Construction of interval-valued fuzzy preference relations from ignorance functions and fuzzy preference relations. Application to decision making

Barrenechea, Edurne; Fernández, Javier; Pagola, Miguel; Chiclana, Francisco; Bustince, Humberto

doi:10.1016/j.knosys.2013.10.002

Cited by 95 publications

(53 citation statements)

References 50 publications

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“…Interval number is an important fuzzy number, and it has been widely used in a lot of fields such as decision making science [2,32,37,41], operational research [6,9,19], [8,33]. The main reasons are as follows:…”

Section: Lq Jin X Fangmentioning

confidence: 99%

Interval Certitude Rule Base Inference Method using the Evidential Reasoning

Jin

Fang

2017

INT J COMPUT COMMUN

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Development of rule-based systems is an important research area for artificial intelligence and decision making, as rule base is one of the most general purpose forms for expressing human knowledge. In this paper, a new rule-based representation and its inference method based on evidential reasoning are presented based on operational research and fuzzy set theory. In this rule base, the uncertainties of human knowledge and human judgment are designed with interval certitude degrees which are embedded in the antecedent terms and consequent terms. The knowledge representation and inference framework offer an improvement of the recently developed rule base inference method, and the evidential reasoning approach is still applied to the rule fusion. It is noteworthy that the uncertainties will be defined and modeled using interval certitude degrees. In the end, an illustrative example is provided to illustrate the proposed knowledge representation and inference method as well as demonstrate its effectiveness by comparing with some existing approaches.

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Section: Lq Jin X Fangmentioning

confidence: 99%

Interval Certitude Rule Base Inference Method using the Evidential Reasoning

Jin

Fang

2017

INT J COMPUT COMMUN

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“…Given a reciprocal preference relation on a set of alternatives, the concept of non-dominance degree introduced by Orlovsky [51] has been extensively used to rank the alternatives [10,23,38,61,63,65,66]. In the following, and in order to improve the understanding of the proposed correlation consensus degree, the consistency of the correlation consensus degree with Orlovsky's non-dominance degree is proved.…”

Section: Consistency Under Maximum Correlation Consensus Degreementioning

confidence: 99%

“…This fact could add to the consideration of the type of disorder as a factor to be taken into account in Clinical Decision-Making. 1.00 0.98 0.99 0.99 P (10) 1.00 0.98 0.97 P (11) 1.00 0.99 P (12) 1.00 Table 4: Correlation consensus degree (CCD) between pairs of patients.…”

Section: A Real Application: Concordance Among Patients' Preferencesmentioning

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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“…Apart from the hesitation, uncertainty may also be present: an expert may not possess a precise or sufficient level of knowledge of the problem to solve. This uncertainty is usually dealt with interval-valued fuzzy preference relations (IVFPRs), in which the elements are interval-valued fuzzy numbers (IVFNs) [20]- [25]. Recently, the relationship between hesitation and uncertainty has attracted some interest from researchers.…”

Section: Introductionmentioning

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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Construction of interval-valued fuzzy preference relations from ignorance functions and fuzzy preference relations. Application to decision making

Cited by 95 publications

References 50 publications

Interval Certitude Rule Base Inference Method using the Evidential Reasoning

Interval Certitude Rule Base Inference Method using the Evidential Reasoning

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

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

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