A Multimodal Retrieval and Ranking Method for Scientific Documents Based on HFS and XLNet

Aiming at the defects of traditional full-text retrieval models in dealing with mathematical expressions, which are special objects different from ordinary texts, a multimodal retrieval and ranking method for scientific documents based on hesitant fuzzy sets (HFS) and XLNet is proposed. This method integrates multimodal information, such as mathematical expression images and context text, as keywords to realize the retrieval of scientific documents. In the image modal, the images of mathematical expressions are recognized, and the hesitancy fuzzy set theory is introduced to calculate the hesitancy fuzzy similarity between mathematical query expressions and the mathematical expressions in candidate scientific documents. Meanwhile, in the text mode, XLNet is used to generate word vectors of the mathematical expression context to obtain the similarity between the query text and the mathematical expression context of the candidate scientific documents. Finally, the multimodal evaluation is integrated, and the hesitation fuzzy set is constructed at the document level to obtain the final scores of the scientific documents and corresponding ranked output. The experimental results show that the recall and precision of this method are 0.774 and 0.663 on the NTCIR dataset, respectively, and the average normalized discounted cumulative gain (NDCG) value of the top-10 ranking results is 0.880 on the Chinese scientific document (CSD) dataset.

Two Trigonometric Intuitionistic Fuzzy Similarity Measures

Intuitionistic Fuzzy Sets(1986) invented by Atanassov(Atanassov, 1986) has gained the wide popularity among various researchers because of its applications in various fields such as image processing, edge detection, medical diagnosis, pattern recognition etc. One of the significant tool by which the decision can be made is Intuitionistic Fuzzy Similarity Measure. In this communication, the authors have introduced two new Intuitionistic fuzzy similarity measures based on the trigonometric functions and its validity is proved. The proposed similarity measure is applied to medical diagnosis and pattern recognition.

On Comparing Cross-Validated Forecasting Models with a Novel Fuzzy-TOPSIS Metric: A COVID-19 Case Study

Time series cross-validation is a technique to select forecasting models. Despite the sophistication of cross-validation over single test/training splits, traditional and independent metrics, such as Mean Absolute Error (MAE) and Root Mean Square Error (RMSE), are commonly used to assess the model’s accuracy. However, what if decision-makers have different models fitting expectations to each moment of a time series? What if the precision of the forecasted values is also important? This is the case of predicting COVID-19 in Amapá, a Brazilian state in the Amazon rainforest. Due to the lack of hospital capacities, a model that promptly and precisely responds to notable ups and downs in the number of cases may be more desired than average models that only have good performances in more frequent and calm circumstances. In line with this, this paper proposes a hybridization of the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and fuzzy sets to create a similarity metric, the closeness coefficient (CC), that enables relative comparisons of forecasting models under heterogeneous fitting expectations and also considers volatility in the predictions. We present a case study using three parametric and three machine learning models commonly used to forecast COVID-19 numbers. The results indicate that the introduced fuzzy similarity metric is a more informative performance assessment metric, especially when using time series cross-validation.

Ensemble Creation using Fuzzy Similarity Measures and Feature Subset Evaluators

Current machine learning research is addressing the problem that occurs when the data set includes numerous features but the number of training data is small. Microarray data, for example, typically has a very large number of features, the genes, as compared to the number of training data examples, the patients. An important research problem is to develop techniques to effectively reduce the number of features by selecting the best set of features for use in a machine learning process, referred to as the feature selection problem. Another means of addressing high dimensional data is the use of an ensemble of base classifiers. Ensembles have been shown to improve the predictive performance of a single model by training multiple models and combining their predictions. This paper examines combining an enhancement of the random subspace model of feature selection using fuzzy set similarity measures with different measures of evaluating feature subsets in the construction of an ensemble classifier. Experimental results show that in most cases a fuzzy set similarity measure paired with a feature subset evaluator outperforms the corresponding fuzzy similarity measure by itself and the learning process only needs to occur on typically about half the number of base classifiers since the features subset evaluator eliminates those feature subsets of low quality from use in the ensemble. In general, the fuzzy consistency index is the better performing feature subset evaluator, and inclusion maximum is the better performing fuzzy similarity measure.

Fuzzy Similarity Measure and its Application to High Resolution Colour Remote Sensing Image Processing

The focus for the study in this thesis is placed on developing basic algorithms and tools for high-resolution colour remote sensing image processing tasks such as colour morphology, multivariate clustering, and multivariate filtering. First, the fuzzy similarity measure (FSM) among vectors in a vector space is introduced. This measure is based on two assumptions for the relationship among vectors: short-range ordering and fuzzification. Second, based on the FSM, the colour morphology, multivariate fuzzy clustering, and multivariate filtering are defined. The performances of all proposed methods will be evaluated numerically and subjectively. Third, this study also places more emphases on solving some applied problems related to recognizing colour edges, detecting and extracting complex road network and building rooftops, and reducing noise in high-resolution remote sensing images such as QuickBird, Ikonos, and aerial images. The results obtained in the study demonstrate the effectiveness and efficacy of the FMS and the proposed methods.

Fuzzy Similarity Measure and its Application to High Resolution Colour Remote Sensing Image Processing

The focus for the study in this thesis is placed on developing basic algorithms and tools for high-resolution colour remote sensing image processing tasks such as colour morphology, multivariate clustering, and multivariate filtering. First, the fuzzy similarity measure (FSM) among vectors in a vector space is introduced. This measure is based on two assumptions for the relationship among vectors: short-range ordering and fuzzification. Second, based on the FSM, the colour morphology, multivariate fuzzy clustering, and multivariate filtering are defined. The performances of all proposed methods will be evaluated numerically and subjectively. Third, this study also places more emphases on solving some applied problems related to recognizing colour edges, detecting and extracting complex road network and building rooftops, and reducing noise in high-resolution remote sensing images such as QuickBird, Ikonos, and aerial images. The results obtained in the study demonstrate the effectiveness and efficacy of the FMS and the proposed methods.

Revision of Pseudo-Ultrametric Spaces Based on m-Polar T-Equivalences and Its Application in Decision Making

In mathematics, distance and similarity are known as dual concepts. However, the concept of similarity is interpreted as fuzzy similarity or T-equivalence relation, where T is a triangular norm (t-norm in brief), when we discuss a fuzzy environment. Dealing with multi-polarity in practical examples with fuzzy data leadsus to introduce a new concept called m-polar T-equivalence relations based on a finitely multivalued t-norm T, and to study the metric behavior of such relations. First, we study the new operators including the m-polar triangular norm T and conorm S as well as m-polar implication I and m-polar negation N, acting on the Cartesian product of [0,1]m-times.Then, using the m-polar negations N, we provide a method to construct a new type of metric spaces, called m-polar S-pseudo-ultrametric, from the m-polar T-equivalences, and reciprocally for constructing m-polar T-equivalences based on the m-polar S-pseudo-ultrametrics. Finally, the link between fuzzy graphs and m-polar S-pseudo-ultrametrics is considered. An algorithm is designed to plot a fuzzy graph based on the m-polar SL-pseudo-ultrametric, where SL is the m-polar Lukasiewicz t-conorm, and is illustrated by a numerical example which verifies our method.