LoPM - Limits on Property Method

Overview

Higher m_i = better property satisfaction. Lower-limit: limit/x ≤ 1 if x meets or exceeds limit; upper-limit: x/limit ≤ 1 if x is at or below limit. Score = 1 when exactly at limit. Primarily designed for material selection problems.

Data

Crisp

Weights

Needs a weight source

How it works

1. 1

   Compute property satisfaction scores for each type. Lower-limit (type=1): score_j = limit_j / x_ij (penalty if x_ij < limit_j). Upper-limit (type=-1): score_j = x_ij / limit_j (penalty if x_ij > limit_j). Target (type=0): score_j = |x_ij/limit_j − 1| (deviation from target). Sum with weights: m_i = Σ w_j·score_j (lower-limit) + Σ w_j·score_j (upper-limit) + Σ w_j·score_j (target). Rank descending (higher m = better satisfaction).

   $$m_i=\sum _{j\in J_{lower}}{w}_j\frac{{\ell }_j}{x_{ij}}+\sum _{j\in J_{upper}}{w}_j\frac{x_{ij}}{{\ell }_j}+\sum _{j\in J_{target}}{w}_j\left|\frac{x_{ij}}{{\ell }_j}-1\right|,\text{rank descending}$$

   Farag 2020 Material selection §LoPM

Edge cases and pitfalls

• •if x_ij < limit_j). Upper-limit (type=-1): score_j = x_ij / limit_j (penalty if x_ij > limit_j). Target (type=0): score_j = |x_ij/limit_j − 1| (deviation from target). Sum with weights: m_i = Σ w_j·sc

• criteria_types uses {1, -1, 0} convention (not max/min). Type 0 (target) contributes |x/limit - 1| - unlike lower/upper limit types, lower deviation = better.

• All values must be strictly positive - LoPM computes limit/x and x/limit ratios.

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