P-AROMAN - Plithogenic extension of P-AROMAN

Overview

p-aroman extends P-AROMAN to handle Plithogenic uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Plithogenic Set (PltS: attribute values with contradiction degrees) algebra. The final scores are defuzzified via dominant value defuzzification; approach varies by appurtenance function before ranking.

Output

utility, higher is better

Data

Plithogenic, uncertainty tuples complete

Weights

Needs a weight source

Size

2+ alternatives, 3-10 criteria works best

Used for

Plithogenic MCDM, MAGDM under epistemic uncertainty, expert-driven evaluation with linguistic terms

How it works

1. 1

   Contradiction adjustment; score extraction.

   $$s_{ij}=s({\hat{p}}_{ij})=(1+\hat{T}-2\hat{I}-\hat{F})/2$$

   Bošković et al. 2023 DMAME 6(1); Plithogenic variant

2. 2

   Step-1 linear + Step-2 vector normalisation; combined value.

   $$r_{ij}=s_{ij}/s_j^{\max }(j\in {\Omega }_b);z_{ij}=r_{ij}/\sqrt{\sum _i{r}_{ij}^2};t_{ij}=(r_{ij}+z_{ij})/2$$

   Bošković et al. 2023 Sec.3

3. 3

   AROMAN score.

   $$AROMA{N}_i=\sum _j{w}_j{t}_{ij}$$

   Bošković et al. 2023

4. 4

   Rank descending by AROMAN_i.

   $$\text{rank descending}$$

   Bošković et al. 2023

5. 5

   Final ranking output.

   $$A_{\sigma (1)}\succ A_{\sigma (2)}\succ \cdots \succ A_{\sigma (m)}$$

   Bošković et al. 2023

Fits when / Look elsewhere when

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

Edge cases and pitfalls

• Value-space violation: ensure all entries satisfy Plithogenic: each attribute has a set of values V with appurtenance degrees and contradiction degrees c(v,D) before computation.

• Defuzzification method affects ranking: dominant value defuzzification; approach varies by appurtenance function is the canonical choice but alternatives exist.

Works with

How to cite