Fuzzy Analytical Hierarchy Process for Ecological Risk Assessment

Transcription

1 Inforation Technology and Manageent Science Fuzzy Analytical Hierarchy Process for Ecological Risk Assessent Andres Radionovs 1 Oļegs Užga-Rebrovs Rezekne Acadey of Technologies ISSN (online) ISSN (print) Deceber 2016 vol. 19 pp doi: /its Abstract Being able to evaluate risks is an iportant task in any areas of huan activity: econoics ecology etc. Usually environental risk assessent is carried out on the basis of ultiple and soeties conflicting factors. Using ultiple criteria decision-aking (MCDM) ethodology is one of the possible ways to solve the proble. Analytic hierarchy process (AHP) is one of the ost coonly used MCDM ethods which cobines subective and personal preferences in the risk assessent process. However the AHP involves huan subectivity which introduces vagueness type of uncertainty and requires the use of decision aking under those uncertainties. In this paper work with uncertainty is considered using fuzzy-based techniques. The paper also analyses the ecological risk assessent towards huan health in case of gaseous substance escape at a cheical factory using the fuzzy analytical hierarchy process. Keywords Fuzzy logic fuzzy representation of knowledge fuzzy analytical hierarchy process risk assessent. I. INTRODUCTION Risk anageent is an integral part of environental risk analysis. This is the process of weighing the alternatives (options) choosing the ost appropriate action integrating engineering social and econoic data into risk assessent results. Usually the environental risk assessent process includes obective data while the risk anageent includes the preferences and attitudes that have both obective and subective eleents [1]. Environental risk assessent aong the other tasks includes aking decisions that involve the choice of alternatives on the basis of ultiple and soeties conflicting factors. The ultiple criteria decision-aking (MCDM) ethodology is one of the possible ways to solve the proble. MCDM has proven to be a proising and growing field of study since the early 1970s and any applications in the fields of engineering social sciences and business have been reported. One of the ost widely used ethods of MCDM group is an Analytic Hierarchy Process (AHP) which was developed and first published in [2] [3]. There is a growing list of publications on the application of AHP ethod. The AHP provides an ideal platfor for coplex decision-aking probles. Ecological risk assessent usually takes place in the conditions of lack or absence of valid initial data [4]. Nevertheless even if the data are available in sufficient aounts the analysed risk factors often contain linguistic definitions associated with huan udgents and subectivity that in turn introduce uncertainty in decision-aking processes. Quite a big nuber of ethods are eant for acquiring and using abiguous probabilistic assessents including interval probability probability of second degree etc. Difficulty of these ethods and a bad interpretation of uncertain results ake the ethods iperfect. The ain goal of this paper is to quantify the effect of ultiple risk factors in the ecological risk assessent process. Aiing at archiving this goal the fuzzy analytic hierarchy process (FAHP) is applied in the risk assessent towards huan health in case of gaseous substance escape at a cheical factory. Using this ethod as an exaple the risk analysis hierarchy odel of the gaseous substance escape is established and then the safety level coprehensively assessed. Also the s of various risk factors are defined to find the ost influential factors on the total risk level. The present article analyses the ecological risk assessent towards huan health in case of gaseous substance escape at a cheical factory using the fuzzy analytical hierarchy process. II. FUZZY ANALYTIC HIERARCHY PROCESS Analytic Hierarchy Process (AHP) [5] was first proposed in the 1970s by T. L. Saaty an Aerican expert in the field of operational analysis. The AHP ethod uses special atheatical ethods for the processing of personal subective preferences of the individual or a group of individuals on the pairs of relevant factors assessing and analysing decisions. In ost cases the individuals are the experts in a particular field [6]. The AHP ethod works on the preise that the process of aking a global decision on coplex tasks can be perfored by separating and structuring coplex tasks into any siple tasks displaying the in the for of hierarchal structure. In its turn after the hierarchical structure is fored the pairwise coparison of assessent factors is carried out according to the iportance on a lower level of the hierarchy. The results of pairwise coparisons are displayed by nubers ranging fro 1 to 9 where 1 eans that the two evaluation factors are equally iportant while the other extree rating 9 reflects the fact that one assessent factor is absolutely ore iportant than the other. Next the pairwise coparison of alternatives for each of the risk factors is carried out. Then the obtained estiates are translated to the next level of the hierarchy the level of the criteria where the aggregation of previously obtained estiates is perfored. Next the interi assessents are transferred to the upper level of the hierarchy the level of obectives. There the final aggregation of previous estiates is ade. Thus the resultant estiation is obtained for each alternative decision. The 2016 Andres Radionovs Oļegs Užga-Rebrovs. This is an open access article licensed under the Creative Coons Attribution License ( in the anner agreed with De Gruyter Open. 16

2 Inforation Technology and Manageent Science selection of the optial solution is ade on the basis of coparison of these estiates. Value adustent --- Forulate the hierarchical tree Create fuzzy pairwise coparison atrix Check for consistency (Cl) for ost likely value No C/<10% Yes Calculate the fuzzy s Aggregate individual preferences Def u zz i fi cation Final ranking and decision aking Fig. 1. Fuzzy analytic hierarchy process. Risk attitude In the risk analysis the AHP ethod is upgraded and it can be reduced to three ain stages: 1) the creation of a hierarchical odel of risk factors; 2) deterination of the s of risk factors; 3) quantitative estiation of the risk level. S. Lopez and others in their study [7] have proposed a odernised AHP ethod that produces risk prioritisation according to their threat level. Currently there are any studies that cobine the AHP ethodology with the echanis of fuzzy logic. Fuzzy logic ethodology is used with the analytic hierarchy process to for a odel for risk assessent. These odels of risk assessent are used in various spheres for exaple risk assessent of floor water invasion in coal ines [8] oil and gas offshore wells [9] inforation technology proects [10]. In ost cases the fuzzy AHP ethod assues that each risk factor is displayed as an eleent of lower level of the hierarchical structure and is expressed as a fuzzy nuber which is the cobination of fuzzy evaluation of the probability of a corresponding adverse event and the fuzzy evaluation of potential losses related to the ipleentation of this event. The fuzzy analytic hierarchy process (FAHP) described in this paper is based on the interpretation of the decision aker s attitude towards a risk level in the decision-aking process and was originally proposed by H. Deng in [11]. In this study the FAHP ethodology is forulated as a series of eight steps and is shown scheatically in Fig. 1. These eight steps are followed through a hierarchical structure exaple shown in Fig. 2. III. HIERARCHY MODEL OF RISK FACTORS Identification of risk factors is the first step in the environental risk assessent. In accordance with the features of environental risk analysis as well as with the cobination of existing data and expertise 12 factors have been defined. Those factors affect the level of risk in the event of an accident at a cheical plant and a leak of poisonous substances. The factors ay also be divided into four categories. All the factors and categories are presented in Fig. 2 where the categories of factors are designated as F = {F1 F2 F3 F4} where F1 represents a factor category of soil and groundwater vulnerability F2 hazardousness of substance F3 preventive and protective easure F4 huan factor. Each category of the above 4 categories also represents one factor set illustrated as fi Fi = {fi1 fi2... fi} i = In order to support the risk assessent based on the hierarchy of the risk factors shown in Fig. 2 a coprehensive risk assessent ethod is established the FAHP ethod. The FAHP ethod includes the iportant procedures of the deterination of s of various risk factors the quantitative analysis of risk factors and the establishent of the coprehensive risk calculation odel. Ecological risk (F) Soil and groundwater vulnerability (F1) Hazardousness of substance (F2) Preventive and protective easure (F3) Huan factor (F4) Water table conditions (f11) Pereability (f12) Groundwater depth (f13) Toxicity and/or Radiation (f21) Concentration (f22) Mobility (f23) Level of eergency response training (f31) Safety easures (f32) Equipent stability audit (f33) Work experience (f41) Workers skill sets (f42) Age (f43) Fig. 2. The hierarchy of the risk factors in case of gaseous substance escape at a cheical factory. The FAHP ethod is based on the idea that on the basis of the hierarchical odel of risk factors for each factor the risk factor is deterined. This is achieved by using fuzzy 17

3 Inforation Technology and Manageent Science atheatics perforing the operations described below step by step. All atheatical calculations used at all stages and illustrated in the article have been ipleented by Microsoft Excel. A. Step 1: Definition of the Judgent Matrix The values in the cells of atrix of udgents reflect subective udgents in relation to iportance of each factor in the hierarchical structure towards other factors. Table I presents a fuzzy version of T.L. Saaty s coon fuzzy scale [12] in which the result of each coparison is shown as a triangular fuzzy nuber and its inverse equivalent. A triangular fuzzy nuber is represented by [lower value ean value upper value] i.e. [l u]. TABLE I LINGUISTIC SCALE OF RELATIVE IMPORTANCE Linguistic scale for relative iportance Triangular fuzzy scale Reciprocal of triangular fuzzy scale Exactly the sae (1 1 1) (1 1 1) The sae iportance (1/2 1 3/2) (2/3 1 2) Slightly iportant (1 3/2 2) (1/2 2/3 1) Serious iportance (3/2 2 5/2) (2/5 1/2 2/3) More serious iportance (2 5/2 3) (1/3 2/5 1/2) Absolute iportance (5/2 3 7/2) (2/7 1/3 2/5) According to the risk factor hierarchy (shown in Fig. 2) through coparison of the iportance of each pair of risk factors the udgent atrix of the 4 categories of risk factors in ecological risk assessent is shown in Table II. For exaple an expert has concluded that the risk category hazardousness of substance (F2) is ore iportant than factor of soil and groundwater vulnerability (F1) the result of coparison is displayed by the fuzzy nuber in the atrix. TABLE II JUDGMENT MATRIX OF RISK CATEGORIES F F 1 F 2 F 3 F 4 F 1 (1 1 1) (2/5 1/2 2/3) (1/3 2/5 1/2) (2/3 1 2) F 2 (3/2 2 5/2) (1 1 1) (1/3 2/5 1/2) (2/3 1 2) F 3 (2 5/2 3) (2 5/2 3) (1 1 1) (2/3 1 2) F 4 (1/2 1 3/2) (1/2 1 3/2) (1/2 1 3/2) (1 1 1) Siilarly the udgent atrix of risk factors can be obtained respectively as Tables III IV V and VI. TABLE III JUDGMENT MATRIX OF RISK CATEGORY SOIL AND GROUNDWATER VULNERABILITY F1 f 11 f 12 f 13 f 11 (1 1 1) (1/2 2/3 1) (2/5 1/2 2/3) f 12 (1 3/2 2) (1 1 1) (1 3/2 2) f 13 (3/2 2 5/2) (1/2 2/3 1) (1 1 1) TABLE IV JUDGMENT MATRIX OF RISK CATEGORY HAZARDOUSNESS OF SUBSTANCE F2 f 21 f 22 f 23 f 21 (1 1 1) (3/2 2 5/2) (3/2 2 5/2) f 22 (2/5 1/2 2/3) (1 1 1) (1/2 2/3 1) f 23 (2/5 1/2 2/3) (1 3/2 2) (1 1 1) TABLE V JUDGMENT MATRIX OF RISK CATEGORY PREVENTIVE AND PROTECTIVE MEASURE F3 f 31 f 32 f 33 f 31 (1 1 1) (1 3/2 2) (3/2 2 5/2) f 32 (1/2 2/3 1) (1 1 1) (1/2 1 3/2) f 33 (2/5 1/2 2/3) (2/3 1 2) (1 1 1) TABLE VI JUDGMENT MATRIX OF RISK CATEGORY HUMAN FACTOR F4 f 41 f 42 f 43 f 41 (1 1 1) (3/2 2 5/2) (3/2 2 5/2) f 42 (2/5 1/2 2/3) (1 1 1) (2/5 1/2 2/3) f 43 (2/5 1/2 2/3) (3/2 2 5/2) (1 1 1) B. Step 2: Consistency Test Consistency is iportant in huan thinking and enables us to order the world according to doinance [13]. It is significant to ensure pairwise coparisons consistency in experts evaluations that are defined in Step 1 of the atrix. Results of pairwise coparisons ay differ due to the uncertainty of experts assessents. The AHP ethod introduces a consistency test and easure to avoid this proble. The sae consistency test is used in the Fuzzy AHP ethodology. The ain idea of this ethod is the following: once the udgent atrix is populated the axiu eigenvalue is obtained. In his works [2] [3] T.L. Saaty described in detail the ethodology and forulas necessary for calculating the values and showed that in a consistent udgent atrix λ ax = n where λ ax the axiu eigenvalue and n the diension of the udgent atrix. Then using (1) consistency index (CI) is obtained. Consistency index indicates whether a decision aker provides the coparison of consistent values in a set of evaluations. ax n CI. (1) n 1 The final possible inconsistency of pairwise coparisons of the results is deterined using the consistency ratio CR = CI/RI where RI is a rando index which is obtained by averaging the CI of a randoly generated reciprocal atrix [3]. Values of RI are shown in Table VII. 18

4 Inforation Technology and Manageent Science According to [3]: the threshold of consistency ratio is 10 % and in case of exceeding the threshold value to reduce inconsistencies in the pairwise coparisons the following actions are perfored: 1) the ost controversial udgent in the atrix is deterined 2) the range of adissible values for inor corrections of udgents is deterined to achieve reductions in inconsistencies and 3) the expert is offered to correct soe of the results of his/her pairwise coparisons. TABLE VII RANDOM INDICES OF N DIMENSIONAL MATRIX [3] n RI where and n 1 i1 1 M M gi gi 1 1 l u (3) u (4) l 1 The calculation results of consistency of pairwise coparison results for F1 F4 risk factor categories are shown in Table VIII. TABLE VIII RESULTS OF CONSISTENCY TEST FOR MATRIX λ ax CI RI CR F % F % F % F % F % For a atrix of pairwise coparisons of the results presented in Table II the axiu eigenvalue (λ ax ) = for the F1 risk factor category the diension of the atrix n = 4 consistency index (CI) fro (1) CI = the value of a rando index (fro Table VII) RI = This iplies that the value of the consistency ratio CR = 6.81 %. This value does not exceed the axiu adissible value of 10 %; therefore the atrix results of pairwise coparisons can be correctly used in further calculations. C. Step 3: Weight Calculation for Risk Factors There are a nuber of different ethods for calculating s of factors (for exaple [14]). One of the ost popular FAHP techniques has been proposed by Chang [15] which uses the Fuzzy Extent Analysis in order to calculate the crisp s fro fuzzy coparison atrices. Applying this theory in the fuzzy coparison atrix one can calculate the value of fuzzy synthetic extent with respect to the i th obect as follows: S i 1 M gi n M gi i (2) The results of coputing according to (2) in a atrix of pairwise coparisons shown in Table II are presented in the following for: SF1 ( ) S F 2 ( ) S F3 ( ) S F 4 ( ). Next in the decision aking process a crisp fro these fuzzy triangular s should be deterined. D. Chang [15] suggests using the concept of coparison of fuzzy nubers in order to deterine crisp s fro the fuzzy s. Next for each fuzzy a pair wise coparison with the other fuzzy s is perfored (using (5)) and the degree of possibility of being greater than these fuzzy s is obtained. The iniu of these possibilities is used as the overall score for each factor. Applying (5) to the previous results we obtain the following values: V ( S F 2) F1 S 0.65 V ( S F 3) F1 S V ( S F 4) F1 S 0.77 V ( S 2 3 ) F S F 0.58 V ( S 2 1 ) F S F 1.00 V ( S 2 4 ) F S F 1.00 V ( S 3 1 ) F S F 1.00 V ( S 3 2 ) F S F V ( S F 3 S F 4) 1.00 V ( S F 4 S F 1) V ( S F S 2) 0.92 V ( S F S 3) F 4 F Finally these scores are noralised (they su up to 1) and the corresponding noralised scores of the 4 categories of risk factors are obtained: W F ( ) (5) 19

5 Inforation Technology and Manageent Science Siilarly using the extent analysis ethod the vectors of the risk factors are obtained as follows: W F1 ( ) W F 2 ( ) W F3 ( ) W F 4 ( ). The overall of the risk factor equals ultiplication of the local to of its father factor. The iportance of the categories and risk factors is shown in Table IX. TABLE IX WEIGHT TABLE FOR RISK FACTORS IN ECOLOGICAL RISK ASSESSMENT TOWARDS HUMAN HEALTH IN CASE OF GASEOUS SUBSTANCE ESCAPE AT A CHEMICAL FACTORY Risk categories Local F F F F Risk factor Local Overall f f f f f f f f f f f f IV. QUANTITATIVE ANALYSIS OF RISK FACTORS In the previous section the iportance of each risk factor at the general level of risk to the environent in case of leakage of poisonous substances has been identified on the basis of experts opinions but that is not enough for the full assessent of the environental risk. It is also necessary to include in the calculations the value that will display the real situation at the Criteria of eergency response training level (f 33 ) Safety easure levels of the cheical plant (f 32 ) TABLE X QUANTITATIVE ASSESSMENT CRITERIA OF RISK FACTORS plant for each risk factor. Three risk groups have been defined to assess each risk factor in the study: low ediu and high level which correspond to the nuerical equivalent of 1 3 and 5 points and are taken into account in the calculations of the ecological risk in case of leakage of poisonous substances at a cheical plant. Table X deonstrates several risk factors and the description of their values. V. CASE STUDY In this article the environental risk assessent in relation to huan health in the event of leakage of poisonous substances at a cheical plant is regarded as the case study. For visual clarity of display of the FAHP ethodology results it is supposed that a group of experts gave their opinion on the real state of the plant according to the factors presented in Fig. 2 and their values (Table X). For exaple the experts after exaining the plant have drawn the conclusion that the safety easure levels of the cheical plant (f 32 ) correspond to a ediu risk group; therefore taking into account the iportance of this risk factor the overall risk level of this factor is units. The quantitative results of all risk factors are presented in Table XI. The weighed quantity risk and factor results are displayed as a graph in Fig. 3. Fig. 3. The histogra of risk level of risk factors in case of gaseous substance escape at a cheical factory. High (5 points) Mediu (3 points) Low (1 point) Min.2 4-hour safety training In eergency they would leave the area then call for help and keep others out of the area. The plant does not correspond to necessary safety requireents. Risk level Min. 8-hour safety training Personnel priary function is to contain the release fro a safe distance keep it fro spreading and prevent exposures. May be involved in decontaination. Generally the plant corresponds to necessary safety conditions Min. 24-hour safety training Personnel will stop the release by plugging patching or shutting down the process. The plant fully corresponds to the safety requireents f11 f12 f13 f21 f22 f23 f31 f32 f33 f41 f42 f43 Risk Sub-factors Criteria equipent stability audit level (f 33 ) The absence or lack of safety checks repairs or in rare cases replaceent of the equipent only after the failure. Replaceent or repair of equipent if possible after detection of significant deviations fro the nors of operability. Constant autoatic and anual security and equipent operability checks conducted by the experts of highest classification. Replaceent of the equipent iediately after the detection of the sallest deviations. 20

6 Inforation Technology and Manageent Science TABLE XI RISK FACTORS TABULAR STATEMENT FOR ECOLOGICAL RISK ASSESSMENT PROCESS Risk factor Overall Cheical plant risk level Real plant situation Risk level f f f f f f f f f f f f VI. FAHP LIMITATIONS Notwithstanding a big nuber of advantages of FAHP ethodology in the ecological risks assessents there are also liitations. The liitations of Chang s FAHP ethodology [15] include: 1) the noralisation forula does not take into account constraints derived fro the AHP ethod [16]; 2) the ethod in very rare cases could lead to a wrong decision because it ight assign zero s to soe ites (criteria sub-criteria or alternatives) excluding the fro the decision analysis [17]; 3) crisp values are not fully capable of reflecting a person s vague thoughts [18]. Despite the liitations of Chang s FAHP ethodology [15] nowadays it reains one of the ost popular FAHP ethods for analysis of experts evaluation. VII. CONCLUSION AND FUTURE RESEARCH On the basis of the current conditional situation analysis 12 risk factors and 4 risk factor categories have been identified which affect the overall level of risk to huan health in case of leakage of gaseous substances at a cheical plant. The hierarchy and patterns aong factors have been deterined on the basis of the risk factors. Using the coprehensive risk assessent ethod (FAHP) the factors have been deterined that represent the iportance of each risk factor. The quantitative analysis of risk factors has also been perfored. As an exaple ecological risk assessent towards huan health in case of gaseous substance escape at a cheical factory has been carried out and the risk factors have coprehensively been assessed. The factors have been ranked according to their effect on the overall level risk. It has been deonstrated fro the application in actual cases that the risk assessent FAHP ethod is easy and effective in engineering applications which can provide technical support for the accident risk assessent in the ecological risk assessent process. The application of the FAHP ethod to the assessent of risk of environent and people s health in case of gaseous substance escape at a cheical allows aking a coplex algorith of analysis ore affordable in order to obtain risk assessent in case of incoplete and reduced input data. The use of this odel allows for realistic preliinary assessent of the risk of accidental cheical releases. The ethodology can be used not only by public authorities but also by plant anagers since it is a ethod that allows evaluating the risk level of the site and deterining whether the safety easureents are suitable. This application can be used as a preliinary risk assessent tool which can highlight critical situations and the need for ore in-depth and coplete analysis. It can also be used in case of the necessity to ake thoughtful decisions in order to reduce a risk level. In the future it is planned to investigate a possibility of using other FAHP ethodologies for the ecological risk analysis. The entioned ethods can be the following: Van Laarhoven and Pedrycz s FAHP odel (1983); Buckley s FAHP odel (1985) etc. It would be possible to consider their differences and analyse the results of identical experts evaluation (initial data) as well as to ake conclusions on the basis of the analysis results concerning positive and negative aspects of each ethod in case of their usage in the ecological risk analysis. REFERENCES [1] D. K. Asante-Duah Hazardous waste risk assessent Ann Arbor: Lewis Publishers pp [2] T. L. Saaty A scaling ethod for priorities in hierarchical structure Journal of Matheatical Psychology vol. 15 pp [3] T. L. Saaty The analytic hierarchy process New York: McGraw-Hill [4] M. A. Harwell C. C. Harwell and J. R. Kelly Regulatory endpoints ecological uncertainties and environental decision-aking OCEANS 86 Washington DC USA 1986 pp [5] T. L. Saaty The analytical hierarchy process Pittsburg: PWS Publications [6] T. L. Saaty and L. G. Vargas How to ake a decision? in Models ethods concepts and applications of the analytic hierarchy process vol. 1. Kluwer Dordrecht [7] C. Lopez and J. L. Saleron Ranking risks in abient intelligence proects Journal of Applied Research and Technology vol. 9 no. 3 pp [8] Y. Wang et al. Risk assessent of floor water inrush in coal ines based on secondary fuzzy coprehensive evaluation International Journal of Rock Mechanics and Mining Sciences vol. 52 pp [9] S. Lavasani et al. Fuzzy risk assessent of oil and gas offshore wells Process Safety and Environental Protection vol. 89 pp [10] F. Tuysuz and C. Kahraan Proect risk evaluation using a fuzzy analytic hierarchy process: an application to inforation technology proects International Journal of Intelligent Systes vol. 21 pp [11] H. Deng Multi-criteria analysis with fuzzy pairwise coparison International Journal of Approxiate Reasoning vol. 21 no. 3 pp [12] C. Kahraan and T. Ertay A fuzzy optiization odel for QFD planning process using analytic network approach European Journal of Operational Research vol. 171 pp [13] T. L. Saaty Theory and applications of the analytical network process: decision-aking with benefits opportunities costs and risk University of Pittsburgh Pittsburgh RWS Publications

7 Inforation Technology and Manageent Science [14] S. K. Vaidya Analytic hierarchy process: an overview of applications European Journal of Operational Research vol. 169 pp [15] D. Chang Applications of the extent analysis ethod on fuzzy AHP European Journal of Operational Research vol. 95 pp [16] M. Enea and T. Piazza Proect selection by constrained fuzzy AHP Fuzzy Optiization and Decision Making vol. 3 issue 1 pp March [17] Y. M. Wang Y. Luo and Z. Hua On the extent analysis ethod for fuzzy AHP and its applications European Journal of Operational Research vol. 186 pp [18] A. C. Kutlu and M. Ekekçioğlu Fuzzy failure odes and effects analysis by using fuzzy TOPSIS-based fuzzy AHP Expert Systes with Applications vol. 39 no. 1 p Andres Radionovs is a Doctoral student at Rezekne Acadey of Technologies (Latvia). He received his M. Sc. degree in Coputer Science fro Daugavpils University (Latvia). His research interests include inforation systes fuzzy inforation uncertainty and in particular fuzzy set theory and its applications in risk assessent. E-ail: a.radionovs@gail.co Oļegs Užga-Rebrovs is a Professor at the Faculty of Econoics Rezekne Acadey of Technologies (Latvia). He received his Doctoral degree in Inforation Systes fro Riga Technical University in His research interests include different approaches to processing incoplete uncertain and fuzzy inforation in particular fuzzy set theory rough set theory as well as fuzzy classification and fuzzy clustering techniques and their applications in bioinforatics. E-ail: rebrovs@tvnet.lv. 22