Clustering method for production of Z-number based if-then rules

Aliev, R. A.; Pedrycz, Witold; Guirimov, B. G.; Huseynov, Oleg H.

doi:10.1016/j.ins.2020.02.002

Cited by 41 publications

(5 citation statements)

References 37 publications

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“…[8], including addition, subtraction, multiplication, division, square, square root, absolute value, ranking and distance of Z-numbers. On this basis, more advanced arithmetic is proposed, including Z-numbers based Linear Program (Z-LP) [4], Z-numbers function [6], Approximate Reasoning [7], the parametric form [21], the negation operator [17], total utility [14], Z-Differential equations [19], multidimensional Z-numbers [23], Z-number ifthen rules [5], soft likelihood function [24], Z-mixture-numbers [27]. Ref.…”

Section: Instructionmentioning

confidence: 99%

“…The uncertainty of Z-numbers in decision matrix are displayed in ((70, 100, 120), (0, 0.17, 0.33)) ((3, 5, 7), (0.33, 0.5, 0.67)) a 2 ((20, 24, 25), (0, 0, 0.17)) ((40, 70, 100), ((0.33, 0.5, 0.67)) ( (5,8,11), (0.67, 0.83, 1)) a 3 ((14, 15, 16), (0.83, 1, 1)) ((60, 80, 100), (0.67, 0.83, 1)) ((1, 4, 7), (0.67, 0.83, 1)) AS there are negative numbers, we add a constant:…”

Section: Applicationmentioning

confidence: 99%

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A Modified Uncertainty Measure of Z-numbers

Cabrerizo

Herrera‐Viedma

Morente-Molinera

2022

INT J COMPUT COMMUN, Int. J. Comput. Commun. Control

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The Z-number is a more adequate construct for describing real-life information. While considering the uncertainty of the information, it also models the partial reliability of the information. It is a combination of probabilistric restriction and possibilistric restriction. In this paper, we modified the uncertainty measurement of the discrete Z-number and proposed the uncertainty measurement of the continuous Z-number. Some numerical examples are used to illustrate the calculation processes and advantages of the proposed method. An application of journey vehicle selection shows the effectiveness of the proposed uncertainty measurement in determining the weights of criteria.

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Section: Instructionmentioning

confidence: 99%

Section: Applicationmentioning

confidence: 99%

A Modified Uncertainty Measure of Z-numbers

Cabrerizo

Herrera‐Viedma

Morente-Molinera

2022

INT J COMPUT COMMUN, Int. J. Comput. Commun. Control

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“…A method for clustering Z-information based on c-means fuzzy clustering algorithm with a preliminary transformation of Z-numbers into ordinary fuzzy numbers was developed in [29]. In [30], the basic problem of bimodal clustering is investigated and a method for constructing Z-valued clusters is proposed. In [31], an approach to clustering Z-information based on the relationship between Z-numbers and type II fuzzy sets is proposed.…”

Section: Introductionmentioning

confidence: 99%

Clustering Z-information based on a system of fuzzy reference requirements

Poleshchuk

2023

E3S Web Conf.

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The paper develops a clustering model of multi-criteria object evaluations, taking into account the reliability of the results obtained. Clustering is based on a system of fuzzy reference requirements about the importance of the evaluated characteristics of objects for each of the clusters. Object evaluations are formalized on the basis of linguistic Z-numbers, both fuzzy numbers of which are the values of linguistic variables. Information for each object and each cluster is presented as a set of pairs (according to the number of characteristics) consisting of a fuzzy number (importance of a characteristic for the corresponding cluster) and a Z-number (an evaluation of the object within this characteristic and its reliability). Using this information, fuzzy ratings are determined for each object in accordance with fuzzy reference requirements for each cluster. Fuzzy ratings of objects, defined as fuzzy numbers, reflect the compliance of multi-criteria ratings of objects with fuzzy reference requirements. The comparative analysis of fuzzy ratings of all objects within one cluster proposed in the paper makes it possible to identify the best representative (or best representatives) of the cluster under consideration and determine the degree of belonging of the remaining objects to this cluster. The analysis is carried out for all clusters. A numerical example is given, which shows the effectiveness of the developed method under Z-information.

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“…In [29], a fuzzy clustering algorithm is described that combines the conversion of Z-numbers into fuzzy numbers and then the application of c-means fuzzy clustering algorithm. In [30], the problem of bimodal clustering is formulated in terms of constructing Z-valued clusters. This paper explores the fundamentals of the bimodal clustering problem and proposes a comprehensive solution method.…”

Section: Introductionmentioning

confidence: 99%

Clustering Z-Information Based on Semantic Spaces

Poleshchuk

2021

Lecture Notes in Networks and Systems

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In the paper a model for clustering Z-information is developed. Zinformation is represented by the sets of Z-numbers. Each of the sets is an expert criterion model for assessing a certain characteristic. The first and the second components of Z-numbers are the values of full orthogonal semantic spaces. The first components of Z-numbers are the formalizations of the levels of the linguistic scale used by experts to assess the characteristic. The second components of Znumbers are the formalizations of the levels of the linguistic scale used by experts to assess the reliability of their results. The distances between expert criteria (sets of Z-numbers) are found using aggregating indicators for Z-numbers. Based on pairwise distances between sets of Z-numbers (expert criteria), fuzzy binary relation of similarity is determined on a set of criteria. A fuzzy conformity relation is constructed using the transitive closure of the determined fuzzy similarity relation. The constructed fuzzy conformity relation is decomposed into equivalence relations. Depending on α-levels of fuzzy conformity relations, the set of expert criteria, represented by sets of Z-numbers, can be divided into clusters of criteria similar among themselves with α-levels of confidence.

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Clustering method for production of Z-number based if-then rules

Cited by 41 publications

References 37 publications

A Modified Uncertainty Measure of Z-numbers

A Modified Uncertainty Measure of Z-numbers

Clustering Z-information based on a system of fuzzy reference requirements

Clustering Z-Information Based on Semantic Spaces

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