainty thrugh sensitivity analysis Mrever, the data requirements t run them are less stringent In fact they may als allw brader factrs t be included int the decisin-making prcess, incrprating risk, and ptimizing scial and ecnmic factrs, etc An envirnmental decisin ught t depend n a criterin meeting a numerical bjective with uncertainty treated explicitly The way f including the uncertainty is t assume that the criterin invlves the membership f a fuzzy set This is an bvius applicatin f fuzzy lgic t envirnmental decisin-making In sme cases, the envirnmental criterin is vague r imprecise, such as when dealing with the quality f life, the ranking f ecsystems in terms f envirnmental cnditins, and impacts [3], r envirnmental impact assessment [4] V-432

2 Hwever, much f the infrmatin related t envirnmental perfrmance appraisal is nt quantifiable and precise with crisp bundaries Rather, this infrmatin is presented in expressins r wrds in natural language and withut precisin Fuzzy lgic mdels prvide a reasnable slutin t these cmmn situatins, which may easily be cnverted int human linguistic frms and subjective cnstructs Fuzzy lgic is a prblem slving methdlgy that prvides a simple way f drawing definite cnclusins frm vague and imprecise infrmatin Fuzzy set thery was first intrduced by Zadeh[5] He was mtivated by bserving that human reasning can utilize cncepts and knwledge that dn t h well-defined bundaries [6] Fuzzy set thery is a generalizatin f the rdinary set thery A useful apprach fr examining many real-wrld prblems is fuzzy apprximate reasning r fuzzy lgic Fuzzy set thery [5] was develped t address cntexts in which decisin makers need t accurately analyze and prcess infrmatin that is imprecise in nature Fuzzy sets prvide a cnceptual framewrk, as well as an analytical tl t slve real wrld prblems where there is a lack f specific facts and precisin ([7] and [8]) Hwever, the applicatin f fuzzy set thery and lgic t management decisins has been generally lacking despite its ptential value in many cmmn situatins [9] On the ther hand, the usage f multigranularity linguistic infrmatin can eliminate the difference frm evaluatrs [0] In this paper the envirnmental perfrmance evaluatin criteria, are defined thrugh expert's ideas and the weight f each ne First, thrugh library research the available articles related t the subject were identified and analyzed Then the interviews with managers and experts were cnducted and 6 qualitative criteria was identified as shwn in table The purpse f this paper is t develp a framewrk fr the applicatin f fuzzy lgic t envirnmental perfrmance appraisal This study attempts t develp an assessment apprach t envirnment perfrmance t imprve the previus techniques In this paper, we describe a detailed qualitative prcedure fr evaluating envirnmental perfrmance II BACKGROUND Literature review has expsed that the perspectives prmted in the varius cnceptual framewrks and methds fr implementatin f envirnmental perfrmance evaluatin, that appear t be dependent n the specialized fundatin and field f interest f the researchers The expressin envirnmental perfrmance is ften used in different cntexts with distinct bjectives, meanings, and brad dmains Sme f envirnmental management and plicy tls use these expressins fr envirnmental perfrmance: envirnmental auditing, envirnmental impact assessment, envirnmental risk assessment and envirnmental management systems (EMS), amng thers [] EE helps the management f an rganizatin t assess the status f its envirnmental perfrmance and t identify areas fr imprvement as needed Qualitative factrs, invlving expert judgment f the pedigree f a mdel, shuld be part f an assessment f mdel perfrmance, ging beynd traditinal scientific appraches, such as sensitivity analysis and mdel validatin Fuzzy decisin-making is clsely related t ther envirnmental decisin-making framewrks, such as multicriteria decisin analysis [2], r the weighted utility apprach [3] In this paper different criteria are classified in six categries as shwn in table and are used in the presented mdel It is nt prpsed that fuzzy decisinmaking is superir t these ther methds, but it prvides a structured framewrk within which ther methds may be incrprated A Fuzzy sets structure and analysis The mst fundamental frm f a fuzzy set A in a universe X is: A = { x, A ( x) x X} Where (x) A represents the grade f membership r cmpatibility functin f element x f X in fuzzy set A Element x may shw a full membership in A (ie A(x) = ), as well as partial membership (0< A(x) <) r nnmembership ( (x) A = 0) Fr example, the fuzzy linguistic variable perfrmance can be characterized by terms: very strng, strng, rage, weak, pr, and very pr Each term is called a linguistic mdifier Therefre, a fuzzy set is frmed when a linguistic variable is cmbined with a linguistic mdifier (ie strng perfrmance) In ur example, each linguistic mdifier is linked t a numerical value n a scale f t 7 that represents the level f perfrmance Thus, the perfrmance set A and its mdifiers can be represented by a fuzzy set as: A = {0 0, 20 00,30 0, 40 0,50 0,60 0,70 0} In this fuzzy set, each element represents a crrespnding value in the universe f discurse and a degree f membership That is, 7 has a full membership grade f crrespnding t very strng perfrmance, and with a nnmembership grade f 0 indicating n perfrmance as well as 5 with a partial membership grade f 0 representing rage perfrmance Anther example f cnstructing fuzzy sets fr linguistic variables is presented in Fig, where three fuzzy sets are used t characterize an envirnment s perfrmance The Fuzzy linguistic variable perfrmance can be defined by terms r linguistic mdifiers as pr, rage, utstanding, with the membership value frm 0 t, describing the level f perfrmance n a scale frm 0 t 5 In Fig, if the nrm fr perfrmance is rage, number 3 represents the highest level f the term rage with a membership grade f and number 4 defines rage with a grade f 00 r utstanding with a grade f 0 Therefre, number 4 describes the perfrmance f an envirnment that is 60 per cent utstanding and 0 percent rage Fig represents three fuzzy sets: V-433

3 rperfrmance = {0 0, 050 0,0 050,50 0, 20 0, 25 0,30 00,350 00, 40 00, ,50 00} rageperfrmance = {0 00, ,0 00,50 erfrmance evaluatins f envirnment are nt easy 00, 20 00, 250 0,30 0, , 40 Many criteria and standards that are invlved shuld be cnsidered Hwever, fr illustratin purpses and t keep 00, ,50 00} matters relatively simple t fllw, the example used in this paper includes seven Envirnments ( E,,, E 7) and six Outs tan dingperfrmance = {0 00,0 00,50 00, 20categries f perfrmance evaluatins fr each Envirnment These categries are shwn in Table 00, ,30 00, , 450 We frm a fuzzy set C in a universe U with the unit interval 0,50 0} [0, ], where: C = { u C ( u), u U} These sets represent the decisin maker s intuitive understanding f the linguistic variable perfrmance and its C ( u) = {0,0,0,0,090,0} mdifiers: pr, rage, and utstanding B Fuzzy set peratins Fuzzy sets can be manipulated by ne f the fur standard fuzzy set peratins: unin, Intersectin, cmplementatin, and implicatin peratins [4] Fr mre details, assume A and B are fuzzy sets with membership functins ( x A ) = {,3,5,7,8} and ( y B ) = {,2,4,6,9}, respectively The unin f A and B is a fuzzy set C = A B, where C( z) = A B( z) = A( x) B( y) A unin peratin is identical t a lgical OR peratin and a fuzzy set unin is perfrmed by applying the Max functin t the elements f tw sets, thus: ( z A B ) = {,3,5,7,9} A lgical AND can be used t determine a fuzzy set D = A B with D( ω) = A B( ω) = A( x) B( y) Fuzzy set intersectins are dne by applying the min functin; therefre: A B( ω) = {0,2,4,6,8} The cmplement f a set is cmputed by subtracting each element f the set frm its Maximum pssible value, in ur example 0 S: A ( x) = 0 A( x) = {0,7,5,3,2} B ( y) = 0 B ( y) = {9,8,6,4,} The implicatin functin is emplyed t decide if A is true, t what extent that implies that B is true? The implicatin peratin is dne by cmputing ( u ), A B knwn as Kleene-Dienes implicatin, where: B( u) = ( x) B( y) A A ( u ) = {0,7,5,6,9} A B It shuld be nted that fuzzy set peratins are nt limited t thse used here; fr ther fuzzy peratins see [4] III ENVIRONMENTAL ERFORMANCE ARAISAL WITH FUZZY LOGIC: A NUMERICAL EXAMLE Each element f the set is given a scre between 0 and ; the scre signifies the relative imprtance f that categry (fuzzy element) t the decisin maker Equal membership means equal imprtance Fr each f the six categries, a qualitative judgment is emplyed t determine the degree f envirnment perfrmance fr that categry These qualitative judgments culd be: nt acceptable, pr, belw rage, slightly belw rage, rage, slightly abve rage, abve rage, and utstanding, thus frming a fuzzy set in universe V with unit interval [0, ] and a fuzzy membership functin: = { v ( v), v V} ( v) = {00,020,0,0,0,0,0,0} As shwn in Table 2 T illustrate hw the manipulatin f fuzzy sets can result in a decisin making system fr envirnment perfrmance evaluatin, several steps must be taken The first step is t assess the perfrmance f each envirnment by each categry that is based n the fuzzy pinin f the decisin maker, as depicted in Table 3 Table 4 cntains seven fuzzy sets, 2,, 7 with membership functins ( v), ( ),, ( ) v 2 v Fr 7 example, the fuzzy set and membership functin fr Envirnment is: = {0 0,20 00,30 0,40 0,50 0,60 0} ( v) = {0,00,0,0,0,0} The principal step in the decisin making prcess is t establish a fuzzy implicatin relatin between a specific categry and each Envirnment s perfrmance fr that categry That is t say, given the relative imprtance f a categry, des that imply a gd perfrmance by the envirnment fr that categry? Assuming that the imprtance assigned t each categry is the maximum value fr that categry, the implicatin relatinship is established by taking the cmplement f the categry imprtance This V-434

4 cmplementatin creates a minimum perfrmance value assigned t all envirnments given the categry The Max functin is applied t each envirnment s perfrmance set, ie ( v), 2( v),, 7( v) and the cmplement f set ( ) C () r = () u () v C C C ( r) = {0,0,0,020,00,0} {0, 00, 0, 0, 0, 0} = {0, 0, 0, 0, 0, 0} The final step is t cmbine varius perfrmances f the envirnment acrss all categries in rder t btain an verall evaluatin This is dne by applying the min functin t the set derived frm the previus step Table 5 shws the verall rating f the envirnments nce the prcess is cmpleted It is nt surprising that Envirnment 7 has been ranked tp perfrmer in this example since the prpsed system favrs the envirnment with a high rating in the mst imprtant categry S, the higher the relative imprtance f the categry is, the mre influence that categry has in the final utput IV DISCUSSION AND CONCLUSIONS This study develps an evaluatin apprach t measure envirnment perfrmance Many factrs are subjective and difficult t quantify in the envirnment evaluatin prcess Fuzzy lgic enables the evaluatr r the decisin maker t incrprate infrmatin in the envirnment evaluatin system which is vague and subjective There are several advantages in using the mdel presented in this paper as ppsed t a previus technique The mathematics is extremely simple and can be easily cmputerized by such sftware as MATLAB It is als extremely flexible, allwing the decisin maker t use a brad range f linguistic variables and mdifiers fr finer discriminatin r t make changes t membership values and/r envirnment perfrmance categries Finally, it is an ideal system when the decisin maker is faced with a series f sub-decisins where available data is based n vagueness, uncertainty, and pinin These sub-decisins are then cmbined int an verall system fr envirnment perfrmance evaluatin Fuzzy lgic can be a pwerful tl fr managers t evaluate the envirnments perfrmance The flexibility f the mdel allws the decisin maker t intrduce vagueness, uncertainty, and subjectivity int the envirnment perfrmance evaluatin system This research calls attentin t an alternative methd f the envirnment perfrmance evaluatin system Applying principles f qualitative envirnmental perfrmance measurement pens up many prmising areas f research First, ne needs t cntinue t analyze and cmpare varius types f methds, t determine which design is apprpriate fr envirnmental perfrmance evaluatin Secnd, we believe that emissins envirnmental perfrmance evaluatin is a natural applicatin f ecnmic cntrl, fr which extensive thery exists but relatively little practical implementatin Third, better understanding f the precise frm f regulatry measurements is needed Future research in this area is needed t develp a methd fr relating envirnment perfrmance values t linguistic variables in envirnment perfrmance evaluatin, as well as testing the sensitivity f envirnment perfrmance values and their impact n the utcme This paper prvides a simple-t-use fuzzy lgic mdel fr establishing a mre meaningful envirnment perfrmance evaluatin system REFRENCES [] Internatinal Organizatin fr Standardizatin, Internatinal Standard ISO 403: Envirnmental Management; Envirnmental erfrmance Evaluatin: Guidelines, Geneva, Switzerland, 999 [2] J Hunt, Mathematics and Envirnmental rblems Methdlgies and Future Develpments, NERC-ESRC Wrkshp, 2000 [3] LT Tran, CG Knight, RV O Neill, ER Smith, KH Riitters and J Wickham, Fuzzy Decisin Analysis fr Integrated Envirnmental Vulnerability Assessment f the Mid-Atlantic Regin, Jurnal f Envirnmental Management, 29: , 2002 [4] M Enea, and G Salemi, Fuzzy Apprach t the Envirnmental Impact Evaluatin, Eclgical Mdeling, 35: 3 47, 200 [5] LA Zadeh, Fuzzy sets, Infrmatin and Cntrl, 8(3): , 965 [6] J Yen and R Langari, Fuzzy Lgic Intelligence, Cntrl, and Infrmatin, rentice Hall ublishing Cmpany, 999 [7] J F Baldwin, Fuzzy Lgic Jhn Wiley and Sns, New Yrk, 996 [8] G J Klir, and B Yuan, Fuzzy Sets and Fuzzy Lgic, rentice-hall ublishing Cmpany, 995 [9] DW Drsey and M D Cvert, Mathematical Mdeling f Decisin Making: a Sft and Fuzzy Apprach t Capturing Hard Decisin, Human Factrs, 45(): 7-35, 2003 [0] F Herrera, E Herrera-Viedma and L Martínez, A Fusin Apprach fr Managing Multi-granularity Linguistic Term Sets in Decisin Making, Fuzzy Sets and Systems, 4():43 58, 2000 [] B R Tmas, Ineˆs Alves, Rui Subtil, Ja Janaz de Mel, The State f Envirnmental erfrmance Evaluatin in the ublic Sectr: the Case f the rtuguese Defense Sectr, Jurnal f Cleaner rductin, 7: 36 52, 2009 [2] Y-K Tung, In: Wu, et al (Eds), Risk-Based Design f Fld Defense Systems Fld Defence Science ress, New Yrk, 2002 [3] C errings, The Ecnmics f Abrupt Climate Change hil Trans R Sc Lnd A 36, , 2003 [4] J M Mendel, Uncertain Rule-Based Fuzzy Lgic Systems: Intrductin and New Directins, rentice-hall ublishing Cmpany, 200 V-435

5 Figure Fuzzy set structure f perfrmance Table : Imprtance f criteria in the numerical example Criteria Gvernment relatins Valuatin f envirnmental issues lanning hrizn Effects n resurces Eclgical end effects Effects n human health Symbl C Relative Imprtance 09 Table 2: Imprtance f linguistics variables in the numerical example Relative Imprtance 0 02 Symbl Na ba Sba S O linguistics variables nt acceptable pr belw rage slightly belw rage rage slightly abve rage abve rage utstanding Table 3: Envirnment perfrmance by categry (envirnment perfrmance rating) E C Ba S S S S S s p ba s s Table 4: Membership grades f Envirnment perfrmance by categry E C 0 02 Reference: Tables, 2, 3 Table 5: Envirnments verall rating in the numerical example Envirnment E Reference: Calculatins f present paper Scre V-436