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  • A pair-wise comparison matrix is the result of pair-wise comparison a powerful method in multi-criteria optimization. When comparing two elements, the decision maker assigns the value representing the element of the pair-wise comparison matrix. In AHP, the matrix represents a multiplicative preference relation. Here, consistency property plays an essential role. To provide a consistency measure of the pair-wise comparison matrix, the consistency ratio is defined in AHP. In some situations another interpretation is convenient. The preferences can be represented by a fuzzy preference relation, given by the membership function denoting the preference degree (or intensity) of one alternative over the other. The role of consistency is played by the concept of transitivity. In this paper we investigate relations between several types of transitivity of fuzzy relations and multiplicative preference relations. Similarly to the consistency ratio we also define the grade of transitivity.
  • A pair-wise comparison matrix is the result of pair-wise comparison a powerful method in multi-criteria optimization. When comparing two elements, the decision maker assigns the value representing the element of the pair-wise comparison matrix. In AHP, the matrix represents a multiplicative preference relation. Here, consistency property plays an essential role. To provide a consistency measure of the pair-wise comparison matrix, the consistency ratio is defined in AHP. In some situations another interpretation is convenient. The preferences can be represented by a fuzzy preference relation, given by the membership function denoting the preference degree (or intensity) of one alternative over the other. The role of consistency is played by the concept of transitivity. In this paper we investigate relations between several types of transitivity of fuzzy relations and multiplicative preference relations. Similarly to the consistency ratio we also define the grade of transitivity. (en)
Title
  • Measuring transitivity of fuzzy pairwise comparison matrix.
  • Measuring transitivity of fuzzy pairwise comparison matrix. (en)
skos:prefLabel
  • Measuring transitivity of fuzzy pairwise comparison matrix.
  • Measuring transitivity of fuzzy pairwise comparison matrix. (en)
skos:notation
  • RIV/47813059:19520/12:#0002145!RIV13-GA0-19520___
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  • P(GA402/09/0405)
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  • 149078
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  • RIV/47813059:19520/12:#0002145
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  • multi-criteria optimization, pair-wise comparison matrix, AHP (en)
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  • [A6F3AADE2C1D]
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  • Karviná
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  • Karviná
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  • Proceedings of 30th International Conference Mathematical Methods in Economics
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  • Ramík, Jaroslav
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number of pages
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  • Slezská univerzita v Opavě. Obchodně podnikatelská fakulta v Karviné
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  • 978-80-7248-779-0
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  • 19520
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