Distance Measures for Intuitionistic Fuzzy Sets and Interval Valued Intuitionistic Fuzzy Sets

Baccour, Leila; Alimi, Adel M.

doi:10.1109/fuzz-ieee.2019.8858789

Cited by 13 publications

(11 citation statements)

References 34 publications

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“…Distance measures are very powerful in comparing two objects based on their inequality content. For FSs and IFSs there are a lot of studies [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] concerning distance measures along with their various applications. Karmakar et al [43] suggested a Minkowski distance measure for Type-2 IFSs (T2IFSs) using the Hausdorff metric.…”

Section: Related Workmentioning

confidence: 99%

Some t-conorm-based distance measures and knowledge measures for Pythagorean fuzzy sets with their application in decision-making

Ganie

2022

Complex Intell. Syst.

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The Pythagorean fuzzy sets are more robust than fuzzy sets and intuitionistic fuzzy sets in dealing with the problems involving uncertainty. To compare two Pythagorean fuzzy sets, distance measures play a crucial role. In this paper, we have proposed some novel distance measures for Pythagorean fuzzy sets using t-conorms. We have also discussed their various desirable properties. With the help of suggested distance measures, we have introduced some new knowledge measures for Pythagorean fuzzy sets. Through numerical comparison and linguistic hedges, we have established the effectiveness of the suggested distance measures and knowledge measures, respectively, over the existing measures in the Pythagorean fuzzy setting. At last, we have demonstrated the application of the suggested measures in pattern analysis and multi-attribute decision-making.

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Section: Related Workmentioning

confidence: 99%

Some t-conorm-based distance measures and knowledge measures for Pythagorean fuzzy sets with their application in decision-making

Ganie

2022

Complex Intell. Syst.

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“…Fuzzy measure is a powerful method to describe the crossinteractions, especially the non-linear Choquet integral. It has been successfully applied in evidence fusion and intelligence information processing [5], [9], [19], [26]. Since the massive MIMO system's throughput is a multi-dimensional factor influenced conception, the interaction among contribution of contributions towards the objective system throughput can be measured adequately through a non-additive FM, which is the main feature of the Choquet integral model.…”

Section: Choquet Integral-based Interdependency and Significance Analysis Algorithmmentioning

confidence: 99%

DRESIA: Deep Reinforcement Learning-Enabled Gray Box Approach for Large-Scale Dynamic Cyber-Twin System Simulation

Lin

Yang

et al. 2021

IEEE Open J. Comput. Soc.

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The massive data generated by large-scale dynamic systems makes its optimization facing a tough challenge. Traditional White Box-based methods directly model the internal operating mechanism of the system, so massive amounts of measured data need to be handled, which is costly and time-consuming. The poor interpretability of the Black Box-based methods makes it difficult to adapt to the dynamic environment. Thus we propose a novel Gray Box-based approach namely Deep Reinforcement Learning-enabled Constraint Set Inversion Algorithm (DRESIA), which establishes a quantitative model of the nonlinear interoperability effects of system internal states which simplifies the White Box's complex mechanism of reconstruction and prediction and retains the interpretability of the model, therefore improves the prediction efficiency of feasible region while also improving the generalization ability. It further improves the dynamic adaptability of the modeling environment, which provides a new performance balancing scheme for system modeling. Under the premise that the large-scale 5G Cyber-Twin system satisfies the given Quality of Service(QoS) requirements, we perform DRESIA to realize the efficient and dynamic optimal search of feasible region, the results show that the DRESIA reduces the computational cost, and balances the accuracy and robustness of the feasible region, which validate the effectiveness and superiority of Gray Box-based approach.

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“…Once the Type-1 membership functions have been chosen, all the uncertainty disappears, because Type-1 membership functions are totally precise. Different Type-1 generalizations such as Hesitant Fuzzy Sets [2], Fuzzy Multi Sets [3], Intuitionistic Fuzzy Sets (IFSs) [4], Interval and General Type-2 Fuzzy Sets (IT-2 FSs and T-2 FSs respectively) [5]- [9] have been adopted. In fact, T-2 FSs have been applied especially to handle high uncertainty levels in some real world data and applications.…”

Section: Introductionmentioning

confidence: 99%

“…In some real world applications, data optimization, feature selection [15], [16], classification and similarity factorization [17], [18] are based essentially on the definition of adequate measures. In this context, several types of measures such as distance [4], entropy [19], correlation [20], divergence [21], dissimilarity [22] and similarity measures [10] were introduced in the literature. In order to indicate the degree of closeness between fuzzy sets (FSs) in applications like pattern recognition, computing with words and data mining, Fuzzy Similarity Measures (FSMs) were utilized.…”

Section: Introductionmentioning

confidence: 99%

Novel Intuitionistic-Based Interval Type-2 Fuzzy Similarity Measures With Application to Clustering

Cherif¹,

Baklouti

Hagras

et al. 2022

IEEE Trans. Fuzzy Syst.

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Similarity measures have been widely used in applications dealing with reasoning, classification and information retrieval. In this paper, we first propose three new Interval Type-2 Fuzzy Similarity measures (IT-2 FSMs) as a dual concept of some semi-metric distances between Intuitionistic Fuzzy Sets (IFSs). We also prove that the extended IT-2 FSMs satisfy many common properties (i.e. reflexivity, transivity, symmetry and overlapping). Experiments are carried out on a variety of datasets including UCI Learning Machine and real data. Comparative studies between the proposed IT-2 FSMs and the other well-known existing similarity measures (Gorzalczany, Bustince, Mitchell, Zeng and Li as well as VSM and Jaccard) are performed. Obviously, the best results are obtained with the IT-2 FSMs being resilient to the high levels of uncertainty noise. We also prove that our IT-2 FSMs can overcome the drawbacks of some existing similarity measures based on the accuracy rate measure. In addition, the proposed IT-2 FSMs are joined with Fuzzy cmeans algorithm as a clustering method and the proposed system is compared against the existing clustering algorithms (Type-1 Fuzzy k-means, Type-1 and Type-2 Fuzzy c-means, Cluster Forest, Bagged Clustering, Evidence Accumulation and Random Projection). Relying on the clustering quality parameters R and C (equivalent to the standard classification accuracy), the advanced IT-2FSMs show higher classification accuracy of about 86% which outperforms nearly the other classifiers.

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Distance Measures for Intuitionistic Fuzzy Sets and Interval Valued Intuitionistic Fuzzy Sets

Cited by 13 publications

References 34 publications

Some t-conorm-based distance measures and knowledge measures for Pythagorean fuzzy sets with their application in decision-making

Some t-conorm-based distance measures and knowledge measures for Pythagorean fuzzy sets with their application in decision-making

DRESIA: Deep Reinforcement Learning-Enabled Gray Box Approach for Large-Scale Dynamic Cyber-Twin System Simulation

Novel Intuitionistic-Based Interval Type-2 Fuzzy Similarity Measures With Application to Clustering

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