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

Outline

• Research Background• Methods• Discussion• Outlook

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

User interfaces (CNC and other machines)

•Large - small, •Many colors, •Buttons, (types of buttons)•Acoustic and optical signals/support,•Consultation with trained staff

In order to abstract from subjectivisms, introduction of indicators

Set of user interfaces

User interfaces described byIndicators

Requirement:An idea of orientation: What is good, what isbad

Table (or „evaluation matrix“)

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-indicatorsystem, and the first job is to order them

The general strategy…

Interviews, Tests The set of user interfaces Partial Order

Interpretation of itsstructure

Modification of MISExtension/Reduction/Reorientation

Main Task:

IdentificationOf optimal andSuboptimal elements(for example to take into regardeconomical restrictions)

Suppose:4 user interfacesof main interestDescribed by fourindicators

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!

Skill profiles, FP, of (groups) ofmentally 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, hapticalabstraction level etc.)

Our indicators (user interfaces and skill profiles)

2) Probable:Linguistic, qualitative, but:Any indicator should define a linear or weak order.

a*b+c*d1) Probably not fulfilled:The axioms of an algebraic field

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 profilesof skill, described by 3 indicators of person‘s abilities

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:

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)

Matching Matrix M

M =

F1 F2 F3

I1 1 0 0I2 0 1 0I3 0 1 1I4 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 2Indicatortypes 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

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 = 0G(r,s,i,j) = (Ir,i,Fs,j) if Mi,j = 1

?

Formally

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‘

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.

Example:Indicator values of user interfaces: BM-matrix:

3300130121212112

BM

Indicator values of skill profiles: FM-matrix

100010001

FM

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

Copeland-Indexcombination 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).

With help of M and the data given before…

B1,…,Br

FP1,…..FPrFFP1 FP2 FP3

B1 B2 B3 B4

r = 4

rF = 3

Discussion

•The defined interaction of M with the two matrices describinguser 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)

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

Thank you for attention!

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 ContentAims

Project Partner and ParticipantsCVJM-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

Research Methods

ExpertInterviews Production

and factory supervisors, team leaders

Employees with intellectual disabilities

Goal-orientedWorkshops with trainedstaff andemployees with intellectualdisabilities Creative

Laboratory Tablet-

Usability-Test Design

Thinking

ParticipativeObservation Work flows

Follow-up Project

Prototype Development

Requirements Analysis Development

2015–2017March March April–September

1.1.2014 31.12.2014

Possibilities

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".

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