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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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Examples of balanced (a) and unbalanced (b) linguistic term sets with five labels.
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fig1: Examples of balanced (a) and unbalanced (b) linguistic term sets with five labels.

Mentions: Although the OWA and IOWA operators have been traditionally applied to numerical data, we can find many applications where they have been used with linguistic variables [11]. Most of the studies in this area have assumed a uniform and symmetrical distribution of the linguistic terms that define the linguistic variable [12, 13] (see Figure 1(a)). However, there are some situations that cannot be modelled with symmetric linguistic variables [14–16]. For example, some decision making problems, such as personnel examination or project investment selection, often require a linguistic scale that assigns a different precision to each label. This issue is illustrated in the term set (b) in Figure 1, where the deviation between the indices of two adjoining labels is much larger between very low and medium than between medium and high. Some unbalanced and linguistic aggregation operators have recently appeared [2, 16–19].


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)

Examples of balanced (a) and unbalanced (b) linguistic term sets with five labels.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig1: Examples of balanced (a) and unbalanced (b) linguistic term sets with five labels.
Mentions: Although the OWA and IOWA operators have been traditionally applied to numerical data, we can find many applications where they have been used with linguistic variables [11]. Most of the studies in this area have assumed a uniform and symmetrical distribution of the linguistic terms that define the linguistic variable [12, 13] (see Figure 1(a)). However, there are some situations that cannot be modelled with symmetric linguistic variables [14–16]. For example, some decision making problems, such as personnel examination or project investment selection, often require a linguistic scale that assigns a different precision to each label. This issue is illustrated in the term set (b) in Figure 1, where the deviation between the indices of two adjoining labels is much larger between very low and medium than between medium and high. Some unbalanced and linguistic aggregation operators have recently appeared [2, 16–19].

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