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Zeitschriftenartikel zum Thema „Possibilistic similarity“

Autor: Grafiati

Veröffentlicht am 8. Februar 2025

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1

SGARRO, ANDREA. „UTILITIES AND DISTORTIONS: AN OBJECTIVE APPROACH TO POSSIBILITIES CODING“. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 13, Nr. 02 (April 2005): 139–61. http://dx.doi.org/10.1142/s0218488505003369.

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We re-take the possibilistic (as opposed to probabilistic) approach to information coding put forward in 1,2. To enhance the possibilistic approach also outside the realm of "subjective" uncertainties, in this paper we adopt an "objective" interpretation of possibilistic source coding based on utility functions and an "objective" interpretation of possibilistic channel coding based on distortion measures and similarity indices. We stress the relationship between possibilistic coding as based on distortions between sequences and algebraic coding as based on minimum distances between codewords. We compute the operational (coding-theoretic) entropy for a new class of possibilistic sources.

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2

Singh, Abhishek, und Anil Kumar. „Introduction of Local Spatial Constraints and Local Similarity Estimation in Possibilistic c-Means Algorithm for Remotely Sensed Imagery“. Journal of Modeling and Optimization 11, Nr. 1 (15.06.2019): 51–56. http://dx.doi.org/10.32732/jmo.2019.11.1.51.

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This paper presents a unique Possibilistic c-Means with constraints (PCM-S) with Adaptive Possibilistic Local Information c-Means (ADPLICM) in a supervised way by incorporating local information through local spatial constraints and local similarity measures in Possibilistic c-Means Algorithm. PCM-S with ADPLICM overcome the limitations of the known Possibilistic c-Means (PCM) and Possibilistic c-Means with constraints (PCM-S) algorithms. The major contribution of proposed algorithm to ensure the noise resistance in the presence of random salt & pepper noise. The effectiveness of proposed algorithm has been analysed on random “salt and pepper” noise added on original dataset and Root Mean Square Error (RMSE) has been calculated between original dataset and noisy dataset. It has been observed that PCM-S with ADPLICM is effective in minimizing noise during supervised classification by introducing local convolution.

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3

Miyamoto, Sadaaki, Youhei Kuroda und Kenta Arai. „Algorithms for Sequential Extraction of Clusters by Possibilistic Method and Comparison with Mountain Clustering“. Journal of Advanced Computational Intelligence and Intelligent Informatics 12, Nr. 5 (20.09.2008): 448–53. http://dx.doi.org/10.20965/jaciii.2008.p0448.

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In addition to fuzzy c-means, possibilistic clustering is useful because it is robust against noise in data. The generated clusters are, however, strongly dependent on an initial value. We propose a family of algorithms for sequentially generating clusters “one cluster at a time,” which includes possibilistic medoid clustering. These algorithms automatically determine the number of clusters. Due to possibilistic clustering's similarity to the mountain clustering by Yager and Filev, we compare their formulation and performance in numerical examples.

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4

Juarez, Jose M., Francisco Guil, Jose Palma und Roque Marin. „Temporal similarity by measuring possibilistic uncertainty in CBR“. Fuzzy Sets and Systems 160, Nr. 2 (Januar 2009): 214–30. http://dx.doi.org/10.1016/j.fss.2008.05.017.

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5

Yu yu Liao, Ke xin Jia und Zi shu He. „Similarity Measure based Robust Possibilistic C-means Clustering Algorithms“. Journal of Convergence Information Technology 6, Nr. 12 (31.12.2011): 129–38. http://dx.doi.org/10.4156/jcit.vol6.issue12.17.

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6

Charfi, Amal, Sonda Ammar Bouhamed, Eloi Bosse, Imene Khanfir Kallel, Wassim Bouchaala, Basel Solaiman und Nabil Derbel. „Possibilistic Similarity Measures for Data Science and Machine Learning Applications“. IEEE Access 8 (2020): 49198–211. http://dx.doi.org/10.1109/access.2020.2979553.

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7

Bai, Xiangzhi, Yuxuan Zhang, Haonan Liu und Zhiguo Chen. „Similarity Measure-Based Possibilistic FCM With Label Information for Brain MRI Segmentation“. IEEE Transactions on Cybernetics 49, Nr. 7 (Juli 2019): 2618–30. http://dx.doi.org/10.1109/tcyb.2018.2830977.

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8

Alsahwa, B., B. Solaiman, É. Bossé, S. Almouahed und D. Guériot. „A Method of Spatial Unmixing Based on Possibilistic Similarity in Soft Pattern Classification“. Fuzzy Information and Engineering 8, Nr. 3 (September 2016): 295–314. http://dx.doi.org/10.1016/j.fiae.2016.11.004.

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9

Devi, R. „Unsupervised Kernel-Induced Fuzzy Possibilistic C-Means Technique in Investigating Real-World Data“. Journal of Physics: Conference Series 2199, Nr. 1 (01.02.2022): 012033. http://dx.doi.org/10.1088/1742-6596/2199/1/012033.

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Abstract The goal of this study is to break down a large dataset into meaningful groupings. Due to the vast dimension and significant resemblance seen among data, exploring divided clusters in real-world datasets is the most difficult assignment. As a result, this work proposes a fuzzy set-based unsupervised effective clustering technique that includes possibilistic memberships, and fuzzy membership degrees into the membership, weighted Cauchy kernel-based similarity measure and center equations. The empirical findings demonstrate the feasibility of the proposed effective clustering technique.

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10

Schockaert, Steven, und Henri Prade. „An Inconsistency-Tolerant Approach to Information Merging Based on Proposition Relaxation“. Proceedings of the AAAI Conference on Artificial Intelligence 24, Nr. 1 (03.07.2010): 363–68. http://dx.doi.org/10.1609/aaai.v24i1.7583.

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Inconsistencies between different information sources may arise because of statements that are inaccurate, albeit not completely false. In such scenarios, the most natural way to restore consistency is often to interpret assertions in a more flexible way, i.e. to enlarge (or relax) their meaning. As this process inherently requires extra-logical information about the meaning of atoms, extensions of classical merging operators are needed. In this paper, we introduce syntactic merging operators, based on possibilistic logic, which employ background knowledge about the similarity of atomic propositions to appropriately relax propositional statements.

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11

Prema, S., und P. Umamaheswari. „Similarity based Fuzzy and Possibilistic K-Means Clustering on Biomedical Data for Disease Evaluation“. Asian Journal of Research in Social Sciences and Humanities 6, Nr. 6 (2016): 1062. http://dx.doi.org/10.5958/2249-7315.2016.00266.5.

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12

Sangüesa, Ramón, Joan Cabós und Ulises Cortés. „Possibilistic conditional independence: A similarity-based measure and its application to causal network learning“. International Journal of Approximate Reasoning 18, Nr. 1-2 (Januar 1998): 145–67. http://dx.doi.org/10.1016/s0888-613x(98)00012-7.

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13

Cristaldi, Loredana, Alessandro Ferrero, Simona Salicone und Giacomo Leone. „A Possibilistic Approach for Uncertainty Representation and Propagation in Similarity-Based Prognostic Health Management Solutions“. Open Journal of Statistics 10, Nr. 06 (2020): 1020–38. http://dx.doi.org/10.4236/ojs.2020.106058.

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14

A. Viattchenin, Dmitri. „Distances and Similarity Measures in Heuristic Possibilistic Clustering the Intuitionistic Fuzzy Data: A Comparative Study“. International Journal of Sustainability Management and Information Technologies 3, Nr. 6 (2017): 57. http://dx.doi.org/10.11648/j.ijsmit.20170306.11.

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15

Alsinet, Teresa, und Lluı́s Godo. „Adding similarity-based reasoning capabilities to a Horn fragment of possibilistic logic with fuzzy constants“. Fuzzy Sets and Systems 144, Nr. 1 (Mai 2004): 43–65. http://dx.doi.org/10.1016/j.fss.2003.10.013.

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16

Ye, Fei, und Qiang Lin. „Partner Selection in a Virtual Enterprise: A Group Multiattribute Decision Model with Weighted Possibilistic Mean Values“. Mathematical Problems in Engineering 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/519629.

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This paper proposes an extended technique for order preference by similarity to ideal solution (TOPSIS) for partner selection in a virtual enterprise (VE). The imprecise and fuzzy information of the partner candidate and the risk preferences of decision makers are both considered in the group multiattribute decision-making model. The weighted possibilistic mean values are used to handle triangular fuzzy numbers in the fuzzy environment. A ranking procedure for partner candidates is developed to help decision makers with varying risk preferences select the most suitable partners. Numerical examples are presented to reflect the feasibility and efficiency of the proposed TOPSIS. Results show that the varying risk preferences of decision makers play a significant role in the partner selection process in VE under a fuzzy environment.

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17

DUBOIS, DIDIER, LLUÍS GODO, HENRI PRADE und ADRIANA ZAPICO. „ON THE POSSIBILISTIC DECISION MODEL: FROM DECISION UNDER UNCERTAINTY TO CASE-BASED DECISION“. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 07, Nr. 06 (Dezember 1999): 631–70. http://dx.doi.org/10.1142/s0218488599000532.

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This paper improves a previously proposed axiomatic setting for qualitative decision under uncertainty in the von Neumann and Morgenstern' style, where only ordinal linear scales are required for assessing uncertainty and utility. Two qualitative criteria are axiomatized in a finite setting: a pessimistic one and an optimistic one, respectively obeying an uncertainty aversion axiom and an uncertainty-attraction axiom. These criteria generalize the well-known maximin and maximax criteria, making them more realistic. They are suited to one-shot decisions and they are not based on the notion of mean value, but take the form of medians. Elements for a qualitative case-based decision methodology are also proposed, with pessimistic and optimistic evaluations formally similar to the expressions which cope with uncertainty, up to modifying factors which cope with the lack of normalization of similarity evaluations. Finally two extensions of the model are analysed: (i) the case of generalized possibilistic mixtures, using a t-norm instead of min, and (ii) the case of evaluating either preferences or uncertainty on Cartesian products of ordinal scales.

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Shan, Jian Feng, und Liang Wei Wang. „Circuit Fault Diagnosis Based on OEMD and SVDD Classifier of KFPCM Optimal Algorithm“. Applied Mechanics and Materials 738-739 (März 2015): 366–72. http://dx.doi.org/10.4028/www.scientific.net/amm.738-739.366.

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Hilbert-Huang transform (HHT) has some problems such as insufficient characteristic, modal aliasing, illusive component in circuit fault feature extraction, a new method is proposed to obtain the transient characteristic which is especially suitable to process non-stationary signal. The method consists of orthogonal empirical mode decomposition (OEMD) and Hilbert transform. Use the OEMD algorithm to gain strict orthogonal intrinsic mode function (IMF) and obtain the characteristics such as time, amplitude and frequency after the Hilbert transform. Support vector data description (SVDD) is sensitive to noise and outliers. It needs to classify the data in advance, reduce noise and traversal data to the specific sample which has good similarity by using Kernelized Fuzzy Possibilistic C-Means clustering (KFPCM). Then put the sample into SVDD classifier for training and diagnosis. The results of experiments show that the SVDD improved by KFPCM has higher accuracy of fault diagnosis than original SVDD.

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19

Kurniasari, Dian, Virda Kurniawati, Aang Nuryaman, Mustofa Usman und Rizki Khoirun Nisa. „IMPLEMENTATION OF FUZZY C-MEANS AND FUZZY POSSIBILISTIC C-MEANS ALGORITHMS ON POVERTY DATA IN INDONESIA“. BAREKENG: Jurnal Ilmu Matematika dan Terapan 18, Nr. 3 (31.07.2024): 1919–30. http://dx.doi.org/10.30598/barekengvol18iss3pp1919-1930.

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Cluster analysis involves the methodical categorization of data based on the degree of similarity within each group to group data with similar characteristics. This study focuses on classifying poverty data across Indonesian provinces. The methodologies employed include the Fuzzy C-Means (FCM) and Fuzzy Probabilistic C-Means (FPCM) algorithms. The FCM algorithm is a clustering approach where membership values determine the presence of each data point in a cluster. On the other hand, the FPCM algorithm builds upon FCM and Possibilistic C (PCM) algorithms by incorporating probabilistic considerations. This research compares the FCM and FPCM algorithms using local poverty data from Indonesia, specifically examining the Partition Entropy (PE) index value. It aims to identify the optimal number of clusters for provincial-level poverty data in Indonesia. The findings indicate that the FPCM algorithm outperforms the FCM algorithm in categorizing poverty in Indonesia, as evidenced by the PE validity index. Furthermore, the study identifies that the ideal number of clusters for the data is 2.

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Bodyanskiy, Ye V., A. Yu Shafronenko und I. N. Klymova. „ONLINE FUZZY CLUSTERING OF INCOMPLETE DATA USING CREDIBILISTIC APPROACH AND SIMILARITY MEASURE OF SPECIAL TYPE“. Radio Electronics, Computer Science, Control 1, Nr. 1 (27.03.2021): 97–104. http://dx.doi.org/10.15588/1607-3274-2021-1-10.

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Context. In most clustering (classification without a teacher) tasks associated with real data processing, the initial information is usually distorted by abnormal outliers (noise) and gaps. It is clear that “classical” methods of artificial intelligence (both batch and online) are ineffective in this situation.The goal of the paper is to propose the procedure of fuzzy clustering of incomplete data using credibilistic approach and similarity measure of special type. Objective. The goal of the work is credibilistic fuzzy clustering of distorted data, using of credibility theory. Method. The procedure of fuzzy clustering of incomplete data using credibilistic approach and similarity measure of special type based on the use of both robust goal functions of a special type and similarity measures, insensitive to outliers and designed to work both in batch and its recurrent online version designed to solve Data Stream Mining problems when data are fed to processing sequentially in real time. Results. The introduced methods are simple in numerical implementation and are free from the drawbacks inherent in traditional methods of probabilistic and possibilistic fuzzy clustering data distorted by abnormal outliers (noise) and gaps. Conclusions. The conducted experiments have confirmed the effectiveness of proposed methods of credibilistic fuzzy clustering of distorted data operability and allow recommending it for use in practice for solving the problems of automatic clusterization of distorted data. The proposed method is intended for use in hybrid systems of computational intelligence and, above all, in the problems of learning artificial neural networks, neuro-fuzzy systems, as well as in the problems of clustering and classification.

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Dik, Amina, Khalid Jebari und Aziz Ettouhami. „An Improved Robust Fuzzy Algorithm for Unsupervised Learning“. Journal of Intelligent Systems 29, Nr. 1 (25.10.2018): 1028–42. http://dx.doi.org/10.1515/jisys-2018-0030.

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Abstract This paper presents a robust, dynamic, and unsupervised fuzzy learning algorithm (RDUFL) that aims to cluster a set of data samples with the ability to detect outliers and assign the numbers of clusters automatically. It consists of three main stages. The first (1) stage is a pre-processing method in which possible outliers are determined and quarantined using a concept of proximity degree. The second (2) stage is a learning method, which consists in auto-detecting the number of classes with their prototypes for a dynamic threshold. This threshold is automatically determined based on the similarity among the detected prototypes that are updated at the exploration of a new data. The last (3) stage treats quarantined samples detected from the first stage to determine whether they belong to some class defined in the second phase. The effectiveness of this method is assessed on eight real medical benchmark datasets in comparison to known unsupervised learning methods, namely, the fuzzy c-means (FCM), possibilistic c-means (PCM), and noise clustering (NC). The obtained accuracy of our scheme is very promising for unsupervised learning problems.

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Biswas, Animesh, und Biswajit Sarkar. „Interval-valued Pythagorean fuzzy TODIM approach through point operator-based similarity measures for multicriteria group decision making“. Kybernetes 48, Nr. 3 (04.03.2019): 496–519. http://dx.doi.org/10.1108/k-12-2017-0490.

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Purpose The purpose of this paper is to develop a methodology based on TODIM (an acronym in Portuguese for interactive and multicriteria decision-making) approach for the selection of the best alternative in the context of multi criteria group decision-making (MCGDM) problems under possibilistic uncertainty in interval-valued Pythagorean fuzzy (IVPF) environment. Design/methodology/approach In this paper, IVPF-TODIM method is proposed. Some new point operator-based similarity measures (POSMs) for IVPF sets (IVPFSs) are introduced which have the capability to reduce the degree of uncertainty of the elements in the universe of discourse corresponding to IVPFS. Then the newly defined POSMs are used to compute the measure of relative dominance of each alternative over other alternatives in the IVPF-TODIM context. Finally, generalized mean aggregation operator is used to find the best alternative. Findings As the TODIM method is used to solve the MCGDM problems under uncertainty, POSMs are developed by using three parameters which can control the effect of decision-makers’ psychological perception under risk. Research limitations/implications The decision values are used in IVPF numbers (IVPFNs) format. Practical implications The proposed method is capable to solve real-life MCGDM problems with not only IVPFNs format but also with interval-valued intuitionistic fuzzy numbers. Originality/value As per authors’ concern, no approach using TODIM with IVPFNs is found in literature to solve MCGDM problems under uncertainty. The final judgment values of alternatives using the extended TODIM methodology are highly corroborate in compare to the results of existing methods, which proves its great potentiality in solving MCGDM problems under risk.

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Hüllermeier, Eyke, Michael Richter und Rosina Weber. „Prelude to the papers “Fuzzy case based reasoning for facial expression recognition” and “Temporal similarity by measuring possibilistic uncertainty in CBR”“. Fuzzy Sets and Systems 160, Nr. 2 (Januar 2009): 212–13. http://dx.doi.org/10.1016/j.fss.2008.05.018.

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24

Duan, Chen, und Yongli Liu. „Collaborative possibilistic fuzzy clustering based on information bottleneck“. Journal of Intelligent & Fuzzy Systems, 18.02.2023, 1–12. http://dx.doi.org/10.3233/jifs-223854.

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In fuzzy clustering algorithms, the possibilistic fuzzy clustering algorithm has been widely used in many fields. However, the traditional Euclidean distance cannot measure the similarity between samples well in high-dimensional data. Moreover, if there is an overlap between clusters or a strong correlation between features, clustering accuracy will be easily affected. To overcome the above problems, a collaborative possibilistic fuzzy clustering algorithm based on information bottleneck is proposed in this paper. This algorithm retains the advantages of the original algorithm, on the one hand, using mutual information loss as the similarity measure instead of Euclidean distance, which is conducive to reducing subjective errors caused by arbitrary choices of similarity measures and improving the clustering accuracy; on the other hand, the collaborative idea is introduced into the possibilistic fuzzy clustering based on information bottleneck, which can form an accurate and complete representation of the data organization structure based on make full use of the correlation between different feature subsets for collaborative clustering. To examine the clustering performance of this algorithm, five algorithms were selected for comparison experiments on several datasets. Experimental results show that the proposed algorithm outperforms the comparison algorithms in terms of clustering accuracy and collaborative validity.

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Zhang, Yong, Tianzhen Chen, Yuqing Jiang und Jianying Wang. „Possibilistic c-means clustering based on the nearest-neighbour isolation similarity“. Journal of Intelligent & Fuzzy Systems, 30.07.2022, 1–12. http://dx.doi.org/10.3233/jifs-213502.

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Clustering is widely used in data mining and machine learning. The possibilistic c-means clustering (PCM) method loosens the constraint of the fuzzy c-means clustering (FCM) method to solve the problem of noise sensitivity of FCM. But there is also a new problem: overlapping cluster centers are not suitable for clustering non-cluster distribution data. We propose a novel possibilistic c-means clustering method based on the nearest-neighbour isolation similarity in this paper. All samples are taken as the initial cluster centers in the proposed approach to obtain k sub-clusters iteratively. Then the first b samples farthest from the center of each sub-cluster are chosen to represent the sub-cluster. Afterward, sub-clusters are mapped to the distinguishable space by using these selected samples to calculate the nearest-neighbour isolation similarity of the sub-clusters. Then, adjacent sub-clusters can be merged according to the presented connecting strategy, and finally, C clusters are obtained. Our method proposed in this paper has been tested on 15 UCI benchmark datasets and a synthetic dataset. Experimental results show that our proposed method is suitable for clustering non-cluster distribution data, and the clustering results are better than those of the comparison methods with solid robustness.

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Gao, Can, Yangbo Wang, Jie Zhou, Weiping Ding, Linlin Shen und Zhihui Lai. „Possibilistic Neighborhood Graph: A New Concept of Similarity Graph Learning“. IEEE Transactions on Emerging Topics in Computational Intelligence, 2022, 1–15. http://dx.doi.org/10.1109/tetci.2022.3225173.

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„Dynamic Evolving Cauchy Possibilistic Clustering Based on the Self-Similarity Principle (DECS) for Enhancing Intrusion Detection System“. International Journal of Intelligent Engineering and Systems 15, Nr. 5 (31.10.2022): 252–60. http://dx.doi.org/10.22266/ijies2022.1031.23.

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28

Ghosh, Indranil, Rabin K. Jana und Paritosh Pramanik. „New business capacity of developed, developing and least developing economies: inspection through state-of-the-art fuzzy clustering and PSO-GBR frameworks“. Benchmarking: An International Journal, 07.06.2022. http://dx.doi.org/10.1108/bij-09-2021-0528.

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PurposeIt is essential to validate whether a nation's economic strength always transpires into new business capacity. The present research strives to identify the key indicators to the proxy new business ecosystem of countries and critically evaluate the similarity through the lens of advanced Fuzzy Clustering Frameworks over the years.Design/methodology/approachThe authors use Fuzzy C Means, Type 2 Fuzzy C Means, Fuzzy Possibilistic C Means and Fuzzy Possibilistic Product Partition C Means Clustering algorithm to discover the inherent groupings of the considered countries in terms of intricate patterns of geospatial new business capacity during 2015–2018. Additionally, the authors propose a Particle Swarm Optimization driven Gradient Boosting Regression methodology to measure the influence of the underlying indicators for the overall surge in new business.FindingsThe Fuzzy Clustering frameworks suggest the existence of two clusters of nations across the years. Several developing countries have emerged to cater praiseworthy state of the new business ecosystem. The ease of running a business has appeared to be the most influential feature that governs the overall New Business Density.Practical implicationsIt is of paramount practical importance to conduct a periodic review of nations' overall new business ecosystem to draw action plans to emphasize and augment the key enablers linked to new business growth. Countries found to lack new business capacity despite enjoying adequate economic strength can focus effectively on weaker dimensions.Originality/valueThe research proposes a robust systematic framework for new business capacity across different economies, indicating that economic strength does not necessarily transpire to equivalent new business capacity.

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Chebil, Wiem, und Lina F. Soualmia. „Improving semantic information retrieval by combining possibilistic networks, vector space model and pseudo-relevance feedback“. Journal of Information Science, 24.04.2023, 016555152311672. http://dx.doi.org/10.1177/01655515231167293.

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To improve the performance of information retrieval systems (IRSs), we propose in this article a novel approach that enriches the user’s queries with new concepts. Indeed, query expansion is one of the best methods that plays an important role in improving searches for a better semantic information retrieval. The proposed approach in this study combines possibilistic networks (PNs), the vector space model (VSM) and pseudo-relevance feedback (PRF) to evaluate and add relevant concepts to the initial index of the user’s query. First, query expansion is performed using PN, VSM and domain knowledge. PRF is then exploited to enrich, in a second round, the user’s query by applying the same approach used in the first expansion step. To evaluate the performance of the developed system, denoted conceptual information retrieval model (CIRM), several experiments of query expansion are performed. The experiments carried out on the OHSUMED and Clinical Trials corpora showed that using the two measures of possibility and necessity combined the cosinus similarity and PRF improves the query expansion process. Indeed, the improvement rate of our approach compared with the baseline is +28, 49% in terms of P@5.

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Cheval, Vincent, Raphaëlle Crubillé und Steve Kremer. „Symbolic protocol verification with dice1“. Journal of Computer Security, 12.06.2023, 1–38. http://dx.doi.org/10.3233/jcs-230037.

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Symbolic protocol verification generally abstracts probabilities away, considering computations that succeed only with negligible probability, such as guessing random numbers or breaking an encryption scheme, as impossible. This abstraction, sometimes referred to as the perfect cryptography assumption, has shown very useful as it simplifies automation of the analysis. However, probabilities may also appear in the control flow where they are generally not negligible. In this paper we consider a framework for symbolic protocol analysis with a probabilistic choice operator: the probabilistic applied π-calculus. We define and explore the relationships between several behavioral equivalences. In particular we show the need for randomized schedulers and exhibit a counter-example to a result in a previous work that relied on non-randomized ones. As in other frameworks that mix both non-deterministic and probabilistic choices, schedulers may sometimes be unrealistically powerful. We therefore consider two subclasses of processes that avoid this problem. In particular, when considering purely non-deterministic protocols, as is done in classical symbolic verification, we show that a probabilistic adversary has – maybe surprisingly – a strictly superior distinguishing power for may testing, which, when the number of sessions is bounded, we show to coincide with purely possibilistic similarity.

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