COMET: Characteristic Objects METhod

Overview

Fuzzy rule base on characteristic objects: rank-reversal free. Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Fuzzy rule base on characteristic objects: rank-reversal free

Limitations

• •Assumes: Expert function is consistent with CO preference ordering
• •Assumes: cvalues span the range of actual alternative values
• •Assumes: Number of criteria ≤ 4-5 (exponential CO explosion otherwise)

Assumptions to verify

• •Expert function is consistent with CO preference ordering
• •cvalues span the range of actual alternative values
• •Number of criteria ≤ 4-5 (exponential CO explosion otherwise)

When not to use

• •Many criteria (≥6) → exponential CO count impractical
• •No domain expert available to define or validate scoring function

Edge cases

• •If n criteria each with c_j characteristic values, total COs = Π_j c_j.

Common pitfalls

• •Hatalı: 'COMET bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Expert function is consistent with CO preference ordering
• •Hatalı: 'COMET bu varsayımı kontrol etmeden uygulamak'. Doğrusu: cvalues span the range of actual alternative values
• •Hatalı: 'COMET bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Number of criteria ≤ 4-5 (exponential CO explosion otherwise)
• •Hatalı: COMET'yi 'Many criteria (≥6) → exponential CO count impractical' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: COMET'yi 'No domain expert available to define or validate scoring function' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Generate all Characteristic Objects (COs): Cartesian product of cvalues (Gray-code order for efficiency). If n criteria each with c_j characteristic values, total COs = Π_j c_j. Formül: CO = \{(c^{(1)}_{q_1}, c^{(2)}_{q_2}, \ldots, c^{(n)}_{q_n}) : q_j \in \{1,\ldots,|cvalues_j|\}\} Anchor: Sałabun 2015 §3.1
2. 2.Adım 2 (F2): Step 2: Expert evaluation: apply expert_function to CO_matrix to obtain preference scores p(CO_k) ∈ [0,1] for each characteristic object. This is the knowledge elicitation step: captures DM preferences over the structured CO space. Formül: p(CO_k) \in [0,1],\quad k=1,\ldots,\prod_j |cvalues_j| Anchor: Sałabun 2015 §3.2: MEJ matrix
3. 3.Adım 3 (F3): Step 3: For each alternative x_i, compute membership degrees μ_ij for each criterion j relative to the characteristic values using Triangular Fuzzy Numbers (TFNs). Each x_ij triggers membership in adjacent characteristic levels. Formül: \mu(x,a,m,b) = \begin{cases} 0 & x\le a \text{ or } x\ge b \\ (x-a)/(m-a) & a<x<m \\ (b-x)/(b-m) & m\le x<b \\ 1 & x=m \end{cases} Anchor: Sałabun 2015 §3.3
4. 4.Adım 4 (F4): Step 4: Aggregate membership degrees across all COs to compute final preference P(x_i) = Σ_k [p(CO_k) · Π_j μ_j(x_ij, CO_k)]. Rank descending. Formül: P(x_i) = \sum_{k} p(CO_k) \cdot \prod_j \mu_j(x_{ij}, CO_k),\quad \text{rank descending} Anchor: Sałabun 2015 §3.4

Commonly paired with

• •AHP + COMET (common)
• •ENTROPY + COMET (uncommon)

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