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

Alam, Nik Muhammad Farhan Hakim Nik Badrul; Khalif, Ku Muhammad Naim Ku; Jaini, Nor Izzati; Gegov, Alexander

doi:10.3390/info14070400

Cited by 14 publications

(3 citation statements)

References 96 publications

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“…However, future research on Z-numbers may include extensions of MCDM (multi-criteria decision-making) models based on these generalized Z-numbers: intuitionistic Z-numbers, neutrosophic Z-numbers, Pythagorean Z-numbers, and Fermatean Z-numbers. These generalized Z-numbers are considered the best representation of Z-numbers and have advantages that deserve further study [18]. This will effectively identify the strengths of these generalized Z-numbers and their application in various decision-making contexts.…”

Section: Discussion Of the Results Of The Study On Developing Methods...mentioning

confidence: 99%

Development of the method of general interpolation for Z-number-valued if-then rules

Jabbarova,

Rzayeva,

Jabbarova

2023

EEJET

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Rule interpolation-based methods are used when the rule base is sparse. This frequently being the case, as information relevant to real-world problems is not usually comprehensive. At the same time, relevant information is often characterized by both fuzziness and partial reliability. To deal with such kind of information, the concept of Z-number was introduced by Zadeh. This paper is devoted to an extension of the general interpolation method for fuzzy rules to the case of if-then rules with Z-number-valued antecedents and consequents. The proposed approach relies on the determination of the distance between the current observation vector and vectors of rules antecedents. By determining the distance between the current vector and the antecedents of the rules, decisions can be made based on the nearest antecedents. In this context, rule antecedents are vectors that represent certain conditions. The resulting output is computed as a weighted sum of rules consequents. Weighting factors are used to account for the importance of each rule in the interpolation. Weights of interpolations are found on the basis of mentioned distance values. The results of this study are aimed at developing an approach to decision-making in terms of Z-valued information. The method is characterized by relatively low computational complexith. Regarding the application of the proposed approach, the job satisfaction evaluation problem is considered. Consequently, the obtained results confirm the efficiency of the proposed approach. The proposed method can be a useful tool for decision-making in various applications, especially where high computational complexity is unacceptable or impractical

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Section: Discussion Of the Results Of The Study On Developing Methods...mentioning

confidence: 99%

Development of the method of general interpolation for Z-number-valued if-then rules

Jabbarova,

Rzayeva,

Jabbarova

2023

EEJET

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“…The level of confidence varies according to different experts, and the uncertainty and difference in the validity of their opinions cannot be ignored [61]. The advantage of Z-Numbers compared to conventional fuzzy methods is to consider uncertainty in the opinion of experts and assign credit to their opinion for estimating fuzzy parameters [62,63]. This issue was one of the limitations of the present study, which is recommended to be considered in future studies.…”

Section: Uncertaintymentioning

confidence: 90%

Prioritization of control measures in leakage scenario using Hendershot theory and FBWM-TOPSIS

Laal,

Khoshakhlagh,

Moradi Hanifi

et al. 2024

PLoS ONE

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Currently, there is increasing concern about the safety and leakage of process industries. Therefore, the present study aims to prioritize control measures before and after the leakage scenario by using the Hendershot theory and MCDM techniques. In this study, two proactive and reactive layers were selected before and after leakage of tanks, respectively. Then, criteria and alternatives were selected to perform fuzzy TOPSIS (FTOPSIS) and find the best alternative based on the literature review and Hendershot approach. The linear model of the fuzzy Best-Worst method (FBWM) was constructed and resolved using Lingo 17 software. Subsequently, criteria were assigned weights based on thorough calculations of the inconsistency rate. The weight of study experts was equal to 0.25. The results of FBWM showed that the reliability index with a weight of 0.3727 was ranked first and the inconsistency rate (ξ˜*/ξ) was calculated to be equal to 0.040. Inherent Safety Design (ISD) (0.899) and passive safety (0.767) also ranked first before and after tank leaks, respectively. Using the FBWM method leads to fewer pairwise comparisons and at the same time more stability. Although ISD and passive strategies are more valid and strict, elements of all strategies are necessary for a comprehensive process safety management program.

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“…Experts frequently use natural language to express their opinions on the probability of essential events in risk assessment. Still, the information used to make such decisions can often be ambiguous and only slightly reliable 17 . Zadeh introduced the notion of a fuzzy set (FS) to illustrate the ambiguity of information 18 .…”

Section: Introductionmentioning

confidence: 99%

An integrated Z-number and intuitionistic fuzzy sets for considering uncertainty in the risk assessment using the SHIPP methodology

Aliabadi,

Abbassi,

Moshiran

et al. 2024

Preprint

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Uncertainty presents a challenge in assessing risks, often resulting in outcomes that diverge from reality. System Hazard Identification, Prediction and Prevention (SHIPP), as one of the emerging risk assessment methods, aims to predict and effectively prevent accidents. This study aims to enhance the prediction potential of the SHIPP method by reducing uncertainty by combining Z-numbers and intuitionistic fuzzy logic. The experts' opinions and confidence levels regarding the prior probability of basic events (BEs) were measured using Intuitionistic Z-numbers (IZN). Subsequently, the SHIPP method utilized the obtained results and the actual data on unusual events in the industry to determine the posterior probability of barrier failure and consequences. The practical application of the developed methodology was demonstrated by selecting spherical tanks containing LPG. The results indicated that employing IZN to estimate the prior probability of BEs reduces uncertainty in determining the posterior probability of barrier failure and subsequent consequences. Consequently, enhancing the predictive accuracy of the SHIPP method in estimating the likelihood of unusual events will significantly improve the quality of risk management.

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

Cited by 14 publications

References 96 publications

Development of the method of general interpolation for Z-number-valued if-then rules

Development of the method of general interpolation for Z-number-valued if-then rules

Prioritization of control measures in leakage scenario using Hendershot theory and FBWM-TOPSIS

An integrated Z-number and intuitionistic fuzzy sets for considering uncertainty in the risk assessment using the SHIPP methodology

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