Condition of Order Preservation in Pairwise Comparisons Matrix With Fuzzy Elements

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Condition of Order Preservation in Pairwise Comparisons Matrix With Fuzzy Elements

Popis výsledku v původním jazyce

In this paper we deal with Preference Order Preservation (POP) condition of pairwise comparisons (PC) matrix with fuzzy elements. Fuzzy elements are appropriate whenever the decision maker (DM) is uncertain about the value of his/her evaluation of the relative importance of elements in question, or, when aggregating crisp pairwise comparisons of a group of decision makers in the group DM problem. We formulate the problem in a general setting investigating pairwise comparisons matrices with fuzzy elements from Abelian linearly ordered group (alo-group). Such an approach enables extensions of traditional multiplicative, additive or fuzzy approaches. Then we propose new order preservation concept based on alpha-cuts. We define the concept of consistency of PC matrix with fuzzy elements (PCF matrices), generalize the concept of the preference order preservation condition (POP condition) to PCF matrices defining weak POP and strong POP condition and derive sufficient conditions for POP co ndition to be met. Finally, we discuss a numerical example in order to illustrate the proposed concepts and properties.

Název v anglickém jazyce

Condition of Order Preservation in Pairwise Comparisons Matrix With Fuzzy Elements

Popis výsledku anglicky

In this paper we deal with Preference Order Preservation (POP) condition of pairwise comparisons (PC) matrix with fuzzy elements. Fuzzy elements are appropriate whenever the decision maker (DM) is uncertain about the value of his/her evaluation of the relative importance of elements in question, or, when aggregating crisp pairwise comparisons of a group of decision makers in the group DM problem. We formulate the problem in a general setting investigating pairwise comparisons matrices with fuzzy elements from Abelian linearly ordered group (alo-group). Such an approach enables extensions of traditional multiplicative, additive or fuzzy approaches. Then we propose new order preservation concept based on alpha-cuts. We define the concept of consistency of PC matrix with fuzzy elements (PCF matrices), generalize the concept of the preference order preservation condition (POP condition) to PCF matrices defining weak POP and strong POP condition and derive sufficient conditions for POP co ndition to be met. Finally, we discuss a numerical example in order to illustrate the proposed concepts and properties.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10103 - Statistics and probability

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

36-th International Conference Mathematical Methods in Economics 2018

ISBN

978-80-7378-372-3

ISSN

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e-ISSN

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Počet stran výsledku

6

Strana od-do

457-462

Název nakladatele

Silesian Univeristy in Opava, SBA Karviná

Místo vydání

Praha, CZ

Místo konání akce

Jindrichuv Hradec

Datum konání akce

12. 9. 2018

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000427151400094