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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

Unbalanced term set with 5 linguistic labels (b) obtained from a linguistic hierarchy of 3 levels (a).
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fig2: Unbalanced term set with 5 linguistic labels (b) obtained from a linguistic hierarchy of 3 levels (a).

Mentions: The semantics of each linguistic label is usually given by a trapezoidal or triangular membership function μ : X → [0,1] that is represented with a tuple P = (p1,  p2, p3,  p4), where p1 ≤ p2 ≤ p3 ≤ p4 are the points in the reference domain X which define the trapezoid. Some special cases can be defined. If p1 = p2 and p3 = p4, then P corresponds to a crisp interval. If p2 = p3 the fuzzy set P is triangular; otherwise, it is a trapezoid. If p1 = p2 = p3 = p4, then P is called a crisp real number. In most of the applications that use linguistic information, the fuzzy sets associated with each label are equal, symmetric, and uniformly distributed throughout the domain (e.g., the term set (a) in Figure 2). This kind of representation makes it easier to manage and understand the meaning of each label and the mathematical operations carried out over them. For instance, the LOWA aggregation operator takes advantage of this simplicity to consider only the order in which the labels appear in the domain, which means that it can operate in a symbolic way [20] (see Section 2.2).


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)

Unbalanced term set with 5 linguistic labels (b) obtained from a linguistic hierarchy of 3 levels (a).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig2: Unbalanced term set with 5 linguistic labels (b) obtained from a linguistic hierarchy of 3 levels (a).
Mentions: The semantics of each linguistic label is usually given by a trapezoidal or triangular membership function μ : X → [0,1] that is represented with a tuple P = (p1,  p2, p3,  p4), where p1 ≤ p2 ≤ p3 ≤ p4 are the points in the reference domain X which define the trapezoid. Some special cases can be defined. If p1 = p2 and p3 = p4, then P corresponds to a crisp interval. If p2 = p3 the fuzzy set P is triangular; otherwise, it is a trapezoid. If p1 = p2 = p3 = p4, then P is called a crisp real number. In most of the applications that use linguistic information, the fuzzy sets associated with each label are equal, symmetric, and uniformly distributed throughout the domain (e.g., the term set (a) in Figure 2). This kind of representation makes it easier to manage and understand the meaning of each label and the mathematical operations carried out over them. For instance, the LOWA aggregation operator takes advantage of this simplicity to consider only the order in which the labels appear in the domain, which means that it can operate in a symbolic way [20] (see Section 2.2).

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