Goal programming approaches to obtain the priority vectors from the intuitionistic fuzzy preference relations

Gong, Zaiwu; Li, Lian-Shui; Zhou, Feixue; Yao, Tianxiang

doi:10.1016/j.cie.2009.05.007

Cited by 141 publications

(68 citation statements)

References 25 publications

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“…This condition, however, does not hold using the definition by Xu et al [12], which was later acknowledged by Liao and Xu in [13]. This same issue has also been addressed recently (see for example [14], [15]). Therefore, it is necessary to develop a theoretically sound framework for modelling consistency of IFPRs.…”

Section: Introductionmentioning

confidence: 94%

“…The consistency based models for IFPRs proposed in [14]- [16] are based on the application of the corresponding consistency property of FPRs to intuitionistic fuzzy preferences without providing a solid mathematical foundation for its validity, i.e. without taking into account the characteristics of the multiplication of intuitionistic fuzzy sets.…”

Section: Analysis Of the Proposed Multiplicative Transitivity Promentioning

confidence: 99%

“…Indeed, some of the consistency properties for IFPRs proposed in literature have subsequently been proved to be inappropriate to model consistency of IFPRs. This article overcomes this issue by providing the mathematical framework for the correct formulation of the multiplicative transitivity for IFPRs, and as such it presents the following main advantages with respect to the proposed models in [14]- [16]: (1) This article investigates the isomorphic multiplicative transitivity property for IFPRs, which is based on the formal extension of the multiplicative consistency property for FPRs proposed Tanino [19]. The proposed multiplicative transitivity property for IFPRs in this article includes Liao and Xu's definition of the same property given in [13], µ ij µ jk µ ki = µ ik µ kj µ ji , but it also includes another additional original foundation of multiplicative transitivity of IFPRs, (1 − ν ij )(1 − ν jk )(1 − ν ki ) = (1 − ν ik )(1 − ν kj )(1 − ν ji ).…”

Section: Analysis Of the Proposed Multiplicative Transitivity Promentioning

confidence: 99%

See 2 more Smart Citations

Isomorphic Multiplicative Transitivity for Intuitionistic and Interval-Valued Fuzzy Preference Relations and Its Application in Deriving Their Priority Vectors

Chiclana

Liao

2018

IEEE Trans. Fuzzy Syst.

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Intuitionistic fuzzy preference relations (IFPRs) are used to deal with hesitation while interval-valued fuzzy preference relations (IVFPRs) are for uncertainty in multi-criteria decision making (MCDM). This article aims to explore the isomorphic multiplicative transitivity for IFPRs and IVFPRs, which builds the substantial relationship between hesitation and uncertainty in MCDM. To do that, the definition of the multiplicative transitivity property of IFPRs is established by combining the multiplication of intuitionistic fuzzy sets and Tanino's multiplicative transitivity property of fuzzy preference relations (FPRs). It is proved to be isomorphic to the multiplicative transitivity of IVFPRs derived via Zadeh's Extension Principle. The use of the multiplicative transitivity isomorphism is twofold: (1) to discover the substantial relationship between IFPRs and IVFPRs, which will bridge the gap between hesitation and uncertainty in MCDM problems; and (2) to strengthen the soundness of the multiplicative transitivity property of IFPRs and IVFPRs by supporting each other with two different reliable sources, respectively. Furthermore, based on the existing isomorphism, the concept of multiplicative consistency for IFPRs is defined through a strict mathematical process, and it is proved to satisfy the following several desirable properties: weak-transitivity, max-max-transitivity, and center-divisiontransitivity. A multiplicative consistency based multi-objective programming (MOP) model is investigated to derive the priority vector from an IFPR. This model has the advantage of not losing information as the priority vector representation coincides with that of the input information, which was not the case with existing methods where crisp priority vectors were derived as a consequence of modelling transitivity just for the intuitionistic membership function and not for the intuitionistic non-membership function. Finally, a numerical example concerning green supply selection is given to validate the efficiency and practicality of the proposed multiplicative consistency MOP model.

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Section: Introductionmentioning

confidence: 94%

Section: Analysis Of the Proposed Multiplicative Transitivity Promentioning

confidence: 99%

Section: Analysis Of the Proposed Multiplicative Transitivity Promentioning

confidence: 99%

See 1 more Smart Citation

Isomorphic Multiplicative Transitivity for Intuitionistic and Interval-Valued Fuzzy Preference Relations and Its Application in Deriving Their Priority Vectors

Chiclana

Liao

2018

IEEE Trans. Fuzzy Syst.

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“…In order to check the consistency of an IFPR, we should first establish the way to measure the consistency of an IFPR. There are mainly two kinds of consistency for IFPR, namely, the additive consistency 14 and the multiplicative consistency 12,13,15,19 . After in-depth review and analyses over these distinct consistency definitions, Liao and Xu 15 proposed a general definition of multiplicative consistency for IFPR, and showed that this kind of consistency can be used as a standard to measure the consistency for an IFPR.…”

Section: The Consistency Checking and Inconsistency Repairing Processmentioning

confidence: 99%

“…Xu and Liao 12 introduced the framework of the intuitionistic fuzzy AHP (IFAHP) method in which the experts' opinions are described in IFPRs, and applied the IFAHP method to global supplier management. Gong et al 13 proposed some goal programming approaches to obtain the priority vector from an IFPR. Later, Wang 14 introduced a different linear goal programming model to obtain the normalized intuitionistic fuzzy priorities of an IFPR.…”

Section: Introductionmentioning

confidence: 99%

A Comparison of Distinct Consensus Measures for Group Decision Making with Intuitionistic Fuzzy Preference Relations

Liao¹,

Li²,

Zeng³

et al. 2017

IJCIS

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Intuitionistic fuzzy preference relation (IFPR), which express experts' preferences from the preferred, the nonpreferred and the indeterminate aspects, has turned out to be an efficient tool in describing the rough and subjective opinions of experts. This paper focuses on the consensus measures for group decision making (GDM) in which all the experts use the IFPRs to express their preferences. Firstly, we give a brief analysis over the framework, the consistency checking process, and the selection process of intuitionistic fuzzy GDM. After that, two novel consensus measures, namely, the outranking flow based consensus measure and the ordinal consensus measure, are proposed to help an analyst to describe the degree of agreement among the experts in a group. In addition, an indepth comparison is made from both theoretical and empirical points of view over our proposed consensus measures against the existing ones. Furthermore, a numerical example is given to show the difference among these distinct consensus measures. Finally, based on the ordinal consensus measure, a procedure is given to help the decision maker yield a final solution for GDM problems.

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Group decision making based on generalized intuitionistic fuzzy prioritized geometric operator

2012

Int. J. Intell. Syst.

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Intuitionistic fuzzy set was studied by many authors because it is a powerful technique to depict uncertainty, which is a set containing three functions: the membership function; the nonmembership function; and the hesitancy function. The aggregation of intuitionistic fuzzy values (IFVs) is of paramount importance in decision making. In this paper, we research IFVs aggregation problems, where there exist a prioritization relationship over the aggregated arguments. First, we propose the generalized intuitionistic fuzzy prioritized weighted geometric operator based on Archimedean t-conorm and t-norm. Then, some of its desirable properties and special cases are investigated in detail. Furthermore, a multicriteria group decision-making problems is formulated with IFVs using the proposed operator. Finally, the validity and applicability of the proposed method, as well as analysis of the comparison with different generator functions, are illustrated with a real example about talent introduction. C 2012 Wiley Periodicals, Inc.

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Goal programming approaches to obtain the priority vectors from the intuitionistic fuzzy preference relations

Cited by 141 publications

References 25 publications

Isomorphic Multiplicative Transitivity for Intuitionistic and Interval-Valued Fuzzy Preference Relations and Its Application in Deriving Their Priority Vectors

Isomorphic Multiplicative Transitivity for Intuitionistic and Interval-Valued Fuzzy Preference Relations and Its Application in Deriving Their Priority Vectors

A Comparison of Distinct Consensus Measures for Group Decision Making with Intuitionistic Fuzzy Preference Relations

Group decision making based on generalized intuitionistic fuzzy prioritized geometric operator

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