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Measuring the fitness relationship

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Abstract

It is widely acknowledged that the system functionality captured in a system model has to match organisational requirements available in the business model. However, such a matching is rarely used to support design strategies. We believe that appropriate measures of what we refer to as the fitness relationship can facilitate design decisions. The paper proposes criteria and associated generic metrics to quantify to which extent there is a fit between the business and the system which supports it. In order to formulate metrics independent of specific formalisms to express the system and the business models, we base our proposal on the use of ontologies. This also contributes to provide a theoretical foundation to our proposal. In order to illustrate the use of the proposed generic metrics we show in the paper, how to derive a set of specific metrics from the generic ones and we illustrate the use of the specific metrics in a case study.

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Notes

  1. If S is a set of elements, card(S) refers to the cardinality of S and corresponds to the number of elements contained in S.

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Acknowledgments

Sincere thanks are to the anonymous reviewers who provided constructive criticism that has made improvements possible.

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Correspondence to Anne Etien.

Appendix

Appendix

Criterion

Metrics

Data

Support ratio (Sr)

Number of activies represented by system events/Number of activies

Sr=card(A 2 b )/card(a b )

- A b be the set business activies

- E r be the set of system events

- A r b be the set of business activities represented by a system event;

\(A_{b}^{r} = \{a, a \in A_{b} | \exists e \in E_{r} \wedge e \Re a\}\)

Goal satisfaction (Gs)

Number of goals for which each state maps a state in the system/Number of business goals

Gs = card (G) b m/card (G b )

- G b be the set of business goals

- S b be the set of business states

- S r be the set of states of the system

G b m be the set of business goals supported by the system

\(G_{b}^{m} = \{g \in G_{b} | \forall s, s \in S_{b} \wedge s \in g \Rightarrow \exists s' \in S_s \wedge s {\mathcal M} s'\}\)

Actor presence (Ap)

Number of business actors mapping asystem class/Number of business actors

Ap = card(Ac b m)/card(Ac b )

- Ac−b be the set of business actors

- C s be the of system classes

- Ac b m, be the set of business actors mapping a system class that triggers a stste transition on another system class.

\(Ac_{b}^{m} =\{a, a \in A \infty | \exists c, c' \in C_{s} \wedge s \in c \wedge s' \in c' \wedge < s,s'> \wedge a {\mathcal M} c\}\)

Resource presence (Rp)

Number of business resource maping asystem class/Number of business resources

Rp = card (R m b )/card (R b )

- R b be the set of business resources

- L s be the set of system laws

- R m b , be the set of business resource mapping a system class for which there does not exist a stste change.

\(R_{b}^{m} = {r, r \in R_{b} | \exists c \in C_{s} \wedge \forall s \in S_{s} \wedge s \in c \wedge \forall l \in L_{s} \wedge l(s) = s \wedge r {\mathcal M} c}\)

Informational completeness

Number of business class mapping system classes/Number of business classes

Ic = card (T b m)/card (T b )

- C b is the set of business classes

- C b m is the set of business classes mapping a system class

\(C_{b}^{m}\{c, c \in C_{b} | \exists c' \in C_{s} \wedge c {\mathcal M} c'\}\)

Informational accuracy (Ia)

Number of business states mapping system states/Number of business states

card (S b m)/card (S b )

- S b m be the set of business states mapping a system states:

\(S_{b}^{m} = \{s, s \in S_{b} | \exists s' \in S_{s} \wedge s {\mathcal M} s'\}\)

Activity completeness (Ac)

Number of business classes mapping classes/Number of business classes

Ac = card (T m a )/card(T a )

- C a be the set of business classes involved in a business activity a and

- C m a the set of business classes involved in a business activity a and mapping a system class.

\(C_a^m=\{c,c\in C_a|\exists c^\prime\in C_s\wedge c {\mathcal M} c^\prime\}\)

Activity Accuracy (Aa)

Number of business ststes mapping system states/Number of business states

Aa = card (S a m)/card (S a )

- Sa be the set of business states involved in a business activity a,

- S a m be the set of business states involved in a business activity a and for which there is a maping with a system states.

\(S_a^m=\{s,s\in S_a|\exists s^\prime\in S_s\wedge s {\mathcal M} s^\prime\}\)

System Reliability (Sre)

Number of business laws for which each business states maps a system states and the transformation between business states are possible between system states/Number of business laws

Sre = card (L b m)/card (L b )

- L b be the set of business laws

- l r be the set of system laws

- L b m be the set of business laws mapping asystem laws

\(L_b^m=\{l,l\in L_b|\exists l^\prime\in L_s\wedge l {\mathcal M} l^\prime\)

Dynamic realism (Dr)

Number of paths for which each business state map a system states and the succession of these states is possible/Number of possible paths

Dr = card (P b m)/card (P b )

- P b is the set of paths

- P b m the set of paths supported by the system

\(P_b^m=\{p,p\in P_b\wedge p=< s_1 \ldots s_n>\wedge \forall i,\quad s_i\in S_b\wedge s_i \neq s_i\wedge \exists l\in L_s\wedge s_{k+1}=l(S_k)|\exists l^\prime \in L_s\wedge l {\mathcal M}l^\prime\wedge \forall i,\exists s^\prime_m\in S_s\wedge s_i{\mathcal M}s_m^\prime\}\)l

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Etien, A., Rolland, C. Measuring the fitness relationship. Requirements Eng 10, 184–197 (2005). https://doi.org/10.1007/s00766-005-0003-8

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