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Summary

Normalization techniques in Multiple-Criteria Decision Analysis (MCDA) significantly impact ranking stability. This study reveals how data entropy influences these normalization methods, offering an entropy-based approach for robust decision-making.

Keywords:
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Area of Science:

  • Operations Research
  • Decision Science
  • Information Theory

Background:

  • Normalization is crucial in Multiple-Criteria Decision Analysis (MCDA) for comparing heterogeneous data.
  • Different normalization techniques can lead to divergent rankings, introducing uncertainty into decision outcomes.
  • The structure of criterion data, particularly its entropy, influences normalization behavior and ranking stability.

Purpose of the Study:

  • To examine the behavior of seven common normalization techniques within the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) framework.
  • To analyze how criterion data structure, specifically entropy, affects normalization outcomes and ranking stability.
  • To propose an entropy-based method for selecting normalization techniques to improve MCDA transparency and robustness.

Main Methods:

  • Analysis of seven normalization procedures (vector, max, linear sum, max-min) considering mathematical properties, sensitivity, and cost-criteria handling.
  • Utilizing Shannon entropy as a measure of information dispersion and structural uncertainty in criterion data.
  • An experimental study with ten alternatives and four criteria (high- and low-entropy) to demonstrate entropy's mediating role in normalization effects.

Main Results:

  • Normalization choice alone can cause substantial differences in preference values and rankings.
  • High-entropy criteria generally lead to stable rankings, while low-entropy criteria amplify sensitivity, especially with extreme or cost-type data.
  • Entropy acts as a key mediator between data structure and normalization-induced ranking variability.

Conclusions:

  • The selection of normalization techniques significantly impacts MCDA results, with entropy playing a critical mediating role.
  • Low-entropy criteria are more susceptible to ranking instability caused by normalization, particularly with challenging data types.
  • An entropy-based approach can enhance the methodological transparency and robustness of normalization choices in MCDA.