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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.

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Related in: MedlinePlus

Linguistic terms used in the comparison. (a) Basic set of 9 labels equally distributed; (b) terms aggregated in case 1; (c) terms aggregated in case 2; (d) terms aggregated in case 3.
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fig10: Linguistic terms used in the comparison. (a) Basic set of 9 labels equally distributed; (b) terms aggregated in case 1; (c) terms aggregated in case 2; (d) terms aggregated in case 3.

Mentions: In this section we compare the performance of the proposed IULOWA aggregator with another well-known induced linguistic operator with the same name defined by Xu [21]. The method proposed by Xu intends to aggregate the information provided by a set of uncertain linguistic variables. Each of these variables is defined with an interval of two linguistic terms from a fixed finite set of predefined terms. Figure 10(a) shows an example set of 9 labels, numbered from s−4 to s4, whose meaning may be taken to be implicitly represented by a set of symmetric and uniformly distributed triangular fuzzy sets. Moreover, each item to be aggregated has an associated value that is used to induce the order in which the items have to be aggregated; however, Xu does not propose any specific induction order. In Section 2 (10) we have provided the definition of the Xu-IULOWA operator, which only depends on the indexes of the aggregated elements (no operations are performed explicitly on fuzzy sets). The result of the aggregation is also an uncertain linguistic variable that is an interval [sa, sb], where a and b do not have to be values from the original set of terms. For example, the result of an aggregation could be [s−1.3, s2.4].


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)

Linguistic terms used in the comparison. (a) Basic set of 9 labels equally distributed; (b) terms aggregated in case 1; (c) terms aggregated in case 2; (d) terms aggregated in case 3.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig10: Linguistic terms used in the comparison. (a) Basic set of 9 labels equally distributed; (b) terms aggregated in case 1; (c) terms aggregated in case 2; (d) terms aggregated in case 3.
Mentions: In this section we compare the performance of the proposed IULOWA aggregator with another well-known induced linguistic operator with the same name defined by Xu [21]. The method proposed by Xu intends to aggregate the information provided by a set of uncertain linguistic variables. Each of these variables is defined with an interval of two linguistic terms from a fixed finite set of predefined terms. Figure 10(a) shows an example set of 9 labels, numbered from s−4 to s4, whose meaning may be taken to be implicitly represented by a set of symmetric and uniformly distributed triangular fuzzy sets. Moreover, each item to be aggregated has an associated value that is used to induce the order in which the items have to be aggregated; however, Xu does not propose any specific induction order. In Section 2 (10) we have provided the definition of the Xu-IULOWA operator, which only depends on the indexes of the aggregated elements (no operations are performed explicitly on fuzzy sets). The result of the aggregation is also an uncertain linguistic variable that is an interval [sa, sb], where a and b do not have to be values from the original set of terms. For example, the result of an aggregation could be [s−1.3, s2.4].

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