Modeling and implementation of Z-number

Patel, Purvag; Khorasani, Elham S.; Rahimi, Shahram

doi:10.1007/s00500-015-1591-y

Cited by 28 publications

(13 citation statements)

References 22 publications

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“…e angle is measured as the degree of dominance between the two Z-numbers. e geometric measurements of dominance degree for discrete Z j and Z k are defined as follows: 6 Mathematical Problems in Engineering…”

Section: Outranking Relationship and Dominancementioning

confidence: 99%

“…e concepts of Z-valuation [3], Z + -number [4] and Zinformation [5] are closely related to the concept of Znumbers. e proposed four concepts are shown in Table 1, where u A is the membership function of A and p X is the probability distribution of X. e second aspect is languagetype Z-number calculation and related extension [6,7], for example, Zarrin and Azadeh [8] combined Z-number with fuzzy cognitive map (FCM) and proposed a novel approach named Z-number cognitive map. ey evaluated and analyzed the impacts of resilience engineering (RE) principles on integrated health, safety, environment, and ergonomics (HSEE) management system.…”

Section: Introductionmentioning

confidence: 99%

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Dominance Degree Multiple Attribute Decision Making Based on Z‐Number Cognitive Information

Yao

Mao

et al. 2019

Mathematical Problems in Engineering

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Cognitive information can be described by Z-number fully and effectively. However, many problems of Z-number need to be further studied. In this paper, two hidden probability models for calculating Z-number are established to provide more intuitive and abundant information. Next, the dominance degree relationship of Z-number is developed and subdivided. Furthermore, combined with the hidden probability of calculation, three different measurements of dominance degree are defined from three levels of geometry, algebra, and cross entropy based on the outranking relationship. The influencing factors are analyzed for different combinations of two probability models and three dominance degree measures. A multiattribute decision model is established on the basis of new grey association analysis and QUALIFLEX method. Finally, a decision example is given to verify the effectiveness and feasibility of the method. And sensitivity analysis is made to determine the impact of parameters and hidden probability on the decision model.

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Section: Outranking Relationship and Dominancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dominance Degree Multiple Attribute Decision Making Based on Z‐Number Cognitive Information

Yao

Mao

et al. 2019

Mathematical Problems in Engineering

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“…e notion of a Z-number introduced by Zadeh [15] is described by a fuzzy number and its reliability measure to strengthen the reliability of the fuzzy information. After that, Z-numbers have been used for many areas [16][17][18][19][20][21][22]. Based on the truth, falsity, and indeterminacy Z-numbers, Du et al [23] extended the Z-number concept and proposed neutrosophic Z-numbers (NZNs) to enhance the reliability of the neutrosophic information, and then they presented basic operations of NZNs, score and accuracy functions of NZN, and the NZN weighted geometric averaging (NZNWGA) and NZN weighted arithmetic averaging (NZNWAA) operators and further established their MDM method under the environment of NZNs.…”

Section: Introductionmentioning

confidence: 99%

Multicriteria Decision-Making Method and Application in the Setting of Trapezoidal Neutrosophic Z-Numbers

Rui

2021

Journal of Mathematics

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The information expression and modeling of decision-making are critical problems in the fuzzy decision theory and method. However, existing trapezoidal neutrosophic numbers (TrNNs) and neutrosophic Z-numbers (NZNs) and their multicriteria decision-making (MDM) methods reveal their insufficiencies, such as without considering the reliability measures in TrNN and continuous Z-numbers in NZN. To overcome the insufficiencies, it is necessary that one needs to propose trapezoidal neutrosophic Z-numbers (TrNZNs), their aggregation operations, and an MDM method for solving MDM problems with TrNZN information. Hence, this study first proposes a TrNZN set, some basic operations of TrNZNs, and the score and accuracy functions of TrNZN and their ranking laws. Then, the TrNZN weighted arithmetic averaging (TrNZNWAA) and TrNZN weighted geometric averaging (TrNZNWGA) operators are presented based on the operations of TrNZNs. Next, an MDM approach using the proposed aggregation operators and score and accuracy functions is established to carry out MDM problems under the environment of TrNZNs. In the end, the established MDM approach is applied to an MDM example of software selection for revealing its rationality and efficiency in the setting of TrNZNs. The main advantage of this study is that the established approach not only makes assessment information continuous and reliable but also strengthens the decision rationality and efficiency in the setting of TrNZNs.

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“…Z‐number combined with constraint and reliability is proposed by Zadeh, which is an increasingly hot topic in the research field of fuzzy set . Z‐number is a good framework to express the thinking and knowledge of human flexibly .…”

Section: Introductionmentioning

confidence: 99%

“…Z-number combined with constraint and reliability is proposed by Zadeh, which is an increasingly hot topic in the research field of fuzzy set. [1][2][3][4] Z-number is a good framework to express the thinking and knowledge of human flexibly. [5][6][7] For a fuzzy user, the membership function of the constraint is relatively easy to obtain, whereas the possibility distribution of the reliability on the assigned membership function of the constraint is not easy to achieve.…”

Section: Introductionmentioning

confidence: 99%

Generating Z-number based on OWA weights using maximum entropy

Kang

Deng

Hewage

et al. 2018

Int. J. Intell. Syst.

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In the application of Z‐number, how to generate Z‐number is a significant and open issue. In this paper, we proposed a method of generating Z‐number based on the OWA weights using maximum entropy considering the attitude (preference) of the decision maker. Some numerical examples are used to illustrate the effectiveness of the proposed method. Results show that the attitude (preference) of the decision maker can give an optimal possibility distribution of the reliability for Z‐number using maximum entropy.

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Modeling and implementation of Z-number

Cited by 28 publications

References 22 publications

Dominance Degree Multiple Attribute Decision Making Based on Z‐Number Cognitive Information

Dominance Degree Multiple Attribute Decision Making Based on Z‐Number Cognitive Information

Multicriteria Decision-Making Method and Application in the Setting of Trapezoidal Neutrosophic Z-Numbers

Generating Z-number based on OWA weights using maximum entropy

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