Limits...
Induced unbalanced linguistic ordered weighted average and its application in multiperson decision making.

Marin L, Valls A, Isern D, Moreno A, Merigó JM - ScientificWorldJournal (2014)

Bottom Line: We propose a new order-inducing criterion based on the specificity and fuzziness of the linguistic terms.Different relevancies are given to the fuzzy values according to their uncertainty degree.To illustrate the behaviour of the precision-based IULOWA operator, we present an environmental assessment case study in which a multiperson multicriteria decision making model is applied.

View Article: PubMed Central - PubMed

Affiliation: Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Avinguda Països Catalans 26, 43007 Tarragona, Catalonia, Spain.

ABSTRACT
Linguistic variables are very useful to evaluate alternatives in decision making problems because they provide a vocabulary in natural language rather than numbers. Some aggregation operators for linguistic variables force the use of a symmetric and uniformly distributed set of terms. The need to relax these conditions has recently been posited. This paper presents the induced unbalanced linguistic ordered weighted average (IULOWA) operator. This operator can deal with a set of unbalanced linguistic terms that are represented using fuzzy sets. We propose a new order-inducing criterion based on the specificity and fuzziness of the linguistic terms. Different relevancies are given to the fuzzy values according to their uncertainty degree. To illustrate the behaviour of the precision-based IULOWA operator, we present an environmental assessment case study in which a multiperson multicriteria decision making model is applied.

Show MeSH

Related in: MedlinePlus

Two fuzzy sets with the same specificity and different fuzziness.
© Copyright Policy - open-access
Related In: Results  -  Collection


getmorefigures.php?uid=PMC4127207&req=5

fig5: Two fuzzy sets with the same specificity and different fuzziness.

Mentions: If there are ties between terms with the same specificity, a second ordering criterion may be their fuzziness. An increasing ordering of fuzziness will be used, as we prefer those terms with less uncertainty. If this second criterion also leads to some ties, a decreasing ordering on the preference scale S associated with the terms can be used. In Figure 5 we show two fuzzy sets with the same specificity (Sp(A) = Sp(B) = 0.9), according to (18),(21)Sp(A)=1−area  of  Ab−a=1−(0.2∗1)/21−0=0.9,Sp(B)=1−area  of  Bb−a=1−2(0.05/2)+0.051−0=0.9,but different fuzziness (Fz(A) = 0.1 and Fz(B) = 0.05), according to (20),(22)Fz(A)=1−1b−a∫ab/2·A(x)−1/=1−∫01/2·A(x)−1/=1−0.9=0.1,Fz(B)=1−1b−a∫ab/2·B(x)−1/=1−∫01/2·B(x)−1/=1−0.95=0.05.


Induced unbalanced linguistic ordered weighted average and its application in multiperson decision making.

Marin L, Valls A, Isern D, Moreno A, Merigó JM - ScientificWorldJournal (2014)

Two fuzzy sets with the same specificity and different fuzziness.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4127207&req=5

fig5: Two fuzzy sets with the same specificity and different fuzziness.
Mentions: If there are ties between terms with the same specificity, a second ordering criterion may be their fuzziness. An increasing ordering of fuzziness will be used, as we prefer those terms with less uncertainty. If this second criterion also leads to some ties, a decreasing ordering on the preference scale S associated with the terms can be used. In Figure 5 we show two fuzzy sets with the same specificity (Sp(A) = Sp(B) = 0.9), according to (18),(21)Sp(A)=1−area  of  Ab−a=1−(0.2∗1)/21−0=0.9,Sp(B)=1−area  of  Bb−a=1−2(0.05/2)+0.051−0=0.9,but different fuzziness (Fz(A) = 0.1 and Fz(B) = 0.05), according to (20),(22)Fz(A)=1−1b−a∫ab/2·A(x)−1/=1−∫01/2·A(x)−1/=1−0.9=0.1,Fz(B)=1−1b−a∫ab/2·B(x)−1/=1−∫01/2·B(x)−1/=1−0.95=0.05.

Bottom Line: We propose a new order-inducing criterion based on the specificity and fuzziness of the linguistic terms.Different relevancies are given to the fuzzy values according to their uncertainty degree.To illustrate the behaviour of the precision-based IULOWA operator, we present an environmental assessment case study in which a multiperson multicriteria decision making model is applied.

View Article: PubMed Central - PubMed

Affiliation: Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Avinguda Països Catalans 26, 43007 Tarragona, Catalonia, Spain.

ABSTRACT
Linguistic variables are very useful to evaluate alternatives in decision making problems because they provide a vocabulary in natural language rather than numbers. Some aggregation operators for linguistic variables force the use of a symmetric and uniformly distributed set of terms. The need to relax these conditions has recently been posited. This paper presents the induced unbalanced linguistic ordered weighted average (IULOWA) operator. This operator can deal with a set of unbalanced linguistic terms that are represented using fuzzy sets. We propose a new order-inducing criterion based on the specificity and fuzziness of the linguistic terms. Different relevancies are given to the fuzzy values according to their uncertainty degree. To illustrate the behaviour of the precision-based IULOWA operator, we present an environmental assessment case study in which a multiperson multicriteria decision making model is applied.

Show MeSH
Related in: MedlinePlus