Linguistic Multi-Attribute Decision Making with a Prioritization Relationship

Linguistic Multi-Attribute Decision Making with a Prioritization Relationship

Cuiping Wei (Yangzhou University, China), Xijin Tang (CAS Academy of Mathematics and Systems Science, China) and Xiaojie Wang (Qufu Normal University, China)
DOI: 10.4018/978-1-4666-6042-7.ch021
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Abstract

In this paper we consider linguistic information aggregation problems where a prioritization relationship exists over attributes. The authors define a prioritized 2-tuple ordered weighted averaging (PTOWA) operator to aggregate satisfactions of alternatives under attributes with a linear prioritized ordering. The authors then use the PTOWA and a TOWA operator to aggregate linguistic information where attributes are partitioned into some categories of which prioritization between categories exists. Finally, two illustrative examples are employed to show the feasibility of the proposed method.
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2. 2-Tuple Linguistic Representation Model And Towa Operators

For MADM problems with some qualitative attributes, we need to use a linguistic term set to describe the decision information. Herrera and Martínez (2000) introduced a finite and totally ordered discrete linguistic term set: S={sα|α=0, 1,⋯,τ}, whose cardinality value is odd. For example, a set of seven linguistic terms s could be:

Furthermore, Herrera defined 2-tuple to aggregate linguistic information:

  • Definition 1: (Herrera & Martínez, 2001) Let S={s0,s1,…,sτ} be a linguistic term set, then the 2-tuple can be obtained by the translation function θ:(1)

  • Definition 2: (Herrera & Martínez, 2001) Let S={s0,s1,…,sτ} be a linguistic term set, si=S and β∈[0,τ], a value representing the result of a symbolic aggregation operation, then the 2-tuple can be obtained with the following function:

    (2)

where round (∙) is the usual round operation.

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