Fuzzy Similarity Measure Research Articles

Computing semantic relatedness using latent semantic analysis and fuzzy formal concept analysis

Measuring semantic similarity/semantic relatedness is an important task in computational linguistic, natural language processing and ontology creation. In this paper, a new hybrid method using LSA and FFCA is proposed for computing the semantic-relatedness. Latent semantic analysis (LSA) is used to extract the attributes of the concepts and these attributes are further mapped to FFCA to compute semantic relatedness. The latent semantic analysis is used for finding the neighbouring words or attributes and their correlation value. The concepts and their attributes are mapped to FCA table and then to FFCA table by using the correlation value as membership. A fuzzy similarity measure is then used to compute the semantic relatedness between these concepts/words. The proposed method is evaluated on word similarity bench mark dataset WS-353 and found an accuracy of 0.85.

Fermatean Fuzzy Similarity Measure Algorithm and its Application in Students' Admission Process

Fermatean Fuzzy Similarity Measure Algorithm and its Application in Students' Admission Process

Applications of picture fuzzy similarity measures in pattern recognition, clustering, and MADM

Picture fuzzy set (PFS) is a direct extension of fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs) and is quite powerful than FSs and IFSs in expressing the uncertainty and vagueness in our daily life problems. In this article, we propose some new similarity measures for PFSs which are capable of distinguishing highly similar but inconsistent PFSs. We also demonstrate their applications in pattern recognition using some illustrative examples as well as with real data. We assess the performance of the proposed measures using the concept of degree of confidence. We also extend the maximum spanning tree (MST) clustering algorithm to PF (picture fuzzy)-environment and propose a picture fuzzy maximum spanning tree (PFMST) clustering method. Further, we introduce a new attribute weight determining formula based on PF-similarity measures in multi-attribute decision-making (MADM) problem. We also establish the superiority of our proposed PF-similarity measures over some existing PF-similarity measures in view of the structured linguistic variables.

How to choose a fuzzy similarity measure in decision-making?

Purpose The paper is dedicated to the analysis of fuzzy similarity measures in uncertainty analysis in general, and in economic decision-making in particular. The purpose of this paper is to explain how a similarity measure can be chosen to quantify a qualitative description of similarities provided by experts of a given domain, in the case where the objects to compare are described through imprecise or linguistic attribute values represented by fuzzy sets. The case of qualitative dissimilarities is also addressed and the particular case of their representation by distances is presented. Design/methodology/approach The approach is based on measurement theory, following Tversky’s well-known paradigm. Findings A list of axioms which may or may not be satisfied by a qualitative comparative similarity between fuzzy objects is proposed, as extensions of axioms satisfied by similarities between crisp objects. They enable to express necessary and sufficient conditions for a numerical similarity measure to represent a comparative similarity between fuzzy objects. The representation of comparative dissimilarities is also addressed by means of specific functions depending on the distance between attribute values. Originality/value Examples of functions satisfying certain axioms to represent comparative similarities are given. They are based on the choice of operators to compute intersection, union and difference of fuzzy sets. A simple application of this methodology to economy is given, to show how a measure of similarity can be chosen to represent intuitive similarities expressed by an economist by means of a quantitative measure easily calculable. More detailed and formal results are given in Coletti and Bouchon-Meunier (2020) for similarities and Coletti et al. (2020) for dissimilarities.

Novel similarity measures in spherical fuzzy environment and their applications

Spherical fuzzy sets (SFSs) have gained great attention from researchers in various fields. The spherical fuzzy set is characterized by three membership functions expressing the degrees of membership, non-membership and the indeterminacy to provide a larger preference domain. It was proposed as a generalization of picture fuzzy sets and Pythagorean fuzzy sets in order to deal with uncertainty and vagueness information. The similarity measure is one of the essential and advantageous tools to determine the degree of similarity between items. Several studies on similarity measures have been developed due to the importance of similarity measure and application in decision making, data mining, medical diagnosis, and pattern recognition in the literature. The contribution of this study is to present some novel spherical fuzzy similarity measures. We develop the Jaccard, exponential, and square root cosine similarity measures under spherical fuzzy environment. Each of these similarity measures is analyzed with respect to decision-makers’ optimistic or pessimistic point of views. Then, we apply these similarity measures to medical diagnose and green supplier selection problems. These similarity measures can be computed easily and they can express the dependability similarity relation apparently.

New Similarity Measures for Dual Hesitant Fuzzy Sets and Their Application

Dual hesitant fuzzy sets (DHFSs) are powerful and efficient to express hesitant preferred and non-preferred information simultaneously. This paper focuses on similarity measures for DHFSs. To do this, it first analyzes the limitations of previous similarity measures for DHFSs. Then, several new dual hesitant fuzzy similarity measures are defined that can avoid the issues of previous ones. To discriminate the importance of decision-making criteria, several weighted similarity measures are further defined in views of additive and 2-additive measures. When the weighting information is not exactly known, optimization methods for determining additive and 2-additive measures are built, respectively. Furthermore, a method for multi-criteria decision-making based on new weighted similarity measures is developed. Finally, two numerical examples are provided to show the utilization of the new method and compare with previous methods.

Job satisfaction evaluation based on fuzzy conjoint method with continuous fuzzy sets

<span lang="EN-GB">Fuzzy conjoint method (FCM) is one of the available methods suggested for job satisfaction evaluation. The main feature of job satisfaction evaluation is the use of rating of agreement to indicate employee feelings and beliefs about their job. Currently the linguistic terms used for rating of agreement in FCM are represented in the form of discrete fuzzy sets. This paper investigates the potential use of continuous fuzzy sets to represent linguistic terms used in the FCM process. To investigate the consistency of the decision outcomes produced by the proposed approach, four different types of fuzzy similarity measures were used: similarity based on Matching Function, similarity based on Euclidean Distance, similarity based on Set-Theoretic and similarity based on vector. These classification outcomes are also compared with classification drawn on the basis of statistical inference. The finding of this study shows that both discrete fuzzy sets and continuous fuzzy sets produce consistent results regardless of whether the fuzzy similarity measure was used. Hence, the inclusion of other methods in FCM is particularly very useful for calculating the closeness coefficients and specifically addresses the shortcoming in FCM for job satisfaction evaluation. </span>

Decision support system for dementia patients using intuitionistic fuzzy similarity measure

Similarity measure confirms the proximity of two objects to each other. This concept can be applied as fuzzy or intuitionistic fuzzy. There are lots of fuzzy similarity measures which had been extended to intuitionistic fuzzy similarity measure, with application in different domain. There is need to investigate these methods based on their application for further modification. Thus, the aim of this research is to modify existing fuzzy and intuitionistic fuzzy similarity measures, and apply it to cognitive domain for better performance. Existing intuitionistic fuzzy similarity methods were extended and modified. These research showed that the existing methods had been applied to various domains, and researchers had improved and extended most fuzzy similarity measure to intuitionistic fuzzy similarity measure for optimal performance. Experiment showed that the proposed methods gives higher similarity value and lower processing time.

Soft boundary-based neurofeedback training based on fuzzy similarity measures: A method for learning how to control EEG Signal features during neurofeedback training

BackgroundMost commonly used neurofeedback training (NFT) methods are able to assist subjects towards an increase/decrease in EEG features. So, it is possible that the enhancement/inhabitation in a subject’s EEG features exceed normal limits if the process of changes in brain activity in the subject is very successful. This issue may also bring about a reduction in the effectiveness of NFT. New methodA soft boundary-based NFT method was proposed for learning how to control the EEG features during training. According to this method, an initial group was defined within which the training features of subjects’ EEG signals were placed prior to training and a target group was considered referring to what the features of the EEG signals should be shifted towards during training. In the course of training, the fuzzy similarity of EEG features of subject towards the target group center was measured and the subject’s score was increased if their fuzzy similarity was higher than a threshold. Within this method, an adaptive scoring index (the scores assigned to subjects for each achievement) was defined whose value was determined according to brain activity of the subject. ResultsIncrease/decrease in large amounts in the training features of subject’s EEG could lead to a descending trend in the scores received using the proposed method. Comparison with existing methodsThe proposed method may assist subjects to control their EEG signal features within the target group range. ConclusionThe proposed method may be able to prevent the side effects of neurofeedback.

A Fuzzy Word Similarity Measure for Selecting Top-$k$ Similar Words in Query Expansion

Top-k words selection is a technique used to detect and return the k most similar words to a given word from a candidate set. This is a crucial and widely used tool in various tasks. The key issue in top-k words selection is how to measure the similarity between words. One popular and effective solution is to use a word embedding-based similarity measure, which represents words as low-dimensional vectors and measures the similarities between words according to the similarity of the vectors, using a metric. However, most word embedding methods only consider the local proximity properties of two words in a corpus. To mitigate this issue. In this article, we propose to use association rules for measuring word similarity at a global level, and a fuzzy similarity measure for top-k words selection that jointly encodes the local and the global similarities. Experiments on a real-world query task with three benchmark datasets, i.e., TREC-disk 4&5, WT10G, and RCV1, demonstrate the efficiency of the proposed method compared to several state-of-the-art baselines.

M-CFIS-R: Mamdani Complex Fuzzy Inference System with Rule Reduction Using Complex Fuzzy Measures in Granular Computing

Complex fuzzy theory has strong practical background in many important applications, especially in decision-making support systems. Recently, the Mamdani Complex Fuzzy Inference System (M-CFIS) has been introduced as an effective tool for handling events that are not restricted to only values of a given time point but also include all values within certain time intervals (i.e., the phase term). In such decision-making problems, the complex fuzzy theory allows us to observe both the amplitude and phase values of an event, thus resulting in better performance. However, one of the limitations of the existing M-CFIS is the rule base that may be redundant to a specific dataset. In order to handle the problem, we propose a new Mamdani Complex Fuzzy Inference System with Rule Reduction Using Complex Fuzzy Measures in Granular Computing called M-CFIS-R. Several fuzzy similarity measures such as Complex Fuzzy Cosine Similarity Measure (CFCSM), Complex Fuzzy Dice Similarity Measure (CFDSM), and Complex Fuzzy Jaccard Similarity Measure (CFJSM) together with their weighted versions are proposed. Those measures are integrated into the M-CFIS-R system by the idea of granular computing such that only important and dominant rules are being kept in the system. The difference and advantage of M-CFIS-R against M-CFIS is the usage of the training process in which the rule base is repeatedly changed toward the original base set until the performance is better. By doing so, the new rule base in M-CFIS-R would improve the performance of the whole system. Experiments on various decision-making datasets demonstrate that the proposed M-CFIS-R performs better than M-CFIS.

The Similarity Measurement of Human DNA Profile Using Fuzzy Similarity

This research investigated the similarity of human DNA profile using fuzzy similarity measure. The similarity measurement of DNA profile had been done by measuring the similarity between query’s DNA profile and its biological family such as father, mother, brother, sister, grandmother and grandfather. The similarity measurement had been done to the short tandem repeat (STR) alleles in sixteen loci. The result of the experiment showed that each simulation gave matching result. This research is useful for Indonesian National Police (POLRI) in identifying process of disaster victim, terrorism victim and other criminal conduct.

Assessment of the behavior uncertainty level of the short time series

The article considers the problem of assessing the level of uncertainty in the behavior of the short time series. The approach to solving this problem, based on the use of the fuzzy linear regression equation with the asymmetric parameters has been proposed. The methods for assessing the level of uncertainty in the behavior of the short time series using the fuzzy similarity measures have been considered. A herewith, the time series which describes the equation of the classical linear regression is used as the standard time series. The presented results of experimental studies confirm the effectiveness of using the proposed approach to assess the level of uncertainty in the behavior of the short time series.

Two level filtering mechanism to detect phishing sites using lightweight visual similarity approach

The visual similarity-based techniques detect the phishing sites based on the similarity between the suspicious site and the existing database of resources such as screenshots, styles, logos, favicons etc. These techniques fail to detect phishing sites which target non-whitelisted legitimate domain or when phishing site with manipulated whitelisted legitimate content is encountered. Also, these techniques are not well adaptable at the client-side due to their computation and space complexity. Thus there is a need for light weight visual similarity-based technique detecting phishing sites targeting non-whitelisted legitimate resources. Unlike traditional visual similarity-based techniques using whitelists, in this paper, we employed a light-weight visual similarity based blacklist approach as a first level filter for the detection of near duplicate phishing sites. For the non-blacklisted phishing sites, we have incorporated a heuristic mechanism as a second level filter. We used two fuzzy similarity measures, Simhash and Perceptual hash for calculating the similarity score between the suspicious site and existing blacklisted phishing sites. Each similarity measure generates a unique fingerprint for a given website and also differs with less number of bits with a similar website. All three fingerprints together represent a website which undergoes blacklist filtering for the identification of the target website. The phishing sites which bypassed from the first level filter undergo second level heuristic filtering. We used comprehensive heuristic features including URL and source code based features for the detection of non-blacklisted phishing sites. The experimental results demonstrate that the blacklist filter alone is able to detect 55.58% of phishing sites which are either replicas or near duplicates of existing phishing sites. We also proposed an ensemble model with Random Forest (RF), Extra-Tree and XGBoost to evaluate the contribution of both blacklist and heuristic filters together as an entity and the model achieved a significant accuracy of 98.72% and Matthews Correlation Coefficient (MCC) of 97.39%. The proposed model is deployed as a chrome extension named as BlackPhish to provide real time protection against phishing sites at the client side. We also compared BlackPhish with the existing anti-phishing techniques where it outperformed existing works with a significant difference in accuracy and MCC.

Fuzzy number conjoint method to analyse students’ perceptions on the learning of calculus

The fuzzy conjoint method (FCM) based on fuzzy set has been applied in many areas such as education, management and business. However, the FCM uses the fuzzy set to define the membership function of the linguistic values, which the score of weight and overall attribute for different degrees of confidence that cannot be obtained. Besides, the fuzzy set which is in discrete form does not clearly represent human judgement. Thus, in this study, a fuzzy number conjoint method (FNCM) based on triangular fuzzy number is developed. The fuzzy similarity measure based on distance, height and area was used in the procedure. The FNCM was implemented to analyse students’ perception in the learning of calculus at one selected government institution in Selangor, Malaysia. The study involved a set of 5-options Likert scale questionnaire which is in linguistic values of strongly disagree, disagree, indifferent, agree and strongly agree. All the questions were on various items related to the learning of calculus. The findings showed that overall, students agreed at above 0.85 degree of similarity that they perceived positively in the learning of Calculus. The developed FNCM with a degree of agreement for each linguistic value can successfully evaluate the students’ perceptions in the learning of calculus. This study will be as assistance and guidance to academicians and mathematics educators to enhance students’ achievement in the learning of calculus.

On generalized similarity measures for Pythagorean fuzzy sets and their applications to multiple attribute decision‐making

In this paper, we develop a new and flexible method for Pythagorean fuzzy decision-making using some trigonometric similarity measures. We first introduce two new generalized similarity measures between Pythagorean fuzzy sets based on cosine and cotangent functions and prove their validity. These similarity measures include some well-known Pythagorean fuzzy similarity measures as their particular and limiting cases. The measures are demonstrated to satisfy some very elegant properties which prepare the ground for applications in different areas. Further, the work defines a generalized hybrid trigonometric Pythagorean fuzzy similarity measure and discuss its properties with particular cases. Then, based on the generalized hybrid trigonometric Pythagorean fuzzy similarity measure, a method for dealing with multiple attribute decision-making problems under Pythagorean fuzzy environment is developed. Finally, a numerical example is given to demonstrate the flexibility and effectiveness of the developed approach in solving real-life problems.

Approximate bisimulations and state reduction of fuzzy automata under fuzzy similarity measures

For the purpose of reducing the number of states of fuzzy automata, we study approximate bisimulations of fuzzy automata under fuzzy similarity measures, which are induced by residuums of left-continuous t-norms. For a real number α∈[0,1] and a fuzzy similarity measure S, we define α-approximate bisimulation under S between two fuzzy automata and prove that the degree of similarity between them is more than or equal to α if there exists an α-approximate bisimulation between them. Furthermore, we put forward the notion of surjective functional α-approximate bisimulations between two fuzzy automata under S. Using the notion of surjective functional α-approximate bisimulations under S, the α-approximate bisimulations for a fuzzy automaton under S is defined as an equivalence relation with two additional properties. According to an α-approximate bisimulation for a fuzzy automaton, an aggregated fuzzy automaton has been constructed and the degree of similarity between them is also more than or equal to α. It is significant for us to find that there might not possess the greatest α-approximate bisimulation for a fuzzy automaton, and we provide a polynomial-time algorithm for computing all maximal α-approximate bisimulations. Finally, we provide the conditions of the existence of the greatest α-approximate bisimulation.

Counterintuitive Test Problems for Transformed Fuzzy Number-Based Similarity Measures between Intuitionistic Fuzzy Sets

This paper analyzes the counterintuitive behaviors of transformed fuzzy number (FN)- based similarity measures between intuitionistic fuzzy sets (IFSs). Among these transformed FN-based similarity measures, Chen and Chang’s similarity measure (2015) is a novel one. An algorithm of computing Chen and Chang’s similarity measure is proposed. We analyze the counterintuitive behaviors of Chen and Chang’s similarity measure for seven general test problems and four test problems with three inclusive IFSs. The results indicate that there are six counterintuitive test problems for Chen and Chang’s similarity measure.

On Integration Linguistic Factors to Fuzzy Similarity Measures and Intuitionistic Fuzzy Similarity Measures

The article is concerned with integrating linguistic elements into fuzzy similarity measures and intuitionistic fuzzy similarity measure. Some new concepts are proposed: a fuzzy linguistic value (FLv), a fuzzy linguistic vector (FLV), an intuitionistic fuzzy linguistic vector (ILV) and similarity measures. The proposed measures are used to build classification algorithms. As predicted theoretically, experiments show that with the same type of similarity measures, the linguistic-aggregated similarity measures produce better results in classification problems.

New similarity measure and distance measure for Pythagorean fuzzy set

Pythagorean fuzzy set (PFS), disposing the indeterminacy portrayed by membership and non-membership, is a more viable and effective means to seize indeterminacy. Due to the defects of existing Pythagorean fuzzy similarity measures or distance measures (cannot obey third or fourth axiom; have no power to differentiate positive and negative difference; have no power to deal the division by zero problem), the major key of this paper is to explore the novel Pythagorean fuzzy distance measure and similarity measure. Meanwhile, some interesting properties of distance measure and similarity measure are proved. Some counterintuitive examples are presented to state their availability of similarity measure among PFSs.