An intuitionistic fuzzy graded covering rough set

Huang, Bing; Guo, Chunxiang; Li, Huaxiong; Feng, Gao; Zhou, Xianzhong

doi:10.1016/j.knosys.2016.06.006

Cited by 53 publications

(22 citation statements)

References 76 publications

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“…The notion of CSFRS is the generalized structure of intuitionistic fuzzy covering rough sets model given in Reference [38], if 0 ≤ ψ + λ ≤ 1 and η = 0. (b) : The notion of CSFRS is the generalized structure of Pythagorean fuzzy covering rough sets model given in Reference [39], if 0 ≤ (ψ ) 2 + (λ ) 2 ≤ 1 and η = 0.…”

Section: Remark 1 (A)mentioning

confidence: 99%

Covering-Based Spherical Fuzzy Rough Set Model Hybrid with TOPSIS for Multi-Attribute Decision-Making

et al. 2019

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In real life, human opinion cannot be limited to yes or no situations as shown in an ordinary fuzzy sets and intuitionistic fuzzy sets but it may be yes, abstain, no, and refusal as treated in Picture fuzzy sets or in Spherical fuzzy (SF) sets. In this article, we developed a comprehensive model to tackle decision-making problems, where strong points of view are in the favour; neutral; and against some projects, entities, or plans. Therefore, a new approach of covering-based spherical fuzzy rough set (CSFRS) models by means of spherical fuzzy β -neighborhoods (SF β -neighborhoods) is adopted to hybrid spherical fuzzy sets with notions of covering the rough set. Then, by using the principle of TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) to present the spherical fuzzy, the TOPSIS approach is presented through CSFRS models by means of SF β -neighborhoods. Via the SF-TOPSIS methodology, a multi-attribute decision-making problem is developed in an SF environment. This model has stronger capabilities than intuitionistic fuzzy sets and picture fuzzy sets to manage the vague and uncertainty. Finally, the proposed method is demonstrated through an example of how the proposed method helps us in decision-making problems.

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Section: Remark 1 (A)mentioning

confidence: 99%

Covering-Based Spherical Fuzzy Rough Set Model Hybrid with TOPSIS for Multi-Attribute Decision-Making

et al. 2019

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“…Uncertain measures like roughness measure, accuracy measure, entropy and granularity for covering rough set models were studied and a new kind of partial order was suggested [23]. Huang [24] discussed the uncertainty measures of information entropy and rough entropy.…”

Section: Basic Conceptmentioning

confidence: 99%

An Entropy-Based Neighborhood Rough Set and PSO-SVRM Model for Fatigue Life Prediction of Titanium Alloy Welded Joints

Zou

Sun

Yang

2019

Entropy

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In order to obtain comprehensive assessment of the factors influencing fatigue life and to further improve the accuracy of fatigue life prediction of welded joints, soft computing methods, including entropy-based neighborhood rough set reduction algorithm, the particle swarm optimization (PSO) algorithm and support vector regression machine (SVRM) are combined to construct a fatigue life prediction model of titanium alloy welded joints. By using an entropy-based neighborhood rough set reduction algorithm, the influencing factors of the fatigue life of titanium alloy welded joints such as joint type, plate thickness, etc. are analyzed and the reduction results are obtained. Fatigue characteristic domains are proposed and determined subsequently according to the reduction results. The PSO-SVRM model for fatigue life prediction of titanium alloy welded joints is established in the suggested fatigue characteristic domains. Experimental results show that by taking into account the impact of joint type, the PSO-SVRM model could better predict the fatigue life of titanium alloy welded joints. The PSO-SVRM model indicates the relationship between fatigue life and fatigue life influencing factors in multidimensional space compared with the conventional least-square S-N curve fitting method, it could predict the fatigue life of the titanium alloy welded joints more accurately thus helps to the reliability design of the structure. joint thickness and load model, the S-N sample data is compressed into a narrow band. In the present study, comprehensive and quantitative analysis of the influencing factors which affect the fatigue life of welded joints is lacking and the problem of low precision of fatigue life prediction of welded joints still exists.Thermodynamics entropy has been used for fatigue life prediction for a long time. For example, a damage metric based on the second law of thermodynamics and statistical mechanics was presented [8]. The proposed thermodynamic framework treated a solid body as a thermodynamic system and required that the entropy production be non-negative. A thermodynamic framework was presented for damage mechanics of solid materials [9]. It was believed that there was no need for physically meaningless empirical parameters to define a phenomenological damage potential surface or a Weibull function to trace damage evolution in solid continuum. A generalized theory of evolution based on the concept of tribo-fatigue entropy was proposed where tribo-fatigue entropy was determined by the processes of damage ability conditioned by thermodynamic and mechanical effects causing to the change of states of any systems [10]. The Shannon's differential entropies of both distributions of the strain in the loading direction and the first principal strain were employed at the tension peak of the cycles as measuring parameters of strain inhomogeneity [11]. A thermo-mechanical fatigue life prediction model based on the theory of damage mechanics was presented in [12]. The damage evolution, corresponding to the mate...

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“…In this section, we introduce the notions of intuitionistic fuzzy (IF) β-covering approximation space. There are two concepts presented by Huang et al in [33], which are IF β-covering and IF β-neighborhood in this approximation space. We mainly investigate some of their properties, and some new notions are presented.…”

Section: Some Properties Of If β-Covering Approximation Spacementioning

confidence: 99%

Two Types of Intuitionistic Fuzzy Covering Rough Sets and an Application to Multiple Criteria Group Decision Making

Wang

Zhang

2018

Symmetry

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Intuitionistic fuzzy rough sets are constructed by combining intuitionistic fuzzy sets with rough sets. Recently, Huang et al. proposed the definition of an intuitionistic fuzzy (IF) β -covering and an IF covering rough set model. In this paper, some properties of IF β -covering approximation spaces and the IF covering rough set model are investigated further. Moreover, we present a novel methodology to the problem of multiple criteria group decision making. Firstly, some new notions and properties of IF β -covering approximation spaces are proposed. Secondly, we study the characterizations of Huang et al.’s IF covering rough set model and present a new IF covering rough set model for crisp sets in an IF environment. The relationships between these two IF covering rough set models and some other rough set models are investigated. Finally, based on the IF covering rough set model, Huang et al. also defined an optimistic multi-granulation IF rough set model. We present a novel method to multiple criteria group decision making problems under the optimistic multi-granulation IF rough set model.

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An intuitionistic fuzzy graded covering rough set

Cited by 53 publications

References 76 publications

Covering-Based Spherical Fuzzy Rough Set Model Hybrid with TOPSIS for Multi-Attribute Decision-Making

Covering-Based Spherical Fuzzy Rough Set Model Hybrid with TOPSIS for Multi-Attribute Decision-Making

An Entropy-Based Neighborhood Rough Set and PSO-SVRM Model for Fatigue Life Prediction of Titanium Alloy Welded Joints

Two Types of Intuitionistic Fuzzy Covering Rough Sets and an Application to Multiple Criteria Group Decision Making

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