Multiplicative consistency of intuitionistic reciprocal preference relations and its application to missing values estimation and consensus building

Wu, Jian; Chiclana, Francisco

doi:10.1016/j.knosys.2014.07.024

Cited by 151 publications

(120 citation statements)

References 46 publications

(70 reference statements)

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“…In what follows, Zadeh's Extension Principle and the Representation Theorem of fuzzy sets [28] are applied to preference values that are fuzzy sets [32], which will then be characterised for the interval-valued fuzzy sets type, i.e. fuzzy sets whose membership function is always 1 for all values in a closed interval and zero otherwise, and consequently the multiplicative transitivity property for IVFPRs will be formally derived.…”

Section: Multiplicative Transitivity Isomorphism Between Ifprs Amentioning

confidence: 99%

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: Multiplicative Transitivity Isomorphism Between Ifprs Amentioning

confidence: 99%

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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“…A formal approach to modelling the multiplicative consistency property of IVAPR and IAPR, however, can be found in [74]. Definition 14 (Multiplicative Consistent IVAPR [74]).…”

Section: Consistency Of Preferencesmentioning

confidence: 99%

“…For the case of IVPRs two main approaches are analysed: The first one uses consistency properties to estimate the missing PRs [3,29] whereas the second one [98] is based on the rough set theory [55]. For the case of IFPR three iterative approaches have been considered [74,87,93]. Finally an approach presented by Xu et al in [92] to deal with missing interval value intuitionistic additive and multiplicative preference relations (IVIFPR) is also analysed.…”

Section: Managing Missing Preference Values In Ivprs An Ifprsmentioning

confidence: 99%

Managing incomplete preference relations in decision making: A review and future trends

Ureña

Chiclana

Morente-Molinera

et al. 2015

Information Sciences

242

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“…Finally, models to reach consensus where experts assess their preferences using different preference representation structures (preference orderings, utility functions, multiplicative preference relations and fuzzy preference relations) have also been studied and proposed by Dong and Zhang [23], Fedrizzi et al [26] and Herrera-Viedma, Herrera and Chiclana [39]. The problem of measuring and reaching consensus with intuitionistic fuzzy preference relations and triangular fuzzy complementary preference relations have also been covered in detail by Wu and Chiclana in [62,64].…”

Section: Consensus Measurement In the Literaturementioning

confidence: 99%

A new measure of consensus with reciprocal preference relations: The correlation consensus degree

González-Arteaga

Calle

Chiclana

2016

Knowledge-Based Systems

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The achievement of a 'consensual' solution in a group decision making problem depends on experts' ideas, principles, knowledge, experience, etc. The measurement of consensus has been widely studied from the point of view of different research areas, and consequently different consensus measures have been formulated, although a common characteristic of most of them is that they are driven by the implementation of either distance or similarity functions. In the present work though, and within the framework of experts' opinions modelled via reciprocal preference relations, a different approach to the measurement of consensus based on the Pearson correlation coefficient is studied. The new correlation consensus degree measures the concordance between the intensities of preference for pairs of alternatives as expressed by the experts. Although a detailed study of the formal properties of the new correlation consensus degree shows that it verifies important properties that are common either to distance or to similarity functions between intensities of preferences, it is also proved that it is different to traditional consensus measures. In order to emphasise novelty, two applications of the proposed methodology are also included. The first one is used to illustrate the computation process and discussion of the results, while the second one covers a real life application that makes use of data from Clinical Decision-Making.

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Multiplicative consistency of intuitionistic reciprocal preference relations and its application to missing values estimation and consensus building

Cited by 151 publications

References 46 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

Managing incomplete preference relations in decision making: A review and future trends

A new measure of consensus with reciprocal preference relations: The correlation consensus degree

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