ISM: Interpretive Structural Modeling

Overview

Hierarchical decomposition via reachability. Output typically weight_or_utility (higher value = preferred).

Strengths

• •Method-specific: Hierarchical decomposition via reachability

Edge cases

• •if e_i affects e_j).

Common pitfalls

• •Bkz. ISM F.steps citation_anchor'lar ve P.verification_status.

Worked example

1. 1.Adım 1 (F1): Step 1: Binary relation matrix D = [π_ij] (1 if e_i affects e_j). Formül: D = [\pi_{ij}]_{n\times n},\ \pi_{ij} \in \{0,1\} Anchor: Warfield 1973, p.405 Sec.2
2. 2.Adım 2 (F2): Step 2: Reachability matrix M* via Boolean powers until stable. Formül: M = D + I,\quad M^{*} = M^{k}\text{ s.t. } M^{k} = M^{k+1} Anchor: Warfield 1973, p.406 Eq.(1)
3. 3.Adım 3 (F3): Step 3: Reachability set R(t_i) and antecedent set A(t_i). Formül: R(t_{i}) = \{e_{j} \mid m_{ji}^{*}=1\},\quad A(t_{i}) = \{e_{j} \mid m_{ij}^{*}=1\} Anchor: Warfield 1973, p.406 Eqs.(2)-(3)
4. 4.Adım 4 (F4): Step 4: Level partition: e_i at current level iff R(t_i) ∩ A(t_i) = R(t_i). Formül: R(t_{i}) \cap A(t_{i}) = R(t_{i}) \implies e_{i} \in \text{level }l Anchor: Warfield 1973, p.407 Eq.(4)
5. 5.Adım 5 (F5): Step 5: Build hierarchical digraph from level partition. Formül: \mathcal{G} = (V,E),\ V=\{e_{1},\ldots,e_{n}\} Anchor: Warfield 1973, p.407 Sec.4

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