Rough-MOORA - Rough extension of MOORA

Rough outranking/ranking - Rough number (lower approximation L, upper approximation U)

Brauers, W.K.M., Zavadskas, E.K.2006

Overview

ROUGH-MOORA extends MOORA Ratio System (RS) to Rough [L,U] interval arithmetic. Steps: (1) vector normalization in IRN domain using r_ij=[l_ij/√(Σu²), u_ij/√(Σl²)], (2) scalar weighting v_ij=[w_j·l_ij, w_j·u_ij], (3) RS score: y_i^IRN = [Σ_ben w·l_R − Σ_cost w·u_R, Σ_ben w·u_R − Σ_cost w·l_R] (Zhai 2009 subtraction rule), (4) defuzzify y_i=(L+U)/2 and rank descending. NOTE: This is an INTERNAL EXTENSION - no dedicated ROUGH-MOORA paper exists. RS only; RP and FMF sub-methods not implemented.

Output: utility, higher is better
Data: Rough Number, uncertainty tuples complete
Weights: Needs a weight source
Size: 2+ alternatives, 3-10 criteria works best
Used for: Rough MCDM, MAGDM under epistemic uncertainty, expert-driven evaluation with linguistic terms

Look elsewhere when

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

Assumptions to verify

Decision matrix entries are valid Rough 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 Rough: L ≤ U; approximations defined by equivalence classes before computation.
This internal extension uses midpoint (L+U)/2 defuzzification explicitly (declared in L.formulation). The RS IRN interval y_i^IRN may occasionally have L > U when cost dominates benefit - the midpoint still yields a valid crisp score in such cases.

Works with

Commonly takes its weights from

n_a

How to cite

Brauers, W.K.M.; Zavadskas, E.K. (2006). The MOORA method and its application to privatization in a transition economy. Control and Cybernetics.

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System ID, as it appears in reports and the API

ROUGH-MOORA

Overview

Output

utility, higher is better

Data

Rough Number, uncertainty tuples complete

Weights

Needs a weight source

Size

2+ alternatives, 3-10 criteria works best

Used for

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

Edge cases and pitfalls

Value-space violation: ensure all entries satisfy Rough: L ≤ U; approximations defined by equivalence classes before computation.

This internal extension uses midpoint (L+U)/2 defuzzification explicitly (declared in L.formulation). The RS IRN interval y_i^IRN may occasionally have L > U when cost dominates benefit - the midpoint still yields a valid crisp score in such cases.