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- 1. A matching problem, partial order and an analysis applying Copeland index R. Bruggemann1), D. Edich2) , F. Fuhrmann2) , P. Koppatz2), M. Scholl2), A. Teske2), A. Wiesner-Steiner2) 1) Leibniz-Institut für Gewässerökologie und Binnenfischerei, Abteilung Ökohydrologie 2) Technische Hochschule (TH) Wildau, Fachbereich Wirtschaft, Informatik, Recht (WIR) Flor_iBaMs5.ppt: brg 19.6.2014 – 3.4.2015
- 2. Outline • Research Background • Methods • Discussion • Outlook
- 3. Research Background • The demand on persons working on CNC- machines, in services is increasing • It is a social and economic need to integrate persons with intellectual disabilities • How can this integration be done? – Social component – Motivation – Economical boundary conditions
- 4. User interfaces (CNC and other machines) •Large - small, •Many colors, •Buttons, (types of buttons) •Acoustic and optical signals/support, •Consultation with trained staff
- 5. In order to abstract from subjectivisms, introduction of indicators Set of user interfaces User interfaces described by Indicators Requirement: An idea of orientation: What is good, what is bad Table (or „evaluation matrix“)
- 6. Evaluation matrix User I.Indicator I1 I2 … Im B1 I11 I12 … I1m B2 I21 I22 … I2m …. Br Ir1 Ir2 …Irm Indicator t y p e s User Interfaces are described by a MIS, i.e. a multi-indicator system, and the first job is to order them
- 7. The general strategy… Interviews, Tests The set of user interfaces Partial Order Interpretation of its structure Modification of MIS Extension/Reduction/ Reorientation
- 8. Main Task: Identification Of optimal and Suboptimal elements (for example to take into regard economical restrictions) Suppose: 4 user interfaces of main interest Described by four indicators What else?? How can we help persons with Intellectual disabilities? Selection of user interfaces of interest is only the first step. Still missing: A mapping from the set of user interfaces to the skill profiles of the users!
- 9. Skill profiles, FP, of (groups) of mentally disabled persons Interviews, Tests, DIN ISO-norm, Administrative classifications Skill profiles/ Indicators F1 F2 …FmF FP1 F11 F12 …F1mF FP2 F21 F22 …F2mF …. FPrF FrF1 FrF2 …FrF,mF F1,F2,…,FmF are the indicators describing different abilities of the users (optical, acustical, haptical abstraction level etc.)
- 10. Our indicators (user interfaces and skill profiles) 2) Probable: Linguistic, qualitative, but: Any indicator should define a linear or weak order. a*b+c*d 1) Probably not fulfilled: The axioms of an algebraic field
- 11. Most general matching FP1 FP2 FP3 B1 B2 B3 B4 All skill profiles Are combined with all user interfaces A reminder: we assumed 4 user interfaces. Now here we assume: 3 profiles of skill, described by 3 indicators of person‘s abilities
- 12. Most simple solution of the matching problem: If (!!) indicators would obey the axioms of an algebraic field: Search of the optimum of a goal function: G(r,s) = wij Ir,i*Fs,j Optimum wij are weights. This is, however, in general not allowed!….. Hence:
- 13. Coupling of indicator types Which indikator t y p Ii corresponds best to Indicator t y p Fj F1 F2 … FmF Ii fits does not fit don‘t know „Don‘t know“: here the fuzzy poset concept may be helpful. However actually only: fits? (yes/no)
- 14. Matching Matrix M M = F1 F2 F3 I1 1 0 0 I2 0 1 0 I3 0 1 1 I4 1 1 0 r = 4, m = 4, rF = 3, mF = 3 The meaning of the entries of M: Indicatortype 1 fits with skill profile type 1, but not with the other two. Indicatortype 2 fits only with skill profile indicator 2 Indicatortypes 3 and 4 correspond best with F1 and F2. …describes the bidirectional mapping of indikator t y p e s of user interfaces B1,…,Br and of the skill profiles FP1,…,FPrF. M must be empirically determined, for example by the team of the project iBaMs
- 15. The optimization: G(r,s) = wij Ir,i*Fs,j G(r,s,i,j) = (Ir,i,Mi,j,Fs,j) One possible rule: G(r,s,i,j) = (0, 0) if Mi,j = 0 G(r,s,i,j) = (Ir,i,Fs,j) if Mi,j = 1 ? Formally
- 16. The G(r,s)-Matrix G(1,1) = (a,b), (a,c),……… G(1,2) = (x,y), (x,w),……… …………………………………… G(1,1) = a b a c …… G(1,2) = x y y w ….. ………………………….. User interf. B1 combined with FP1 User interf. B1 combined with FP2 ….. Notation: Notation: (1)we call an element of the tuple of G(r,s) a component of G(r,s), indexed by j. i.e. cj (r,s) (2) n(j,r,s) = count of cj(r,s) > cj(r‘,s‘) for all r‘,s‘
- 17. The mathematical background: tournament theory In the project iBaMs just a pragmatic approach: Copeland-Index (C(r,s)): How often wins G(r,s) over G(r‘,s‘). When we are lucky… G(r,s) C(r,s) = (win- loss) ….sufficiently sharp C(r,s) : Ranking Index to find the best Br,FPs-combinations.
- 18. Example: Indicator values of user interfaces: BM-matrix: 3300 1301 2121 2112 BM Indicator values of skill profiles: FM-matrix 100 010 001 FM
- 19. G-matrix, based on the example: 2.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 1.0 0.0 2.0 1.0 2.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0 0.0 2.0 0.0 2.0 1.0 0.0 0.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 1.0 1.0 2.0 0.0 2.0 0.0 0.0 0.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 1.0 0.0 2.0 1.0 2.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0 1.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0 0.0 2.0 0.0 2.0 1.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 1.0 1.0 2.0 0.0 2.0 0.0 0.0 0.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.0 0.0 3.0 0.0 1.0 1.0 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 3.0 1.0 3.0 0.0 1.0 0.0 1.0 1.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.0 0.0 3.0 1.0 1.0 0.0 1.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.0 0.0 3.0 0.0 3.0 1.0 3.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 3.0 1.0 3.0 0.0 3.0 0.0 3.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.0 0.0 3.0 1.0 3.0 0.0 3.0 0.0 0.0 0.0 B1FP1 … … … … … …. … BrFPFr
- 20. Copeland-Index combination Copeland B1FP1 0 B1FP2 12 B1FP3 -12 B2FP1 -3 B2FP2 9 B2FP3 -15 B3FP1 -12 B3FP2 0 B3FP3 -24 B4FP1 15 B4FP2 27 B4FP3 3 (B4,FP2) >>(B4,FP1) >( B1,FP2) > (B2,FP2) > (B4,FP3) > (B1,FP1) (B3,FP2) > (B2,FP1) > (B1,FP3) (B3,FP1) > (B2,FP3) > (B3,FP3).
- 21. With help of M and the data given before… B1,…,Br FP1,…..FPrF FP1 FP2 FP3 B1 B2 B3 B4 r = 4 rF = 3
- 22. Discussion •The defined interaction of M with the two matrices describing user interfaces and skill profiles may be too crude. •The extension to fuzzy approaches is urgently needed. •Instead of Copeland, other evaluation methods ! •Need of exploration of formal properties of the G-matrix, for example: B1 < B2 implies (FP fixed): G(1,..) G(2,…) FP1 < FP2 implies (fixed B): G(..,1) G(..,2)
- 23. Outlook • Development of control panel prototypes does not depend on the randomness of the user group, but rather creates a generalized basis • Demonstration of the general applicability of PyHasse modeling for the selection of an optimal control panel under consideration of its economic efficiency • PyHasse modeling will be applied in future projects for selecting the optimal prototype concept • Statements regarding efficiency can be expressed not only for one, but for a variety of display solutions
- 25. iBaMs Goals Raising work life involvement level Expand the range of tasks and responsibility Achieve a high level of motivation Increase efficiency of the work site Identify skill profiles and indicators that characterize control panels Solution of the matching problem by means of the Copeland approach The project iBaMs – Barrier- Reduced Machines in innovative Interaction examines the preconditions and requirements for the development of disabled- accessible control panels for computer-controlled machines. Project Content Aims
- 26. Project Partner and Participants CVJM-Sozialwerk Wesermarsch e. V. 380 employees with disabilities 70 trained staff Involvement of production and factory supervisors as well as team leaders Participants 1 female, 5 males, aged 28–60 Work flows: metal processing, carpentry, large-scale catering establishment Experience with the machinery and work process Eager, curious, motivated to learn Various skill levels and limitations
- 27. Research Methods Expert Interviews Production and factory supervisors, team leaders Employees with intellectual disabilities Goal-oriented Workshops with trained staff and employees with intellectual disabilities Creative Laboratory Tablet- Usability-Test Design Thinking Participative Observation Work flows Follow-up Project Prototype Development Requirements Analysis Development 2015–2017March March April–September 1.1.2014 31.12.2014
- 28. Possibilities
- 29. Heterarchy • Holistic understanding of technology: not a neutral representations of their surrounding organizational structures, but rather an effective tool of behavioral control • Lawrence Lessig’s thesis “code of law” • Technologies can be used to render existing procedures and processes more efficient and to advance communication and processes or restrict them • According to control-theorists Wilke, heterarchy is a "coequal, self-organized and decentralized coordination".
- 30. Hasse diagrams fit well into the framework of heterarchy • Neither linear nor do they have the structure of graph- theoretic trees • Considerably more flexible than hierarchical structures and more suited to meet the demands required by heterarchical structures • Identify optimal as well as suboptimal control panels • Optimal control panels, a result by analysis of partially ordered sets
Notes de l'éditeur
- By means of these extended skill profiles, we have demonstrated the general applicability of PyHasse modeling for the selection of an optimal control panel under consideration of its economic efficiency. Furthermore, the program has been expanded in PyHassePro or PyHasse-Inet. It is planned that PyHasse modeling be applied in future projects for selecting the optimal prototype concept, becausecontrol panels can be ranked mathematically in a heterarchy by the analysis of partial orderings. In this way, statements regarding efficiency can be expressed not only for one, but for a variety of display solutions [18 ] .
- The employment of people with intellectual disabilities is increasingly significant in today’s working environment. The goal of the TH Wildau’s project iBaMs (Barrier-Reduced Machines in Innovative Interaction), funded by the BMBF (Federal Ministry of Education and Research), is to improve the control panels of computer-controlled machines (e.g. CNC machines or automatic machines of large-scale catering establishments) so that the efficiency of work can/may be increased. This project also aims to achieve a high level of motivation and an expanded range of tasks and responsibilities.. To provide the transferability to other people, other employers and a wide range of users, indicators will be identified and introduced that characterize the control panels. Once the optimal control panels have been found, it is essential to find the best solution for the allocation of user’s abilities/skills (user profiles) to the optimal control panels that are characterized by indicators.This matching problem will be discussed in this paper and a pragmatic solution will be explained by means of the Copeland approach. There are two long-term aims we are pursuing with iBaMs: Firstly, we intend to raise the involvement level of employees with intellectual disabilities in working life. That means the control panel that should be developed in the intended more extensive follow-up project should serve as an assistive learning technology which enables employees to perform more demanding task on CNC machines. If the employees can more easily operate the machines, then the team leaders, who are at the moment performing a lot of tasks on the machines like setting up and starting them, can have relief from some tasks so they can perform other more demanding ones, for example further educating employees.. So, in the end the efficiency of the facilities should increase. However, before a control panel that can realize these goals in the long-run can be developed, the one-year iBaMs project is aimed at identifying skill levels of the employees and with their help to ascertain appropriate design requirements for control panels.
- To achieve these aims we were working together with CVJM-Sozialwerk Wesermarsch e.V. - a facility that employs 380 employees with intellectual disabilities. Our partner was very committed to the project - which can be seen in the involvement of the production and factory supervisors as well as team leaders in the research process. To explore the user`s perspective six employees were also involved in the research process. This team of participants consisted of one woman and five men who are between 28 and 60 years old. They work on three different shop floors: metal processing, large-scale catering establishment and carpentry They were selected by their team leaders because of their experience with the machinery. Furthermore we have gotten to know them as eager, curious and motivated to learn new things. All of them show and say that they would like to take on more responsibility and perform more demanding tasks. And as we have already discovered in our work with the team they possess both various skill levels and limitations.
- We started by conducting interviews with the trained staff and the employees who are involved in the research process. Parallel to the interviews we observed the work flow in the facility. The first two workshops were aimed at exploring the user’s perspective and skill profiles. Participants of the Design Thinking workshop are the project team, the trained staff of our partner and external independent persons. The aim of this Design Thinking workshop was to reflect the results regarding the user perspective and skill profiles we received from the interviews and workshops. It is important to include at that point not involved persons in order to gain a view from the outside. Furthermore, we discussed how a control panel can be best designed to meet the user’s requirements and skills. The iBaMs project was scheduled for one year and was intended to prepare for a three year follow-up project in which the specifics of control panels can be developed.
- The explicit reference to heterarchy corresponds to our holistic understanding of technology. This understanding implies that technology and software systems are not neutral representations of their surrounding organizational structures, but rather an effective tool of behavioral control. The American jurist Lawrence Lessig already confirmed this relationship with his thesis "code is law" in 1999 [xx]. For that reason, technologies can be used not only to render existing procedures and processes more efficient, but rather they can also be used to advance communication and processes or to restrict them. According to the control-theorists Wilke [xxxx. 89 f], heterarchy is a "coequal, self-organized and decentralized coordination". With this in mind, the Hasse diagrams and the method used (provide) an elegant way to allow greater flexibility in finding results by means of indicators.
- Hasse diagrams are generally neither linear nor do they have the structure of graph-theoretic trees (as in strictly hierarchical structures). For this reason, they are considerably more flexible than hierarchical structures and are more suited to meet the demands required by heterarchical structures[4]. In the context of the iBaMs project it is crucial that optimal control panels are identified and, if surrounding conditions require this, that suboptimal control panels can be identified as well. According to the language of the theory, optimal control panels are partially ordered sets [ 2], so called maximal elements. As a result, these can be chosen as candidates for the allocation to user skill profiles.