A Review on Ranking of Z-numbers

Bilgin, Firat; Alcı, Musa

doi:10.30564/jcsr.v4i2.4499

Cited by 2 publications

(4 citation statements)

References 24 publications

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“…Ezadi et al [96] used the conversion of Z-number into a regular fuzzy number and further ranked it using the sigmoid function, as shown in (17).…”

Section: Sigmoid Function and Convex Combinationmentioning

confidence: 99%

“…Hence, the current research trend on Znumbers has motivated the authors to conduct a literature review, specifically on the decision making with Z-numbers. There have been several review papers on Z-numbers such as [13,16,17], but the topic is quite wide and not only focused on decision making. The review by [13] focused on the arithmetic concepts of Z-numbers and their applications in decision making, regression, system control, machine learning, and computing with words (CWW).…”

Section: Introductionmentioning

confidence: 99%

“…Banerjee et al [16] reviewed the theoretical concepts and applications of Z-numbers in CWW, decision making, multisensor data fusion, dynamic controller, and safety analytics. Bilgin and Alci [17] specifically reviewed the ranking methods of Z-numbers.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, existing MCDM methods based on Z-numbers were explored in this research to make comparative evaluations of the advantages and disadvantages of each of them. Based on the comparative analysis, the strength of each method was identified for the implementation in the development of the MCDM method based There have been several review papers on Z-numbers such as [13,16,17], but the topic is quite wide and not only focused on decision making. The review by [13] focused on the arithmetic concepts of Z-numbers and their applications in decision making, regression, system control, machine learning, and computing with words (CWW).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Application of Z-Numbers in Fuzzy Decision Making: The State of the Art

et al. 2023

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A Z-number is very powerful in describing imperfect information, in which fuzzy numbers are paired such that the partially reliable information is properly processed. During a decision-making process, human beings always use natural language to describe their preferences, and the decision information is usually imprecise and partially reliable. The nature of the Z-number, which is composed of the restriction and reliability components, has made it a powerful tool for depicting certain decision information. Its strengths and advantages have attracted many researchers worldwide to further study and extend its theory and applications. The current research trend on Z-numbers has shown an increasing interest among researchers in the fuzzy set theory, especially its application to decision making. This paper reviews the application of Z-numbers in decision making, in which previous decision-making models based on Z-numbers are analyzed to identify their strengths and contributions. The decision making based on Z-numbers improves the reliability of the decision information and makes it more meaningful. Another scope that is closely related to decision making, namely, the ranking of Z-numbers, is also reviewed. Then, the evaluative analysis of the Z-numbers is conducted to evaluate the performance of Z-numbers in decision making. Future directions and recommendations on the applications of Z-numbers in decision making are provided at the end of this review.

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“…Ezadi et al [96] used the conversion of Z-number into a regular fuzzy number and further ranked it using the sigmoid function, as shown in (17).…”

Section: Sigmoid Function and Convex Combinationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Application of Z-Numbers in Fuzzy Decision Making: The State of the Art

et al. 2023

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On a total order on the set of Z-numbers based on discrete fuzzy numbers

Mir-Fuentes,

De Miguel,

Massanet

et al. 2024

Comp. Appl. Math.

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Z-numbers were introduced by Zadeh in 2011 as a pair of fuzzy numbers (A, B), where A is interpreted as a fuzzy restriction on the values of a variable, while B is interpreted as a measure of certainty or sureness of A. From the initial proposal, several other approaches have been introduced in order to reduce the computational cost of the involved operations. One of such approaches is called discrete Z-numbers where A and B are modelled as discrete fuzzy numbers. In this paper, the construction of total orders on the set of discrete Z-numbers is investigated for the first time. Specifically, the total order is designed for discrete Z-numbers where the second component has membership values belonging to a finite and prefixed set of values. The method relies on solid and coherent linguistic criteria and several linguistic properties are analyzed. The order involves the transformation of the first components of the discrete Z-numbers by using the credibility of the second components in the sense that a lower credibility enlarges in a greater extent the uncertainty of the first component. Then a total order on the set of discrete fuzzy numbers is applied. Finally, a practical example on how to order discrete Z-numbers is presented and a comparison with other ranking methods is performed from which the strengths of our method are stressed.

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A Review on Ranking of Z-numbers

Cited by 2 publications

References 24 publications

The Application of Z-Numbers in Fuzzy Decision Making: The State of the Art

The Application of Z-Numbers in Fuzzy Decision Making: The State of the Art

On a total order on the set of Z-numbers based on discrete fuzzy numbers

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