Power Aggregation Operators and Similarity Measures Based on Improved Intuitionistic Hesitant Fuzzy Sets and their Applications to Multiple Attribute Decision Making

Intuitionistic hesitant fuzzy set(IHFS)is amixture of two separated notions called intuitionistic fuzzy set(IFS)and hesitant fuzzy set(HFS),as an important technique to cope with uncertain and awkward information in realistic decision issues.IHFS contains the grades of truth and falsity in the formof the subset of the unit interval.The notion of IHFS was defined by many scholars with different conditions,which contain several weaknesses.Here,keeping in view the problems of already defined IHFSs,we will define IHFS in another way so that it becomes compatible with other existing notions.To examine the interrelationship between any numbers of IHFSs,we combined the notions of power averaging(PA)operators and power geometric(PG)operators with IHFSs to present the idea of intuitionistic hesitant fuzzy PA(IHFPA)operators,intuitionistic hesitant fuzzy PG(IHFPG)operators,intuitionistic hesitant fuzzy power weighted average(IHFPWA)operators,intuitionistic hesitant fuzzy power ordered weighted average(IHFPOWA)operators,intuitionistic hesitant fuzzy power ordered weighted geometric(IHFPOWG)operators,intuitionistic hesitant fuzzy power hybrid average(IHFPHA)operators,intuitionistic hesitant fuzzy power hybrid geometric(IHFPHG)operators and examined as well their fundamental properties.Some special cases of the explored work are also discovered.Additionally,the similarity measures based on IHFSs are presented and their advantages are discussed along examples.Furthermore,we initiated a new approach to multiple attribute decision making(MADM)problem applying suggested operators and a mathematical model is solved to develop an approach and to establish its common sense and adequacy.Advantages,comparative analysis,and graphical representation of the presented work are elaborated to show the reliability and effectiveness of the presented works.

Shape Similarity Measures of Linear Entities

The essential of feature matching technology lies in how to measure the similarity of spatial entities.Among all the possible similarity measures,the shape similarity measure is one of the most important measures because it is easy to collect the necessary parameters and it is also well matched with the human intuition.In this paper a new shape similarity measure of linear entities based on the differences of direction change along each line is presented and its effectiveness is illustrated.

P-Indeterminate Vector Similarity Measures of Orthopair Neutrosophic Number Sets and Their Decision-MakingMethod with Indeterminate Degrees

In the complexity and indeterminacy of decision making(DM)environments,orthopair neutrosophic number set(ONNS)presented by Ye et al.can be described by the truth and falsity indeterminacy degrees.Then,ONNS demonstrates its advantages in the indeterminate information expression,aggregations,and DM problems with some indeterminate ranges.However,the existing research lacks some similarity measures between ONNSs.They are indispensable mathematical tools and play a crucial role in DM,pattern recognition,and clustering analysis.Thus,it is necessary to propose some similaritymeasures betweenONNSs to supplement the gap.To solve the issue,this study firstly proposes the p-indeterminate cosine measure,p-indeterminate Dice measure,p-indeterminate Jaccard measure of ONNSs(i.e.,the three parameterized indeterminate vector similarity measures of ONNSs)in vector space.Then,a DMmethod based on the parameterized indeterminate vector similarity measures of ONNSs is developed to solve indeterminate multiple attribute DM problems by choosing different indeterminate degrees of the parameter p,such as the small indeterminate degree(p=0)or the moderate indeterminate degree(p=0.5)or the big indeterminate degree(p=1).Lastly,an actual DM example on choosing a suitable logistics supplier is provided to demonstrate the flexibility and practicability of the developed DM approach in indeterminate DM problems.By comparison with existing relative DM methods,the superiority of this study is that the established DMapproach indicates its flexibility and suitability depending on decision makers’indeterminate degrees(decision risks)in ONNS setting.

Novel similarity measures for face representation based on local binary pattern

The successful face recognition based on local binary pattern(LBP)relies on the effective extraction of LBP features and the inferring of similarity between the extracted features.In this paper,we focus on the latter and propose two novel similarity measures for the local matching methods and the holistic matching methods respectively.One is Earth Mover's Distance with Hamming and Lp ground distance(EMD-HammingLp),which is a cross-bin dissimilarity measure for LBP histograms.The other is IMage Hamming Distance(IMHD),which is a dissimilarity measure for the whole LBP images.Experiments on FERET database show that the proposed two similarity measures outperform the state-of-the-art Chi-square similarity measure for extraction of LBP features.

Synthetic Lethal Interactions Prediction Based on Multiple Similarity Measures Fusion

The synthetic lethality(SL)relationship arises when a combination of deficiencies in two genes leads to cell death,whereas a deficiency in either one of the two genes does not.The survival of the mutant tumor cells depends on the SL partners of the mutant gene,thereby the cancer cells could be selectively killed by inhibiting the SL partners of the oncogenic genes but normal cells could not.Therefore,there is an urgent need to develop more efficient computational methods of SL pairs identification for cancer targeted therapy.In this paper,we propose a new approach based on similarity fusion to predict SL pairs.Multiple types of gene similarity measures are integrated and/c-nearest neighbors algorithm(k-NN)is applied to achieve the similarity-based classification task between gene pairs.As a similarity-based method,our method demonstrated excellent performance in multiple experiments.Besides the effectiveness of our method,the ease of use and expansibility can also make our method more widely used in practice.

SOME NEW SIMILARITY MEASURES FOR INTUITIONISTIC FUZZY VALUES AND THEIR APPLICATION IN GROUP DECISION MAKING

We first propose a series of similarity measures for intuitionistic fuzzy values （IFVs） based on the intuitionistic fuzzy operators （Atanassov 1995）. The parameters in the proposed similarity measures can control the degree of membership and the degree of non-membership of an IFV, which can reflect the decision maker’s risk preference. Moreover, we can obtain some known similarity measures when some fixed values are assigned to the parameters. Furthermore, we apply the similarity measures to aggregate IFVs and develop some aggregation operators, such as the intuitionistic fuzzy dependent averaging operator and the intuitionistic fuzzy dependent geometric operator, whose prominent characteristic is that the associated weights only depend on the aggregated intuitionistic fuzzy arguments and can relieve the influence of unfair arguments on the aggregated results. Based on these aggregation operators, we develop some group decision making methods, and finally extend our results to interval-valued intuitionistic fuzzy environment.

Improved binary similarity measures for software modularization

Various binary similarity measures have been employed in clustering approaches to make homogeneous groups of similar entities in the data. These similarity measures are mostly based only on the presence or absence of features. Binary similarity measures have also been explored with different clustering approaches （e.g., agglomera- tive hierarchical clustering） for software modularization to make software systems understandable and manageable. Each similarity measure has its own strengths and weaknesses which improve and deteriorate the clustering results, respectively. We highlight the strengths of some well-known existing binary similarity measures for software mod- ularization. Furthermore, based on these existing similarity measures, we introduce several improved new binary similarity measures. Proofs of the correctness with illustration and a series of experiments are presented to evaluate the effectiveness of our new binary similarity measures.

A Content-Based Medical Image Retrieval Method Using Relative Difference-Based Similarity Measure

Content-based medical image retrieval(CBMIR)is a technique for retrieving medical images based on automatically derived image features.There are many applications of CBMIR,such as teaching,research,diagnosis and electronic patient records.Several methods are applied to enhance the retrieval performance of CBMIR systems.Developing new and effective similarity measure and features fusion methods are two of the most powerful and effective strategies for improving these systems.This study proposes the relative difference-based similarity measure(RDBSM)for CBMIR.The new measure was first used in the similarity calculation stage for the CBMIR using an unweighted fusion method of traditional color and texture features.Furthermore,the study also proposes a weighted fusion method for medical image features extracted using pre-trained convolutional neural networks(CNNs)models.Our proposed RDBSM has outperformed the standard well-known similarity and distance measures using two popular medical image datasets,Kvasir and PH2,in terms of recall and precision retrieval measures.The effectiveness and quality of our proposed similarity measure are also proved using a significant test and statistical confidence bound.

An Information Content and Set of Common Superconcepts-Based Algorithm to Estimate Similarity between Concepts of Ontologies

Ontologies have been used for several years in life sciences to formally represent concepts and reason about knowledge bases in domains such as the semantic web, information retrieval and artificial intelligence. The exploration of these domains for the correspondence of semantic content requires calculation of the measure of semantic similarity between concepts. Semantic similarity is a measure on a set of documents, based on the similarity of their meanings, which refers to the similarity between two concepts belonging to one or more ontologies. The similarity between concepts is also a quantitative measure of information, calculated based on the properties of concepts and their relationships. This study proposes a method for finding similarity between concepts in two different ontologies based on feature, information content and structure. More specifically, this means proposing a hybrid method using two existing measures to find the similarity between two concepts from different ontologies based on information content and the set of common superconcepts, which represents the set of common parent concepts. We simulated our method on datasets. The results show that our measure provides similarity values that are better than those reported in the literature.

Ontology-based similarity measure for text clustering

A method that combines category-based and keyword-based concepts for a better information retrieval system is introduced. To improve document clustering, a document similarity measure based on cosine vector and keywords frequency in documents is proposed, but also with an input ontology. The ontology is domain specific and includes a list of keywords organized by degree of importance to the categories of the ontology, and by means of semantic knowledge, the ontology can improve the effects of document similarity measure and feedback of information retrieval systems. Two approaches to evaluating the performance of this similarity measure and the comparison with standard cosine vector similarity measure are also described.

An intelligent automatic correlation method of oilbearing strata based on pattern constraints:An example of accretionary stratigraphy of Shishen 100 block in Shinan Oilfield of Bohai Bay Basin,East China

Aiming at the problem that the data-driven automatic correlation methods which are difficult to adapt to the automatic correlation of oil-bearing strata with large changes in lateral sedimentary facies and strata thickness,an intelligent automatic correlation method of oil-bearing strata based on pattern constraints is formed.We propose to introduce knowledge-driven in automatic correlation of oil-bearing strata,constraining the correlation process by stratigraphic sedimentary patterns and improving the similarity measuring machine and conditional constraint dynamic time warping algorithm to automate the correlation of marker layers and the interfaces of each stratum.The application in Shishen 100 block in the Shinan Oilfield of the Bohai Bay Basin shows that the coincidence rate of the marker layers identified by this method is over 95.00%,and the average coincidence rate of identified oil-bearing strata reaches 90.02% compared to artificial correlation results,which is about 17 percentage points higher than that of the existing automatic correlation methods.The accuracy of the automatic correlation of oil-bearing strata has been effectively improved.

An Approach to Unsupervised Character Classification Based on Similarity Measure in Fuzzy Model

This paper presents a fuzzy logic approach to efficiently perform unsupervised character classification for improvement in robustness, correctness and speed of a character recognition system. The characters are first split into eight typographical categories. The classification scheme uses pattern matching to classify the characters in each category into a set of fuzzy prototypes based on a nonlinear weighted similarity function. The fuzzy unsupervised character classification, which is natural in the repre...

A Portfolio Selection Method Based on Pattern Matching with Dual Information of Direction and Distance

Pattern matching method is one of the classic classifications of existing online portfolio selection strategies. This article aims to study the key aspects of this method—measurement of similarity and selection of similarity sets, and proposes a Portfolio Selection Method based on Pattern Matching with Dual Information of Direction and Distance (PMDI). By studying different combination methods of indicators such as Euclidean distance, Chebyshev distance, and correlation coefficient, important information such as direction and distance in stock historical price information is extracted, thereby filtering out the similarity set required for pattern matching based investment portfolio selection algorithms. A large number of experiments conducted on two datasets of real stock markets have shown that PMDI outperforms other algorithms in balancing income and risk. Therefore, it is suitable for the financial environment in the real world.

Measuring Musical Rhythm Similarity: Further Experiments with the Many-to-Many Minimum-Weight Matching Distance

Musical rhythms are represented as sequences of symbols. The sequences may be composed of binary symbols denoting either silent or monophonic sounded pulses, or ternary symbols denoting silent pulses and two types of sounded pulses made up of low-pitched (dum) and high-pitched (tak) sounds. Experiments are described that compare the effectiveness of the many-to-many minimum-weight matching between two sequences to serve as a measure of similarity that correlates well with human judgements of rhythm similarity. This measure is also compared to the often used edit distance and to the one-to-one minimum-weight matching. New results are reported from experiments performed with three widely different datasets of real- world and artificially generated musical rhythms (including Afro-Cuban rhythms), and compared with results previously reported with a dataset of Middle Eastern dum-tak rhythms.

Modeling and monitoring of nonlinear multi-mode processes based on similarity measure-KPCA

A new modeling and monitoring approach for multi-mode processes is proposed.The method of similarity measure(SM) and kernel principal component analysis(KPCA) are integrated to construct SM-KPCA monitoring scheme,where SM method serves as the separation of common subspace and specific subspace.Compared with the traditional methods,the main contributions of this work are:1) SM consisted of two measures of distance and angle to accommodate process characters.The different monitoring effect involves putting on the different weight,which would simplify the monitoring model structure and enhance its reliability and robustness.2) The proposed method can be used to find faults by the common space and judge which mode the fault belongs to by the specific subspace.Results of algorithm analysis and fault detection experiments indicate the validity and practicability of the presented method.

Similarity measure design and similarity computation for discrete fuzzy data

The similarity computations for fuzzy membership function pairs were carried out.Fuzzy number related knowledge was introduced,and conventional similarity was compared with distance based similarity measure.The usefulness of the proposed similarity measure was verified.The results show that the proposed similarity measure could be applied to ordinary fuzzy membership functions,though it was not easy to design.Through conventional results on the calculation of similarity for fuzzy membership pair,fuzzy membership-crisp pair and crisp-crisp pair were carried out.The proposed distance based similarity measure represented rational performance with the heuristic point of view.Furthermore,troublesome in fuzzy number based similarity measure for abnormal universe of discourse case was discussed.Finally,the similarity measure computation for various membership function pairs was discussed with other conventional results.

Similarity measure on intuitionistic fuzzy sets

Study of fuzzy entropy and similarity measure on intuitionistic fuzzy sets (IFSs) was proposed and analyzed. Unlike fuzzy set, IFSs contain uncertainty named hesitance, which is contained in fuzzy membership function itself. Hence, designing fuzzy entropy is not easy because of many entropy definitions. By considering different fuzzy entropy definitions, fuzzy entropy on IFSs is designed and discussed. Similarity measure was also presented and its usefulness was verified to evaluate degree of similarity.

Similarity measure application to fault detection of flight system

Fault detection technique is introduced with similarity measure. The characteristics of conventional similarity measure based on fuzzy number are discussed. With the help of distance measure, similarity measure is constructed explicitly. The designed distance-based similarity measure is applicable to general fuzzy membership functions including non-convex fuzzy membership function, whereas fuzzy number-based similarity measure has limitation to calculate the similarity of general fuzzy membership functions. The applicability of the proposed similarity measure to general fuzzy membership structures is proven by identifying the definition. To decide fault detection of flight system, the experimental data （pitching moment coefficients and lift coefficients） are transformed into fuzzy membership functions. Distance-based similarity measure is applied to the obtained fuzzy membership functions, and similarity computation and analysis are obtained with the fault and normal operation coefficients.

Similarity measure design for high dimensional data

Information analysis of high dimensional data was carried out through similarity measure application. High dimensional data were considered as the a typical structure. Additionally, overlapped and non-overlapped data were introduced, and similarity measure analysis was also illustrated and compared with conventional similarity measure. As a result, overlapped data comparison was possible to present similarity with conventional similarity measure. Non-overlapped data similarity analysis provided the clue to solve the similarity of high dimensional data. Considering high dimensional data analysis was designed with consideration of neighborhoods information. Conservative and strict solutions were proposed. Proposed similarity measure was applied to express financial fraud among multi dimensional datasets. In illustrative example, financial fraud similarity with respect to age, gender, qualification and job was presented. And with the proposed similarity measure, high dimensional personal data were calculated to evaluate how similar to the financial fraud. Calculation results show that the actual fraud has rather high similarity measure compared to the average, from minimal 0.0609 to maximal 0.1667.

Deep image retrieval using artificial neural network interpolation and indexing based on similarity measurement

In content-based image retrieval(CBIR),primitive image signatures are critical because they represent the visual characteristics.Image signatures,which are algorithmically descriptive and accurately recognized visual components,are used to appropriately index and retrieve comparable results.To differentiate an image in the category of qualifying contender,feature vectors must have image information's like colour,objects,shape,spatial viewpoints.Previous methods such as sketch-based image retrieval by salient contour(SBIR)and greedy learning of deep Boltzmann machine(GDBM)used spatial information to distinguish between image categories.This requires interest points and also feature analysis emerged image detection problems.Thus,a proposed model to overcome this issue and predict the repeating pattern as well as series of pixels that conclude similarity has been necessary.In this study,a technique called CBIR-similarity measure via artificial neural network interpolation(CBIR-SMANN)has been presented.By collecting datasets,the images are resized then subject to Gaussian filtering in the pre-processing stage,then by permitting them to the Hessian detector,the interesting points are gathered.Based on Skewness,mean,kurtosis and standard deviation features were extracted then given to ANN for interpolation.Interpolated results are stored in a database for retrieval.In the testing stage,the query image was inputted that is subjected to pre-processing,and feature extraction was then fed to the similarity measurement function.Thus,ANN helps to get similar images from the database.CBIR-SMANN have been implemented in the python tool and then evaluated for its performance.Results show that CBIR-SMANN exhibited a high recall value of 78%with a minimum retrieval time of 980 ms.This showed the supremacy of the proposed model was comparatively greater than the previous ones.