WOFEX 03’ Using Modified Concept Lattices for Organizational Structure Modeling and Analysis Ivo Vondrak Jan Kozusznik Dept. of Computer Science VSB-Technical University of Ostrava Czech Republic

WOFEX 03’ Business Modeling Business Process Modeling Data/Object Modeling Organizational Structure Modeling – There is no view capturing organization structure of roles implemented by human resources participating in processes being modeled.

WOFEX 03’ Business Processes

WOFEX 03’ Table of Responsibilities RegClassChck.iChck.hPhonDecPaySend Manager X X XX Claim handler XXXX Accountant XXXXX Assistant XXX Secretary XXXX

WOFEX 03’ Organizational structure creating Re g ClassChck.iChck.hPhoneDe c PaySendManager X X XX Claim handler XXXX Accountant XXXXX Assistant XXX Secretary XXXX

WOFEX 03’ Concept Analysis Concept analysis theory can be used for grouping of objects that have common attributes. Context is a binary relation T between a set of objects O and set of attributes A. It means that T  O  A For any set of objects O  O, their set of common attributes is defined as  (O) = { a  A |  o  O : (o,a)  T } For any set of attributes A  A, their set of common objects is defined as  (A) = { o  O |  a  A : (o,a)  T } A pair (O,A) is called a concept if A =  (O) and in the same time O =  (A).

WOFEX 03’ Informal Description RegClassChck.iChck.hPhonDecPaySen d Manager X X XX Claim handler XXXX Accountant XXXXX Assistant XXX Secretary XXXX Concepts Context The tables of competencies correspond with Boolean tables(context). Objects of the relation are substituted by roles and attributes of objects are substituted by activities that the roles are responsible for.

WOFEX 03’ Concept Lattice  The very important property is that all concepts of a given table form a partial order via (O 1,A 1 )  (O 2,A 2 )  O 1  O 2 (equivalent to A 1  A 2 )  It was proven that such set of concepts constitutes a complete lattice called concept lattice L(T)  Visualization of concept lattice –Graph nodes represent concepts and arcs their ordering –The top-most node is a concept with the biggest number of objects (roles) –Concept node is labeled with an activity if it is the largest concept that contains this activity –Concept node is labeled with role if it is the smallest concept that contains this role

WOFEX 03’ Visualization concept lattice provides alternate views on the information contained in the above-described table - it enables to visualize the structure “hidden” in the binary relation. Obviously, the more complex is the table of responsibilities the more difficult is to understand who is responsible for what.

WOFEX 03’ Roles Related to the Activity In concept lattice we can find who can be responsible for selected activity.

WOFEX 03’ Activities Related to the Role we can easy find what activities is selected role responsible for.

WOFEX 03’ The question is how to evaluate identified concept from point of view if they should or should not be the source of organizational units? Is it appropriate to put together these roles with the common set of activities or not? Organizational Units The nodes of concept lattice can be considered as a potential source of how the organizational units can be defined. An unit related to administrative operations

WOFEX 03’ Let’s introduce the new notion of Knowledge Diversity that reflects the width of knowledge required by the concept Knowledge Sharing and Diversity Knowledge sharing - K share : A  A -> K share (a i, a j ) = 1 for activities a i and a j that share the same common knowledge, K share (a i, a j ) = 0 if no knowledge is shared. K share (a i, a j ) = 1 for i=j. Knowledge diversity – K div : {(O,A)} -> where K div (O,A) = 1 -  K share (a i, a j )/ | A | 2. a  A we would like to have in one organizational unit activities that have something in common - we would call it Knowledge Sharing

WOFEX 03’ Reg. Clas.Chck.i.Chck.h. Phone.Dec.Pay.Send. Reg. 11 Clas. 11 Chck.i. 11 Chck.h 11 Phone. 111 Dec. 11 Pay. 11 Send. 111 Based on Knowledge sharing definition a Table of the knowledge sharing among activities can be defined. K share definition

WOFEX 03’ Visualization of K div Concept of Low Knowledge Diversity Concept of High Knowledge Diversity The higher is the knowledge diversity the darker is the node representing the concept.

WOFEX 03’ Organizational structure construction

WOFEX 03’ Result organizational structure

WOFEX 03’ Conclusion Presented method of concept analysis provides exact and formally well defined way how the organizational structure can be analyzed and constructed future research: – searching for easy and precision way of knowledge sharing definition – searching for some better visualisation of concept lattice – define exact strategy for organize structure construction from concept lattice