From 1479a99c47a4d5183246fcc8c0922609a240818e Mon Sep 17 00:00:00 2001 From: NotXia <35894453+NotXia@users.noreply.github.com> Date: Sun, 24 Dec 2023 13:48:13 +0100 Subject: [PATCH] Add FAIKR2 business process management --- .../module2/img/alpha_algorithm_example.png | Bin 0 -> 32021 bytes .../module2/img/bp_control_flow_loop.png | Bin 0 -> 38083 bytes .../img/bp_control_flow_n_out_of_m_join.png | Bin 0 -> 16352 bytes .../module2/img/bp_control_flow_or_split.png | Bin 0 -> 19755 bytes .../img/bp_control_flow_parallel_join.png | Bin 0 -> 18300 bytes .../img/bp_control_flow_parallel_split.png | Bin 0 -> 12747 bytes .../module2/img/bp_control_flow_sequence.png | Bin 0 -> 47985 bytes .../module2/img/bp_control_flow_xor_join.png | Bin 0 -> 20278 bytes .../module2/img/bp_control_flow_xor_split.png | Bin 0 -> 20744 bytes .../module2/img/bpmn_data.png | Bin 0 -> 396908 bytes .../module2/img/bpmn_example1.png | Bin 0 -> 220457 bytes .../module2/img/declare_chained_response.png | Bin 0 -> 14190 bytes .../module2/img/declare_negated_response.png | Bin 0 -> 16409 bytes .../module2/img/declare_precedence.png | Bin 0 -> 13307 bytes .../module2/img/declare_response.png | Bin 0 -> 13316 bytes .../module2/img/declare_unary_constraint.png | Bin 0 -> 18538 bytes .../module2/img/flower_petri.png | Bin 0 -> 38719 bytes .../module2/img/petri_net_example1.png | Bin 0 -> 184337 bytes .../img/process_mining_conformance.png | Bin 0 -> 87477 bytes .../module2/img/process_mining_discovery.png | Bin 0 -> 55467 bytes .../img/process_mining_enhancement.png | Bin 0 -> 76697 bytes .../module2/img/workflow_nets_example1.png | Bin 0 -> 58077 bytes .../img/workflow_nets_external_trigger.png | Bin 0 -> 2825 bytes .../img/workflow_nets_time_trigger.png | Bin 0 -> 3777 bytes .../module2/img/workflow_nets_transitions.png | Bin 0 -> 143171 bytes .../img/workflow_nets_user_trigger.png | Bin 0 -> 2732 bytes .../module2/main.tex | 2 + .../module2/sections/_business_process.tex | 652 ++++++++++++++++++ 28 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src/fundamentals-of-ai-and-kr/module2/img/bpmn_example1.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/declare_chained_response.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/declare_negated_response.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/declare_precedence.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/declare_response.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/declare_unary_constraint.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/flower_petri.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/petri_net_example1.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/process_mining_conformance.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/process_mining_discovery.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/process_mining_enhancement.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/workflow_nets_example1.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/workflow_nets_external_trigger.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/workflow_nets_time_trigger.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/workflow_nets_transitions.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/img/workflow_nets_user_trigger.png create mode 100644 src/fundamentals-of-ai-and-kr/module2/sections/_business_process.tex diff --git a/src/fundamentals-of-ai-and-kr/module2/img/alpha_algorithm_example.png b/src/fundamentals-of-ai-and-kr/module2/img/alpha_algorithm_example.png new file mode 100644 index 0000000000000000000000000000000000000000..91fc808ee3a79ee33fb3e4f180fcaa4503534d57 GIT binary patch literal 32021 zcmdRW^nD2vZP3NH!Ka3N+YEpAl)hmNK1pT)Y8(OE4lR2-AH#g`@QSu z^TZF&Kk&R>D(u~R@0l}a&YYR|yvH9JY6`g66xa_QJirAj%4$7$fTsT7!NX|GC%_ex 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\rightarrow_L b$ iff $a >_L b$ and $b \cancel{>}_L\, a$. + \item[$\#_L$)] $a \# b$ iff $a \cancel{>}_L\, b$ and $b \cancel{>}_L\, a$. + \item[$\Vert_L$)] $a \Vert_L b$ iff $a >_L b$ and $b >_L a$. + \end{descriptionlist} + + $\alpha$-algorithm works as follows: + \begin{enumerate} + \item Look for the relations in the event log. + \item Focus on the most interesting relations and identify the biggest set of involved activities. + \item Remove redundancies. + \item Represent them as a Petri net. + \end{enumerate} + + \begin{example} + Given the event log $L = \{ \langle \texttt{abcd} \rangle, \langle \texttt{abcd} \rangle, + \langle \texttt{abcd} \rangle, \langle \texttt{acbd} \rangle, \langle \texttt{acbd} \rangle, \langle \texttt{aed} \rangle \}$, + we want to apply the $\alpha$-algorithm: + \begin{enumerate} + \item We determine the relations: + \[ + \begin{split} + >_{L_1} &= \{ (\texttt{a}, \texttt{b}), (\texttt{a}, \texttt{c}), (\texttt{a}, \texttt{e}), (\texttt{b}, \texttt{c}), + (\texttt{c}, \texttt{b}), (\texttt{b}, \texttt{d}), (\texttt{c}, \texttt{d}), (\texttt{e}, \texttt{d}) \} \\ + \rightarrow_{L_1} &= \{ (\texttt{a}, \texttt{b}), (\texttt{a}, \texttt{c}), (\texttt{a}, \texttt{e}), + (\texttt{b}, \texttt{d}), (\texttt{c}, \texttt{d}), (\texttt{e}, \texttt{d}) \} \\ + \#_{L_1} &= \{ (\texttt{a}, \texttt{a}), (\texttt{a}, \texttt{d}), (\texttt{b}, \texttt{b}), (\texttt{b}, \texttt{e}), (\texttt{c}, \texttt{c}), + (\texttt{c}, \texttt{e}), (\texttt{d}, \texttt{a}), (\texttt{d}, \texttt{d}), (\texttt{e}, \texttt{b}), (\texttt{e}, \texttt{c}), (\texttt{e}, \texttt{e}) \} \\ + \Vert_{L_1} &= \{ (\texttt{b}, \texttt{c}), (\texttt{c}, \texttt{b}) \} + \end{split} + \] + And construct the footprint matrix: + \begin{center} + \begin{tabular}{c | c c c c c} + & \texttt{a} & \texttt{b} & \texttt{c} & \texttt{d} & \texttt{e} \\ + \hline + \texttt{a} & $\#_{L_1}$ & $\rightarrow_{L_1}$ & $\rightarrow_{L_1}$ & $\#_{L_1}$ & $\rightarrow_{L_1}$ \\ + \texttt{b} & $\leftarrow_{L_1}$ & $\#_{L_1}$ & $\Vert_{L_1}$ & $\rightarrow_{L_1}$ & $\#_{L_1}$ \\ + \texttt{c} & $\leftarrow_{L_1}$ & $\Vert_{L_1}$ & $\#_{L_1}$ & $\rightarrow_{L_1}$ & $\#_{L_1}$ \\ + \texttt{d} & $\#_{L_1}$ & $\leftarrow_{L_1}$ & $\leftarrow_{L_1}$ & $\#_{L_1}$ & $\leftarrow_{L_1}$ \\ + \texttt{e} & $\leftarrow_{L_1}$ & $\#_{L_1}$ & $\#_{L_1}$ & $\rightarrow_{L_1}$ & $\#_{L_1}$ \\ + \end{tabular} + \end{center} + + \item We determine the interesting relations as the pair of sets $(P, Q)$ of activities such that: + \[ \forall p \in P, q \in Q: (p \rightarrow q) \land (p \# p) \land (q \# q) \] + + This can be algorithmically done by building a footprint table whose rows and columns allow to obtain all the combinations of the activities. + Therefore, the set of interesting relations is: + \[ + \begin{split} + X_{L_1} = \{ + (\{\texttt{a}\}, \{\texttt{b}\}), (\{\texttt{a}\}, \{\texttt{c}\}), (\{\texttt{a}\}, \{\texttt{e}\}), + (\{\texttt{a}\}, \{\texttt{b}, \texttt{e}\}), (\{\texttt{a}\}, \{\texttt{c}, \texttt{e}\}), \\ + (\{\texttt{b}\}, \{\texttt{d}\}), (\{\texttt{c}\}, \{\texttt{d}\}), (\{\texttt{e}\}, \{\texttt{d}\}), + (\{\texttt{b}, \texttt{e}\}, \{\texttt{d}\}), (\{\texttt{c}, \texttt{e}\}, \{\texttt{d}\}) + \} + \end{split} + \] + + \item Then, we remove the redundancies in the set of interesting relations $X_{L_1}$: + \[ Y_{L_1} = \{ (\{\texttt{a}\}, \{\texttt{b}, \texttt{e}\}), (\{\texttt{a}\}, \{\texttt{c}, \texttt{e}\}), + (\{\texttt{b}, \texttt{e}\}, \{\texttt{d}\}), (\{\texttt{c}, \texttt{e}\}, \{\texttt{d}\}) \} \] + It can be seen that all the relations in $X_{L_1}$ can be derived from $Y_{L_1} \subset X_{L_1}$. + + \item With the reduced set of interesting relations, we can build the Petri net. + \begin{center} + \includegraphics[width=0.5\textwidth]{img/alpha_algorithm_example.png} + \end{center} + \end{enumerate} + \end{example} + + $\alpha$-algorithm has the following limitations: + \begin{itemize} + \item It can learn unnecessarily complex networks. + \item It cannot learn loops. + \item The frequency of the traces is not taken into account. + \end{itemize} + + + \item[Model evaluation] + Different models can capture the same process described in a log. + This allows for models that are capable of capturing all the possible traces of a log but + are unable provide any insight (e.g. flower Petri net). + + \begin{figure}[H] + \centering + \includegraphics[width=0.4\textwidth]{img/flower_petri.png} + \caption{Example of flower Petri net} + \end{figure} + + General judging criteria for a model are: + \begin{descriptionlist} + \item[Fitness] \marginnote{Fitness} + How well the model fits the majority of the traces. + \item[Simplicity] \marginnote{Simplicity} + Based on the structure of the model. + \item[Precision] \marginnote{Precision} + How the model is able to capture rare cases. + \item[Generalization] \marginnote{Generalization} + How the model generalize on the training traces. + \end{descriptionlist} +\end{description} + + + +\subsection{Conformance checking} + +\begin{description} + \item[Descriptive model discrepancies] \marginnote{Descriptive model} + The model need to be improved. + + \item[Prescriptive model discrepancies] \marginnote{Prescriptive model} + The traces need to be checked as the model cannot be changed (e.g. model of the law). + The deviation of a trace can be desired or undesired. +\end{description} + +\begin{remark} + A trace can be seen as a sequence of symbols. It is possible to syntactically check them using a regular expression. +\end{remark} + +\begin{description} + \item[Token replay] \marginnote{Token replay} + Given a trace and a Petri net, the trace is replayed on the model by moving tokens around. + The trace is conform if the end event can be reached, otherwise it is not. + + A modified version of token replay allows to add or remove tokens when the trace is stuck on the Petri net. + These external interventions are tracked and used to compute a fitness score (i.e. degree of conformance). + + Limitations: + \begin{itemize} + \item Fitness tend to be high for extremely problematic logs. + \item If there are too many deviations, the model is flooded with tokens and may result in unexpected behaviors. + \item It is a Petri net specific algorithm. + \end{itemize} + + \item[Alignment] \marginnote{Alignment} + Given a trace $l$ and the reference traces $L_\text{ref}$, + alignment is based on the edit distance (i.e. minimum number of modifications) between $l$ and the traces in $L_\text{ref}$. + + The fitness score is based on the lowest and highest edit distances. +\end{description} \ No newline at end of file