Literature review on type-2 fuzzy set theory

De, Arnab Kumar; Chakraborty, Debjani; Biswas, Animesh

doi:10.1007/s00500-022-07304-4

Cited by 22 publications

(6 citation statements)

References 113 publications

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“…Based on the theory of fuzzy mathematics, the fuzzy comprehensive evaluation method established by the fuzzy set [41] can integrate multiple indicators to evaluate the evaluation object. This method divides the scope of the object to evaluate it.…”

Section: Evaluation Methods Of Loess Slope Stabilitymentioning

confidence: 99%

Fuzzy Comprehensive Evaluation Method for Evaluating Stability of Loess Slopes

Deng,

Xiang

2023

Advances in Civil Engineering

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The stability assessment of loess slopes is of great significance for slope reinforcement and safety assessment. This research studies the main factors affecting the stability of the loess slope through the summary and analyzes the failure cases of the loess slope in Shaanxi Province. The importance of influencing factors was studied through numerical simulation method, sensitivity analysis method, and gray correlation analysis method, and the weight value method was given. On this basis, we have developed the fuzzy comprehensive evaluation model method for assessing the stability of loess slopes based on the principle of maximum membership degree. Finally, the method was applied to the stability analysis of the actual loess slope, and the rationality and correctness of the loess slope stability evaluation method proposed in this paper were demonstrated. The results showed that, for the Shaanxi loess slope, the probability of instability of the positive slopes is far greater than that of negative slopes; the greater the slope gradient, the more unstable the loess slopes. Collapse mainly occurs in the range of 10–40 m slope height. There is a significant positive correlation between rainfall and the probability of loess landslides. The degree of correlation between the factors influencing slope stability and the safety factor can be categorized from strong to weak as follows: slope inclination > internal friction angle > height of the slope > gravitational forces > cohesion > Poisson’s ratio > modulus of elasticity, and the influence of Poisson’s ratio and elastic modulus can be ignored. The fuzzy comprehensive evaluation method based on the gray correlation degree method established in this paper was used to evaluate the stability of the loess slopes. The evaluation results attested to the actual data of slope monitoring. The evaluation method proves reasonable and feasible and can be well applied to the stability analysis of the loess slopes.

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Section: Evaluation Methods Of Loess Slope Stabilitymentioning

confidence: 99%

Fuzzy Comprehensive Evaluation Method for Evaluating Stability of Loess Slopes

Deng,

Xiang

2023

Advances in Civil Engineering

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“…The Type-2 FSs and relations were introduced by Zadeh [34] and developed by Mizumoto and Tanaka [35] and Karnik and Mendel [36] as a generalization of a Type-1 FS (that is, an ordinary fuzzy set). A detailed overview of the applications of fuzzy sets and Type-2 fuzzy sets, demonstrating how these concepts have been applied in different fields, one can find in [37]. Similar to a classical Type-1 fuzzy relation (T1FR) (that is, an ordinary fuzzy relation), one can introduce the notion of a T2FR on a universal set X as a Type-2 FS on the Cartesian product X × X.…”

Section: Type-2 Fuzzy Relationsmentioning

confidence: 99%

On Kemeny Optimization Scheme for Fuzzy Set of Relations

Mashchenko,

Kapustian,

Rubino

2023

Axioms

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The present paper investigated the aggregation of individual preferences into a group fuzzy preference relation for a fuzzy set of decision-makers (DMs). This aggregation is based on the Kemeny optimization scheme. It was proven that this group relation is a Type-2 fuzzy relation (T2FR). The decomposition approach was used to analyze the group T2FR. It is shown that the group T2FR can be decomposed according to secondary membership grades into a finite collection of Type-1 fuzzy relations. Each of them is a group fuzzy relation for a crisp set of DMs, which is the corresponding α-cut of the original fuzzy set of DMs. Illustrative examples are given.

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“…Звідси перед розробниками виникає задача вибору типу нечітких множин, за допомогою яких можна було б достатньо просто обробляти різні види невизначеностей. У праці [3] розглядаються питання, пов'язані з розвитком теорії нечітких множин типу-1 і типу-2 та наводиться мотивація адекватно подавати невизначеності, які існують в предметній області, за допомогою множин типу-2.…”

Section: проблемиunclassified

Interval type-2 generalizing fuzzy model for monitoring the states of complex systems using expert knowledge

Kondratenko¹,

Snihur²,

Кондратенко³

2023

SRIT

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A type-2 interval generalizing fuzzy model is proposed for monitoring complex systems’ states. A set-theoretic approach is proposed to generalize the results of type-2 fuzzy models with interval membership functions. The study of the correspondence of expert assessments to the output value of the generalizing fuzzy model over the observation interval is presented. Examples of the use of generalizing fuzzy model type-2 in the task of monitoring the conditions of an artesian well are given. It is shown that in order to improve the quality of decisions made, the expert needs to pay attention to the value of the interval output of the generalizing type-2 fuzzy model. Recommendations are presented to experts to improve decision-making regarding the estimation of the output interval of the generalizing model.

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Literature review on type-2 fuzzy set theory

Cited by 22 publications

References 113 publications

Fuzzy Comprehensive Evaluation Method for Evaluating Stability of Loess Slopes

Fuzzy Comprehensive Evaluation Method for Evaluating Stability of Loess Slopes

On Kemeny Optimization Scheme for Fuzzy Set of Relations

Interval type-2 generalizing fuzzy model for monitoring the states of complex systems using expert knowledge

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