A Knowledge Mining Model for Ranking Institutions using Rough Computing with Ordering Rules and Formal Concept analysis

IJCSI Interna tional Journal of Com puter Scie nce Issue s, Vol. 8, Issue 2, Marc h 2011 ISSN (Online): 1694-0814 www.IJCSI.org 417 A Knowledge Mining Model for Ranking Institutions using Rough Computing with Ordering Rules and Formal Concept Analysis D. P. Acharjya 1 , and L. Ezhilarasi 2 1, 2 School of Computi ng Sciences and Engin eering, VIT Univers ity Vellore, Tamil Nadu, India Abstract Emergences of computers a nd information technological revolution made tremendous changes in the real world and provides a different dime nsion for the intelligent data analysis. Well formed fact, the information at right time a nd at right place deploy a better knowledge . However, the challenge arises when larger volume of inconsistent da ta is given for decision making and knowledge extraction. To handl e such imprecise data certain mathemati cal tools of greater importance has developed by researches in recent past namely fu zzy set, intuitionistic fuzzy set, rough Set, formal concept analysis and ordering rules. It is also observed that many information system cont ains numerical attribute values and the refore they are a lmost similar instea d of exact similar. To handle suc h type of information system, in this paper we use two processes such as pre process and post process. In pre process we use rough set on intuitionistic fuzzy approximation space wit h ordering rules for f inding the knowledge whereas in post process we use formal concept analysis to explore better knowle dge and vital factors affecting decisions. Keywords: Information System, Formal Concept, Cont ext table, Ordering Rules, Intuitionistic Fuzzy Proximity Relation, Rough Sets on Intuitionistic Fu zzy Approximation Space. 1. Introduction In real world, invent of computers have created a new space for knowledge mining. Thus , data handling and data processing is of prime im portance in the inform ation system. I n the hierarchy of data processing, data is the root which transforms into infor mation and further r efined to avail it in the form of knowledge. Know ledge mining specifies the collection of the right information at the r ight level and utilize for the suitable pur poses. It is impor tant to understand that, at human level it involves a thought process. These thoughts ar e responsible to collect the raw data and convert it in to us able data and fur ther to information for an assigned task . The real challenge arises when larger volume of inconsis tent data is presented for extraction of knowledge and decision making. The m ajor issue lies in converting large volume of data into knowledge and to use that knowledge to make a proper decision. Curre nt technologies help in obtaining decisions by creating large databases. Ho we ver, it is failure in m any instances because of irrele vant information in the databases. It leads to attri bute r eduction. Thus, attribute reduction is an important factor for handling such huge data sets by eliminating the superficial data to pr ovide an effective decision. Many methods wher e proposed to mine rules from the growing data. Most of the tools to mine knowledge are crisp, tr aditional, deterministic and pr ecise in notion. Real situations are very often the r everse of it. The detailed description of the real system needs detailed data which is beyond the recognition of the human interpretation. This invoked an extension of the concept of crisp sets so as to model impr ecise data that enable their modeling intellects. Typically, each m odel and method presents a particular and single view of data or discovers a specific type of knowledge embe dded in the data. To carry on with inconsistent data certain mathem atical tools of greater importance got developed in recent past namely fuzzy set [7], intuitionistic fuzzy set [6], rough set [11], formal concept analysis [8], and ordering rules [10] to name a few . Further r ough set is generalized to rough sets on fuzzy approximation space [9], rough sets on intuitionistic fuzzy approxima tion spaces [1]. The notion of rough sets on intuitionistic fuzzy approximation space depends on the concept of intuitionistic fuzzy proxim ity relation. In this paper, we propose an integrated knowledge mining model that combines rough set on intuitionistic fuzzy approximation space with orde ring of objects and formal concept analysis as a new t echnique for extracting better knowledge from the available data set. The motivation behind this study is that the tw o theories aim at differe nt goals and summ arize different types of know ledge. Rough computing is used for predic tion whereas formal concept analysis is used for desc ription. Therefore, the combination of both leads to better knowledge mining model. Howe ver, for completeness of the paper we explain the basic concepts of rough sets in section 2, r ough sets on IJCSI Interna tional Journal of Com puter Scie nce Issue s, Vol. 8, Issue 2, Marc h 2011 ISSN (Online): 1694-0814 www.IJCSI.org 418 intuitionistic fuzzy approximati on spaces in section 3. In section 4, we discuss order infor mation table followed by formal concept analysis in section 5. We present our proposed model in section 6 and is further analyzed in section 7. The paper is concluded in section 8. 2. Foundations of Rough Sets The theory of rough sets has been under continuous development for over few d ecades and a fast growing group of researchers and pr actitioners are interested in this methodology. The me thodology is concerned with the classificatory analysis of imprecise, uncertain or incomplete data. The main advantage of r ough set theory proposed by Pawlak [15] is that it does not need any preliminary or additional info rmation about data. On the other hand, handling vagueness is one of the motivations for proposing the rough set theory [15]. O bjects that belong to the same category of the information are indiscernible [12, 13, 14]. Thus inform ation associated with objects of the universe generates an indiscernibility relation and is the basic concept of r ough set theory. This fact leads to the definition of a set in terms of lower and upper approximations, where approximation space is the basic notion of the rough set theory. Let U be a finite nonempty set called the universe. Suppose RU U  is an equivalence relation defined on U . Thus, the equivalence re lation R partitions the set U into disjoint subsets [15]. Elements of same equivalence class are said to be indisti nguishable. Equivalence classes induced by R are called elementary sets or elementary concepts. The pair (,) UR is called an approximation space. Given a target set , X U  we can characterize X by a pair of lower and upper appr oximations. We associate two subsets RX and RX called the R–Lower and R–Upper approximations of X r espectively and are given by {/ : } RX Y U R Y X    (1) and {/ : } RX Y U R Y X      (2) The R–boundary of X , () R BN X is given by () R BN X  RX RX  . We say X is rough with respect to R if and only if RX RX  or () R BN X   . X is said to be R – definable if and only if RX RX  or () R BN X   . 3. Rough Sets on Intuitionistic Fuzzy Approximatio n Spaces As me ntioned in the previous section, the basic r ough set depends upon equivalence relati ons. H owever, such types of relations are rare in inform ation system containing numerical values. This leads to the dropping of the transitivity property of an e quivalence relation and m aking reflexivity and symm etry property lighter. It leads to fuzzy proximity relation and thus r ough sets on fuzzy approximation spaces [9]. The fu zzy proximity relation is further generalized to intuitionistic fuzzy proximity relation [6]. Thus r ough sets on intuitionistic fuzzy approximation spaces introduced by Tripathy [1] provides a better model over rough set and rough set on fuzzy approximation space. The different prope rties of rough sets on intuitionistic fuzzy approximation spaces were studied by Acharjya and Tripathy [5] . How ever, for completeness of the paper we pr ovide the basic notions of rough sets on intuitionistic fuzzy approximation spaces. We use standard notation  for member ship and  for non-mem bership functions associated with an intuitionistic fuzzy set. Definit ion 3.1 An intuitionistic fuzzy relation R on a universal set U is an intuitionistic fuzzy set defined on UU  . Definit ion 3.2 An intuitionistic fuzzy relation R on U is said to be an intuitionistic fuzzy pr oximity relation if the following properties hold. (, ) 1 a n d (, ) 0 RR x xx x x U      (3) (, ) ( , ) , (, ) ( , ) , RR R R x yy x x y y x x y U       (4) Definitio n 3.3 Let R be an intuitionistic fuzzy (IF) proximity re lation on U . then for any (, ) , J    where   (, ) , [ 0 , 1 ] 0 1 Ja n d         , the (, )   - cut , '' R  of R is given by   , (, ) (, ) a n d (, ) RR Rx y x y x y       Definitio n 3.4 Let R be an IF -proximity r elation on U . We say that two elements x and y are (, )   -similar with respect to R if , (, ) x yR   and we writ e , x Ry  . Definit ion 3.5 Let R is an IF-pr oximity relation on U . We say that two elements x and y are (, )   -identical with respect to R for (, ) , J    , written as (, ) x Ry   if and only if , x Ry  or there exists a sequence of elements 123 ,,,, n uu u u  in U such that ,1 1 , 2 2 ,3 ,, , x Ru u Ru u Ru    , ,. n uR y   In the last case, we say that x is transitively (, )   -similar to y with respect to R . It is also easy to see that for any (, ) J    , (, ) R   is an equivalence relation on U . We denote * , R   the set of equivalence classes generate d by the equivalence relation (, ) R   for each fixed (, ) J    . Definitio n 3.6 Let U be a universal set and R be an intuitionistic fuzzy proximity re lation on U . The pair (, ) UR is an intuitionistic fuzzy approxim ation space (IF- IJCSI Interna tional Journal of Com puter Scie nce Issue s, Vol. 8, Issue 2, Marc h 2011 ISSN (Online): 1694-0814 www.IJCSI.org 419 approximation space). An IF-approximation space (, ) UR generates usual approximation space (, ( , ) ) UR   of Pawlak for every (, ) J    . Definitio n 3.7 The rough set on X in the generalized approximation space (, ( , ) ) UR   is denoted by , , (, ) , XX    where * , , {a n d } X YY R Y X      (5) and * , , {a n d } XY Y R Y X        (6) Definitio n 3.8 Let X be a rough set in the generalized approximation space (, ( , ) ) UR   . Then we define the (, )   -boundary of X with r espect to R denoted by , () BNR X  as , , , () BNR X X X      . Definitio n 3.9 Let X be a rough set in the generalized approximation space (, ( , ) ) UR   . Then X is (, )   - discernible with respect to R if and only if , , X X     and X is (, )   -rough with respect to R if and only if , , X X     . 4. Order Informat ion Table The basic objective of inductive learning and data mining is to learn the know ledge for classification. It is certainly true for rough set theory based approaches. However, in real world problems, we may not be faced with sim ply classification. One such problem is the ordering of objects. We are interested in mining the association between the overall ordering and the individual order ings induced by different attributes. I n many information system s, a set of objects are typically represente d by their values on a finite set of attributes. S uch info rm ation may be conveniently described in a tabular form. Formally, an information table is defined as a quadruple: ( , ,{ : } ,{ : } ) aa I UA V a A f a A   , where U is a finite non-empty set of objects called the universe and A is a non-empty finite set of attributes. For every , a aA V  is the set of values that attribute a may take and : aa f UV  is an information function [2]. In practical appli cations, there are various possible interpretations of objects such as cases, states, patients, processes, and obser vations. Attributes can be interpreted as features, variables, and characteristics. A special cas e of information systems called information table wher e the colum ns are labeled by attributes and rows are by objects. F or example: The information table assigns a particular value () ax from a V to each attribute a and object x in the universe U . With any PA  there is an associated equivalence relation () I ND P such that 2 () { ( ,) , ( ) ( ) } I ND P x y U a P a x a y     The relation () I ND P is called a P -indiscernibility relation. The partition of U is a family of all equivalence classes of () I ND P and is denoted by () UI N D P or UP . If (, ) ( ) x yI N D P  , then x and y ar e indiscernible by attributes from P . For example, consid er the information Table 1, where the attribute 1 a represents the availability of research and development facility; 2 a represents the adoption of state of art facility; 3 a represents the marketing expenses, and 4 a represents the profits in million of rupees. . Table 1. Inform ation ta ble Object R&D facility ( 1 a ) State of art facility ( 2 a ) Marketing expenses ( 3 a ) Profits in million Rs. ( 4 a ) 1 o No Yes High 200 2 o Yes No High 300 3 o Yes Yes Average 200 4 o No Yes Very high 250 5 o Yes No High 300 6 o No Yes Very high 250 An ordered information table ( OIT) is defined as OIT {IT, { : }} a aA    where, IT is a standard information table and a  is an order relation on attribute a . An ordering of values of a particular attribute a naturally induces an ordering of objects: {} () ( ) aa a a x yf x f y   where, {} a  denotes an order relation on U induced by the attribute a . An object x is ranked ahead of object y if and only if the value of x on the attribute a is ra nked ahead of the value of y on the attribute a . For example, information Table 1 is considered as ordered inform ation table if 1 2 3 4 :Y e s N o :Y e s N o : Very high High Av erage : 300 250 200 a a a a       For a subset of attributes PA  , we define: {} () ( ) () ( ) Pa a a aa a aP a aP x yf x f y a P fx f y          In practical applications, there are various possible interpretations of objects such as cases, states, patients, IJCSI Interna tional Journal of Com puter Scie nce Issue s, Vol. 8, Issue 2, Marc h 2011 ISSN (Online): 1694-0814 www.IJCSI.org 420 processes, and observations. A ttributes can be inter preted as features, variables, and ch aracteristics. A special case of information systems called inform ation table where the columns are labeled by attributes and r ows are by objects. For example: Howeve r in real life applications, it is observed that the attribute valu es are not exactly identical but almost identical. This is because objects characterized by the almost same information are almost indiscernible in the view of available information. At this point we generalize Pawlak’s appr oach of indiscernibility. Keeping view to this, the almost indiscer nibility relation generated in this way is the mathem atical basis of rough set on fuzzy approximation space and is discussed by Tripathy and Acharjya [4]. This is fur t her generalized to rough set on intuitionistic fuzzy approxi mation space by Tripathy [1]. Also, generalized inform ation table may be viewed as information tables with added semantics. For the problem of knowledge mining, we introduce order relations on attribute values [2]. How ever, it is not appropriate in case of attribute values that are almost i ndiscernible. In this paper we use r ough sets on intuitionistic fuzzy approximation space to find the attribute values that are (, )   -identical before introducing the order relation. This is because exactly ordering is not possible when the attribute va lues are almost identical. For 1, 0    , the almost indiscer nibility relation, reduces to the indiscernibility relation. Therefor e, it generalizes the Paw lak’s indiscernibility relation. 5. Basics of Formal Concept Analysis Formal Concept A nalysis has been introduced by R. Wille [8] is a method of analyzing data across various domains such as psychology, sociology, anthropology, medicine, biology, linguistics, computer sciences and industrial engineering to name a few. The basic aim of this theor y is to construct a concept latti ce that provides complete information about structure such as re lations between object and attributes; implica tions, and dependencies. At the same time it allow s knowledge acquisition from (or by) an expert by putting very precise questions, which either have to be confirmed or to be r efuted by a counterexample. 5.1 Form al Context and Form al Concept In this section we recall the basic definitions and notations of formal concept analysis developed by R. Wille [8]. A formal context is defined as a set structure (, , ) K GM R  consists of two sets G and M w hile R is a binary relation between G and M , i.e. RG M  . The elements of G are called the objects and the elements of M are called the attributes of the context. The formal concept of the formal context (, , ) GM R is defined with the help of derivation operators. The der ivation operators are defined for arbitrary X G  and YM  as follows: {: } X aM u R a u X     (7) {: } Yu G u R a a Y     (8) A formal concept of a formal context (, , ) K GM R  is defined as a pair (, ) X Y with X G  , , YM  , X Y   and YX   . The f irst me mber X , of the pair (, ) X Y is called the extent whereas the second mem ber Y is called the intent of the formal concept. Objects in X share all properties Y , and only properties Y are possessed by all objects in X . A basic r esult is that th e formal concepts of a formal context are always form ing the mathematical structure of a lattice with respect to the subconcept- superconcept relation. Ther efor e, the set of all formal concepts forms a complete lattice called a concept lattice [8]. The subconcept-superconcept r elation can be best depicted by a lattice diagram a nd we can derive concepts, implication sets, and associa tion rules based on the cross table. Now we present the cr oss table of the information table given in Table 1 in Table 2, where the rows are represented as objects and co lumns are represented as attributes. The relation betw een them is represented by a cross. The lattice diagram is presented in figure 1. Table 2 C ross table of the inform ation syste m Fig. 1 Lattice diagram of the information sy stem 6. Proposed Knowledge Mining Model In this section, we present proposed knowledge m ining model that consists of probl em definition, target data, preprocessed data, processed data, data classification, IJCSI Interna tional Journal of Com puter Scie nce Issue s, Vol. 8, Issue 2, Marc h 2011 ISSN (Online): 1694-0814 www.IJCSI.org 421 ordered inform ation table, knowledge, and computation of the chief attribute as shown in Figure 2. Problem definition and acquiring of prior knowledge ar e the fundamental steps of any model w hen the right problem is identified. The pattern of data elements or the usefulness of the individual data element change dramatically from individual to individual, orga nization to or ganization, or task to task because of th e acquisition of knowledge and reasoning may involve vague ness and incom pleteness. It’s difficult to obtain the useful inform ation that is hidden in the huge database by an individual. Therefore, it is essential to deal with incomp lete and vague infor mation in classification, concept formul ation, and data analysis present in the database. In th is model we use intuitionistic fuzzy proximity relation, ordering rules, and form al concept analysis to identify the chief attribute instead of only fuzzy proximity relation as discussed in [2] . In the preprocess we use intuitionistic fuzzy proxim ity relation as it provides better knowledge over fuzzy proximity relation as stated in [3]. Fi nally, formal concept analysis on these knowledge are inclined to explore better knowledge and to find out most impor tant factors affecting the decision making process. Fig. 2 Proposed knowledge mining m odel 7. Study on Ranking Institutions For demonstr ation of our model we take into consideration an information system of a group of institutions of any country where we study the ranking of institution and the parameters influencing the rank. In Table 3 below, w e specify the attribute descripti ons that influence the ranking of the institutions. The institutes can be judged by the outputs, which ar e produced. The quality of the output can be judged by the placement performance of the institute and is given highest weight with a scor e 385 which comes to around 24% of total weight. To pr oduce the quality output the input should be of high quality. The major inputs for an institute are in general intellectual capital and infrastructure facilities. A ccordingly the scores for intellectual capital and an infr astructure facility are fixed as 250 and 200 respectively that weight 15% and 12% of total weight. The student pl aced in the company shall serve the company up to their expectation and it leads to recruiter’s satisfaction and is given w ith a score of 200 which comes around 12%. At the same tim e students satisfaction and extra curricula r activities plays a vital r ole for prospective students is given with a score 60 and 80 respectively of weight 4% and 6% of the total w eight. We have not considered many other factor s that do not have impact on ranking the institutions and to m ake our analysis simple The membership and non- membership functions have been adjusted such that the sum of their values should lie in [0, 1] and also these functions m ust be symmetr ic. The first requirem ent necessitates a major of 2 in the denominators of the non-m embership functions. Table 3 Attribute descriptions ta ble We consider a small universe of 10 institutions and information related to it ar e given in the following Table 4. Table 4 Sm all universe of information sy stem Intuitionistic fuzzy proximity r elation 1 R corresponding to attribute ‘IC’ is given in Table 5. IJCSI Interna tional Journal of Com puter Scie nce Issue s, Vol. 8, Issue 2, Marc h 2011 ISSN (Online): 1694-0814 www.IJCSI.org 422 Table 5 Intuitionistic fuz zy proxim ity relation for a ttribute IC Intuitionistic fuzzy proximity r elation 2 R corresponding to attribute ‘IF’ is given in Table 6. Table 6 Intuitionistic fuz zy proxim ity relation for a ttribute IF Intuitionistic fuzzy proximity re lation 3 R corresponding to attribute ‘PP ’ is given in Table 7. Table 7 Intuitionistic fuz zy proxim ity relation for a ttribute PP Intuitionistic fuzzy proximity re lation 4 R corre sponding to attribute ‘RS’ is given in Table 8. Table 8. Intuitionistic fuzzy proxi mity re lation for attribute R S Intuitionistic fuzzy proximity re lation 5 R corresponding to the attribute ‘SS ’ is given in Table 9. Table 9 Intuitionistic fuz zy proxim ity relation for a ttribute SS Intuitionistic fuzzy proximity re lation 6 R corresponding to attribute ‘ECA’ is given in Table 10. Table 10 Intuitionistic fuz zy proxim ity relation for attribute ECA On considering the degree of dependency values 0.92   , 0. 08   for membership and non-m embership functions respectively we have obtained the following equivalence classes. IJCSI Interna tional Journal of Com puter Scie nce Issue s, Vol. 8, Issue 2, Marc h 2011 ISSN (Online): 1694-0814 www.IJCSI.org 423 , 1 2 34 56 7 89 1 0 1 , 1 23 456 7 89 1 0 2 , 1 2 43 567 8 9 1 0 3 , 1 23456789 1 0 4 , 1 5 / { { , , },{ , },{ , , } ,{ , } } / { { , , },{ , , },{ },{ , , }} / { { , , } ,{ , },{ },{ , , , } } /{ { , , , , , , , , , } } /{ { , UR i i i i i i i i i i UR i i i i i i i i i i UR i i i i i i i i i i UR i i i i i i i i i i UR i i           235 46789 1 0 , 15 2 3 4 6 7 8 91 0 6 ,, } , { ,, ,,} , { } } / { { , },{ } ,{ , },{ , },{ } ,{ , } } i i iiii i i U R i i ii ii ii i i   From the above analysis, it is clear that the attribute ECA classify the universe into six categories. Let it be low, average, good, very good, excellent, and outstanding and hence can be ordered. S imilarly, the attributes IC, IF, and PP classify the universe into four categories. Let it be low, moderate, high and ver y high and hence can be ordered. The attribute SS cla ssify the universe into three categories namely good, very good, and excellent. Since the equivalence class , 4 / UR   contains only one group, the universe is (, )   -indiscernible accordi ng to the attribute RS and hence do not require any ordering while extracting knowledge from the inform ation system. Therefore, the ordered inform ation table of the small universe Table 4 is given in Table 11. Table 11 Orde red informa tion table of the sma ll universe IC IF PP SS ECA : Ver y high High Moderate Low : Ver y high High Moderate Low : Ve ry high High Moderate Low : Exc ell ent Very good Good : Outstanding Excel lent Very good Good Av er age Poor                 Now, in or der to rank the institutions we assign weights to the attribute values. In order to compute the rank of the institutions ;1 , 2 , , 1 0 k ik   we add the weights of the attribute values and rank them according to the total sum obtained from highest to lowe st. However , it is identified that in some cases the total sum r emains same for certain institutions. It indicates that these institutions cannot be distinguished from one anothe r according to the available attributes and attribute values . In such cases, using further analysis techniques actual ranking of the institutes can also be found out. On considering the weights of outstanding, excellent, (very high, ver y good), (high, good), (moder ate, average) and ( low, poor) as 6, 5, 4, 3, 2 and 1 respectively the ordered information table for ranking the institutions is given in table 12. Table 12 Orde red Informa tion table for ra nking institution From the com putation given in Table 12 shows that the institution 1 i belongs to the first rank whereas 3 i and 5 i belongs to third rank. Sim ilarly, the ranks of the other institutions can also be obtained from the Table 12. In the second part of post process initially, we group the institutions based on their rank. S ince the difference of the total sum between the first three ranks is much less, w e combine these four institutions into a single cluster 1 for our further analysis. S imilarly, w e combine the institutions having rank 4, 5, and 6 as another cluster 2. The rest of the institutions are combined and is the final cluster 3 for our analysis. Formal concept analysis can do the data classification. However, data wa s already classified in this study. The purpose of this research is to use formal concept analysis to diagnose the relationship among attributes belonging to the different cluster s. Now we present the context table in Table 13 and in figur e 3, the lattice diagram for or der information Table 12. Table 13 C ontext table for order informa tion table IJCSI Interna tional Journal of Com puter Scie nce Issue s, Vol. 8, Issue 2, Marc h 2011 ISSN (Online): 1694-0814 www.IJCSI.org 424 Fig. 3 Lattic e diagra m for order inform ation table We generate the implication set for each cluster and are presented in Table 14. Further we find the chief attribute influencing each cluster of institutions by considering the highest frequency obtained in the subconcept superconcept table. For refer ence, we have presented implication relation Tables 15, 16, and 17 for cluster 1, 2, and 3 respectively. Table 14 Im plication se t for all the c lusters 1, 2, a nd 3 Table 15 Im plication re lation table for cluster 1 Table 16 Im plication re lation table for cluster 2 Table 17 Im plication re lation table for cluster 3 Those highest frequency superc oncepts expressed the most important inform ation. In par ticular, the chief attributes that influence cluster 1 are 11 A and 21 A as the frequency is high as obtained in the implication relation table 15. The next influencing factor in the same cluster is 31 A . It indicates that the institutions to be in cluster 1 must be having IC, IF, and PP as very high. Similarly, the influencing factors for cluster 2 obtained from implication table 16 are 13 A (IC mo derate), 64 A (ECA good), and 22 A (IF high). Finally, the chief factor s that influence cluster 3 obtained from im plication Table 17 are 14 A (IC low), and 66 A (ECA poor). 8. Conclusions Rough sets on intuitionistic fuzzy approximation spaces introduced in [1], which extends the ear lier notion of basic rough sets on fuzzy approximation spaces. Ordering of objects is a fundamental i ssue in decision making and plays a vital role in the design of intelligent inform ation systems. The main objective of this w ork is to expand the domain application of rough set on intuitionistic fuzzy approximation space with orde ring of objects and to find the chief factors that in fluence the ranking of the institutions. Our know ledge mi ning m odel depicts a layout for perform ing the ordering of objects using rough sets on intuitionistic fuzzy approximation spaces and the computation of the chief attri butes that influence the rank with formal concept analysis . We have taken a real life example of ranking 10 institutes according to different attributes. We have shown how analysis can be done by taking rough set on intuitionistic fuzzy approximation space with ordering rules and fo rmal concept analysis as a model for mining know ledge. References [1] B. K. Tripathy, “Rough sets on Intuitionistic Fuzzy Approximation Spaces”, Notes on Intuitionistic Fuzzy Sets, Vol. 12, No. 1, 2006, pp 45-54. [2] B. K. Tripathy, and D. P. Acharjya, “K nowledge mining using ordering rules and rough sets on fuzzy approximation spaces”, International Journal of Advances in Science and Technology, Vol. 1, No. 3, 2010, pp. 41-50. IJCSI Interna tional Journal of Com puter Scie nce Issue s, Vol. 8, Issue 2, Marc h 2011 ISSN (Online): 1694-0814 www.IJCSI.org 425 [3] D. P. Acharjya, “Compara tive Study of Rough Sets on fuzzy approximation spaces and Intuitionistic fuzzy approximation spaces ”, International Journal of Computational and A pplied Mathematics , Vol. 4, No. 2, 2009, pp. 95-106. [4] D. P. Acharjya, and B. K. Tripathy, “Rough sets on fuzzy approximation spaces and appli cations to di stributed knowledge systems”, International Jour nal of Artificial Intelligence and Soft Computing, Vol. 1, No. 1, 2008, pp. 1- 14. [5] D. P. Acharjya, and B. K. 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[12] Z. Pawlak, and A. Skow ron, “Rough sets and Boolean reasoning”, Information Sciences -An International Journal, Vol. 177, No. 1, 2007, pp. 41–73. [13] Z. Pawlak, and A. Skowr on, “Rudiments of rough sets”, Information Sciences-An Interna tional Journal, Vol. 177, No. 1, 2007, pp. 3–27. [14] Z. Pawlak, and A. Skowron, “Rough sets: Some extensions”, Information Sciences- An Inte rnational Journal, Vol. 177, No. 1, 2007, pp. 28–40. [15] Z. Pawlak, Rough Sets: Theo retical Aspects of Reasoning about Data, Dordrecht, Neth erlands: Kluwer Academic Publishers, 1991. D. P. Acharjy a received the degree M. Sc. From NIT, Rourkela, India in 1989; M. Phil. from Berhampur University, India in 1994; and M. Tech. degree in computer science from Utkal University, India in 2002. He has been awarded with Gold Medal in M. Sc. He is an associate Professor in School of Computing Scienc es and Engineering at VIT University, Vellore, Tamilnadu, India. He has authored many international and national journal papers to his credit. He has also published three books; Fundamental Approach to Discrete Mathematics, Computer Based on Mathematics, and Theory of Computation; to his credi t. His research interest includes rough sets, knowledge representation, granular computing, mobile ad-hoc network, and business intelligence. Mr. Acharjya is associated with many professional bodies CSI, ISTE, IMS, AMTI, ISIAM, OITS, IACSIT, IEEE, IAENG, and CSTA. He is the founder secretary of OITS, Rourkela chapter. L. Ezhilarasi received the M.C.A from Bharathidasan University , Tr ichy , India in 2000. She is a M. T ech. (CSE) final year student of VIT University , Ve llore, India. She has keen interest in teaching and research. Her research interest includes rough sets, fuzzy sets, granular computing, formal concepts, computer graphics and knowledge mining. She is associated with the professional society IRSS.