A ranking model of Z-mixture-numbers based on the ideal degree and its application in multi-attribute decision making

Xian, Sidong; Chai, Jiahui; Li, Tangjin; Huang, Jie

doi:10.1016/j.ins.2020.10.038

Cited by 32 publications

(5 citation statements)

References 49 publications

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“…Let us take a universal set "A". Now a "K A " is a Z-number [35] that is in fact an order pair restraining fuzzified numbers, such that it is of the following form explained in [37],…”

Section: Definition 1 Let Us Take Into Consideration An Elementary Setmentioning

confidence: 99%

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A Systematic Formulation into Neutrosophic Z Methodologies for Symmetrical and Asymmetrical Transportation Problem Challenges

Kamran,

Abdalla,

Nadeem

et al. 2024

Symmetry

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This study formulates a multi-objective, multi-item solid transportation issue with parameters that are neutrosophic Z-number fuzzy variables such as transportation costs, supplies, and demands. This work covers two scenarios where uncertainty in the problem can arise: the fuzzy solid transportation problem and the interval solid transportation problem. The first scenario arises when we represent data problems as intervals instead of exact values, while the second scenario arises when the information is not entirely clear. We address both models when the uncertainty alone impacts the constraint set. In order to find a solution for the interval case, we generate an additional problem. Since this auxiliary problem is typical of solid transportation, we can resolve it using the effective techniques currently in use. In the fuzzy scenario, a parametric method is used to discover a fuzzy solution to the earlier issue. Parametric analysis identifies that the best parameterized approaches to complementary problems are characterized by the application of parametric analysis. We present a suggested algorithm for determining the stability set. Finally, we provide a numerical example and sensitivity analysis for the transportation problem, which is both symmetrical and asymmetrical.

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“…Let us take a universal set "A". Now a "K A " is a Z-number [35] that is in fact an order pair restraining fuzzified numbers, such that it is of the following form explained in [37],…”

Section: Definition 1 Let Us Take Into Consideration An Elementary Setmentioning

confidence: 99%

“…Assume we have a universal set "A". The neutrosophic Z-number [37] "W A " is of the form demonstrated mathematically below:…”

Section: Definition 1 Let Us Take Into Consideration An Elementary Setmentioning

confidence: 99%

A Systematic Formulation into Neutrosophic Z Methodologies for Symmetrical and Asymmetrical Transportation Problem Challenges

Kamran,

Abdalla,

Nadeem

et al. 2024

Symmetry

View full text Add to dashboard Cite

show abstract

“…[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%

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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“…Wang et al (2017) and combined language and Z-number and proposed linguistic Z-numbers and Z-linguistic variables, respectively. Because of its superiority in the completeness of information representation, it is widely used in decision making (Krohling et al 2019;Peng et al 2019;Dai et al 2008;Tao et al 2020;Xian et al 2021).…”

Section: Introductionmentioning

confidence: 99%

$$\chi$$-linguistic sets and its application for the linguistic multi-attribute group decision making

Xian,

Liu,

Xian

et al. 2024

Artif Intell Rev

Self Cite

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The information in the real world often contains many properties such as fuzziness, randomness, and approximation. Although existing linguistic collections attempt to solve these problems, with the emergence of more and more constraints and challenges, this information cannot fully express the problem, leading to an increasing demand for methods that can contain multiple uncertain information. In this paper, we comprehensively consider the various characteristics of information including membership degree, credibility and approximation based on rough sets, and propose the concept of $$\chi$$ χ -linguistic sets ($$\chi$$ χ LSs), which depend on original data rather than prior knowledge and effectively solve the problem of incomplete information representation. At the same time, the corresponding theories such as the comparison method and operational rules have also been proposed. Subsequently, we construct a new $$\chi$$ χ -linguistic VIKOR ($$\chi$$ χ LVIKOR) method for multi-attribute group decision making (MAGDM) problem with $$\chi$$ χ LSs, and apply it to the risk assessment of COVID-19. Through comparative analysis, we discuss the effectiveness and superiority of $$\chi$$ χ LSs.

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A ranking model of Z-mixture-numbers based on the ideal degree and its application in multi-attribute decision making

Cited by 32 publications

References 49 publications

A Systematic Formulation into Neutrosophic Z Methodologies for Symmetrical and Asymmetrical Transportation Problem Challenges

A Systematic Formulation into Neutrosophic Z Methodologies for Symmetrical and Asymmetrical Transportation Problem Challenges

A Modified Uncertainty Measure of Z-numbers

$$\chi$$-linguistic sets and its application for the linguistic multi-attribute group decision making

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