P-AROMAN: Plithogenic extension of P-AROMAN

Overview

Plithogenic outranking/ranking: Plithogenic Set (PltS: attribute values with contradiction degrees). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Plithogenic outranking/ranking: Plithogenic Set (PltS: attribute values with contradiction degrees)
• •Preserves plithogenic uncertainty through the pipeline rather than premature crispification at elicitation
• •Native group-decision support (multi-DM aggregation built into the pipeline)

Limitations

• •Assumes: Decision matrix entries are valid Plithogenic numbers/tuples
• •Assumes: Underlying crisp method's compensation assumption holds in uncertain space
• •Assumes: All decision-maker(s) and experts use the same linguistic/uncertainty scale

Assumptions to verify

• •Decision matrix entries are valid Plithogenic numbers/tuples
• •Underlying crisp method's compensation assumption holds in uncertain space
• •All decision-maker(s) and experts use the same linguistic/uncertainty scale

When not to use

• •Crisp data sufficient: use base AROMAN directly (avoid unnecessary uncertainty layer)
• •Aggregation operator (PFWA/PFOWA/etc.) not specified: output ambiguous

Edge cases

• •See F.steps and D.parameters for P-AROMAN-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'P-AROMAN bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Plithogenic numbers/tuples
• •Hatalı: 'P-AROMAN bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'P-AROMAN bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: P-AROMAN'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: P-AROMAN'yi 'Aggregation operator (PFWA/PFOWA/etc.) not specified' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Contradiction adjustment; score extraction. Formül: s_{ij}=s(\hat{p}_{ij})=(1+\hat{T}-2\hat{I}-\hat{F})/2 Anchor: Bošković et al. 2023 DMAME 6(1); Plithogenic variant
2. 2.Adım 2 (F2): Step-1 linear + Step-2 vector normalisation; combined value. Formül: r_{ij}=s_{ij}/s_j^{\max}\;(j\in\Omega_b);\;z_{ij}=r_{ij}/\sqrt{\sum_i r_{ij}^2};\;t_{ij}=(r_{ij}+z_{ij})/2 Anchor: Bošković et al. 2023 Sec.3
3. 3.Adım 3 (F3): AROMAN score. Formül: AROMAN_i=\sum_j w_j t_{ij} Anchor: Bošković et al. 2023
4. 4.Adım 4 (F4): Rank descending by AROMAN_i. Formül: \text{rank descending} Anchor: Bošković et al. 2023
5. 5.Adım 5 (F5): Final ranking output. Formül: A_{\sigma(1)}\succ A_{\sigma(2)}\succ\cdots\succ A_{\sigma(m)} Anchor: Bošković et al. 2023

Commonly paired with

• •n_a + P-AROMAN (common)

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