Abstract
In the modern literature related to linguistic decision-making, the 2-tuple linguistic representation model and its useful applications in various fields have been extensively studied and used during the last decade. Recently, some useful multicriteria decision-making (MCDM) methods have been introduced based on fuzzy analytic hierarchy process (AHP) for 2-tuple linguistic representation model. By keeping in mind the importance of this linguistic model, in this paper, we introduce a fuzzy AHP methodology for intuitionistic 2-tuple linguistic sets (I2TLSs) which is a useful extension of the 2-tuple linguistic representation model. This study is comprised of four stages. In the first stage, we define some operational laws for I2TL elements (I2TLEs) and prove some related important properties. In the second stage, intuitionistic 2-tuple linguistic preference relation (I2TLPR) and multiplicative I2TLPR are defined using I2TLSs. In the 3rd stage, a transformation mechanism is introduced which can transform an I2TLPR to a corresponding intuitionistic preference relation (IPR) and vice versa. In the fourth stage, an approach is proposed for checking the consistency of an I2TLPR and presented a method to repair the inconsistent one by using the proposed transformation mechanism. Finally, a numerical example is given and comparative analysis is carried out with the TOPSIS method to verify the validity of the proposed method.
Highlights
Herrera and Martınez [1, 2] proposed the 2-tuple fuzzy linguistic representation model which can handle linguistic and numerical information in decision-making effectively without loss and distortion of information which formerly occur during the processing of linguistic information
Intuitionistic 2-tuple analytic hierarchy process (AHP) method has been proposed for solving the multicriteria decision-making (MCDM) problems based on intuitionistic 2-tuple linguistic sets (I2TLSs)
By using the idea of I2TLSs, two important preference relations, namely, the intuitionistic 2-tuple linguistic preference relation (I2TLPR) and the multiplicative I2TLPR, have been defined along with a transformation mechanism that can transform an I2TLPR to a corresponding intuitionistic preference relation (IPR) and vice versa
Summary
Herrera and Martınez [1, 2] proposed the 2-tuple fuzzy linguistic representation model which can handle linguistic and numerical information in decision-making effectively without loss and distortion of information which formerly occur during the processing of linguistic information. This useful model is basically developed on the basis of symbolic translation of the linguistic variables and has been extensively used in various MCDM problems [3,4,5,6] in recent years.
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