Abstract
We investigate the multiple attribute decision making problems in which attribute values take the form of triangular fuzzy linguistic information. Firstly, the definition and some operational laws of triangular fuzzy linguistic are introduced. Then, we have developed three fuzzy linguistic Choquet integral aggregation operators: fuzzy linguistic choquet ordered averaging operator, fuzzy linguistic choquet ordered geometric operator and fuzzy linguistic choquet ordered harmonic mean operator. The prominent characteristic of the operators is that they cannot only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. We have studied some desirable properties of these operators, such as commutativity, idempotency and monotonicity, and applied these operators to multiple attribute decision making with triangular fuzzy linguistic information. Finally an illustrative example has been given to show the developed method.
Highlights
In order to effectively avoid the loss and distortion of information in triangular fuzzy linguistic information processing process, Xu (2007b) proposed the triangular fuzzy linguistic representation and computational model which has a distinct advantage over other linguistic processing methods in accuracy and reliability and developed some operators for aggregating triangular fuzzy linguistic variables, such as the fuzzy linguistic averaging (FLA) operator, fuzzy linguistic weighted averaging (FLWA) operator, fuzzy linguistic ordered weighted averaging (FLOWA) operator, and induced FLOWA (IFLOWA) operator
Zhao and Wei (2009) proposed some operators for aggregating triangular fuzzy linguistic variables, such as the fuzzy linguistic geometric averaging (FLGA) operator, fuzzy linguistic weighted geometric averaging (FLWGA) operator, fuzzy linguistic ordered weighted geometric (FLOWG) operator, and induced FLOWG (IFLOWG) operator and developed an approach based on FLWGA and IFLOWG operator to multiple attribute group decision making with triangular fuzzy linguistic variables
The traditional Choquet integral aggregation operators are generally suitable for aggregating the information taking the form of numerical values, and yet they will fail in dealing with triangular fuzzy linguistic variable
Summary
Multiple attribute decision making (MADM) refers to making choice of the best alternative from among a finite set of decision alternatives in terms of multiple usually conflicting attributes (or called criteria) (Liu 2009a, 2009b; Zhang, Liu 2010a, 2010b; Liu, Su 2010; Liu, Zhang 2010, 2011; Liu et al 2011a, 2011b; Liu, Wang 2011; Merigó, Gil-Lafuente 2009, 2010; Merigó, Casanovas 2009, 2010; Merigó 2010; Merigó et al 2010; Tan, Chen 2010; Wang 2009a, 2009b, 2010; Wei 2008, 2009a-b, 2010a-d; Wei et al 2010a, 2010b; Xu 2004a-c, 2005a-c, 2006a-d, 2007a-c, 2009b; 2010; Ye 2009a, 2009b). Wei (2009c) proposed some operators for aggregating triangular fuzzy linguistic variables, such as the fuzzy linguistic harmonic mean (FLHM) operator, fuzzy linguistic weighted harmonic mean (FLWHM) operator, fuzzy linguistic ordered weighted harmonic mean (FLOWHM) operator, and fuzzy linguistic hybrid harmonic mean (FLHHM) operator and developed an approach based on FLWHM and FLHHM operator to multiple attribute group decision making with triangular fuzzy linguistic variables. Motivated by the correlation properties of the Choquet integral, in this paper we propose some triangular fuzzy linguistic aggregation operators, whose prominent characteristic is that they cannot only consider the importance of the elements or their ordered positions, and reflect the correlations of the elements or their ordered positions. In the last section we conclude the paper and give some remarks
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