Intuitionistic Fuzzy Divergence Research Articles

Intuitionistic fuzzy divergence for evaluating the mechanical stress state of steel plates subject to bi-axial loads

The uncertainty that characterizes the external mechanical loads to which any connection plate in steel structures is subjected determines the non-uniqueness of the isochoric deformation distributions. Since the eddy currents induced on the plates produce magnetic field maps with a high fuzziness content, similar to those of the isochoric deformations, their use can be exploited to evaluate the extent of the external load that determines a specific induced current map. Starting from an approach known in the literature, according to which the map-external load association is operated through fuzzy similarity computations, in this paper, we generalize this method by reformulating it in terms of intuitionistic fuzzy logic by proposing a classification based on divergence computations. Our approach, acting adaptively on the fuzzification of the maps, results in a better classification percentage, besides significantly reducing the presence of doubtful cases due to the uncertainty of each applied load. Furthermore, a FEM software tool was developed, which turned out to be, to a certain extent, a substitute for the experimental procedure, notoriously more expensive. Even if the procedure was applied on plates subjected to bi-axial loads, it could be used for other types of loads since the classification operator processes the eddy current maps exclusively, regardless of their cause.

Generalized TODIM method based on symmetric intuitionistic fuzzy Jensen–Shannon divergence

Intuitionistic fuzzy (IF) theory has become main approach to representing imprecision and vagueness. The IF divergence measure (IFDivM) based on Jensen–Shannon divergence is perhaps the most widely used measure to compare the similarity of multiple intuitionistic fuzzy sets (IFSs). In the present paper, this IFDivM is examined and applied to multiple examples. It is found that some extant IFDivMs hardly satisfy the axiomatic definition, and in a few cases even unable to show divergence of trivial IFSs. To address these inconsistencies, a new IFDivM based on Jensen–Shannon divergence is proposed, free from these problems. The effectiveness of the proposed IFDivM is tested on several critical cases, and precise analysis of its properties is performed. It is proved that the proposed IFDivM satisfies the axiomatic definition of IFDivMs. To illustrate the practical significance of the IFDivM, a novel intuitionistic fuzzy (IF) TODIM method, based on the proposed IFDivM, is developed, termed as GIF-TODIM method. Unlike the existing IF-TODIM methods, GIF-TODIM does not suffer from the revere ordering inconsistencies. The proposed GIF-TODIM method and the proposed IFDivM are applied to a real-world case study on supplier selection. A detailed comparative analysis is performed taking the TOPSIS method and other IFDivMs as baselines. The role of attitude on the final choice is analyzed in great detail. It is found that the proposed GIF-TODIM method is indeed useful, effective, and superior to the counterpart methods, when it comes to real-world situations. Concomitantly, in the present work, it is also revealed that the TOPSIS method based on the 2-D Hamming distance is a special form of the proposed GIF-TODIM method, when decision-makers have the same attitude towards losses and gains. Thus, an interesting relationship between TOPSIS and TODIM is identified under the intuitionistic fuzzy environment, which is bound to propel significant research in the area of decision making under uncertain conditions. As a whole, the article offers comprehensive analyses of IFDivMs and the TODIM method under the intuitionistic fuzzy environment.

Exponential-Trigonometry Intuitionistic Fuzzy Divergence Measure

Based on the exponential and trigonometry functions, a new divergence measure is introduced under the intuitionistic fuzzy environment. The Intuitionistic Fuzzy Divergence Measure is an indispensable instrument to calculate the variance between two intuitionistic fuzzy sets. Many attractive properties are displayed to enhance the value of introduced intuitionistic fuzzy divergence measure. Many existing divergence measures are reviewed with their counter-intuitive examples. Finally, the invented divergence measure is applicative in the field of medical deliverance to differentiate between diseases with nearby same symptoms, pattern recognition to categorize the unknown into one of the known pattern.

Morphological operations on temporal intuitionistic fuzzy sets

This paper is devoted to develop the theory of temporal intuitionistic fuzzy sets. The matrix representation of a TIFS is also introduced for easy symbolization. In addition to a few basic operations, length of a TIFS and its properties are discussed. Morphological operations on temporal intuitionistic fuzzy sets are defined using (i) mathematical operations, (ii) structuring element, (iii) inclusion indicators, and (iv) temporal intuitionistic fuzzy divergence and verified with suitable examples.

A novel hyperbolic intuitionistic fuzzy divergence measure based mammogram enhancement for visual elucidation of breast lesions

In this article, we have proposed a novel mammogram image enhancement approach for visual interpretation of breast masses using an adaptive intuitionistic fuzzy divergent measure under hyperbolic regularization. The proposed scheme pursuits to raise the underexposed and abnormal growth of cells such as breast masses, deformity tissues, nodules, and lumps in mammogram images. In the first step, a complementary image has been generated from the source mammogram to separate object and background area. Thereafter, both source and background images are mapped into Intuitionistic Fuzzy Set (IFS) plane under Hyperbolic Regularization (HR). A novel entropy based intuitionistic fuzzy divergence measure has been designed using hyperbolic function for the membership modification in this work. In addition, fuzzy ambiguity correction distance function has been obtained from the hesitant score vectors from both source and complementary images. Werner’s AND-OR has been utilized on both of them to generate modified membership function. Finally, we have achieved enhanced mammogram with visually improved breast masses through defuzzification process. It has been shown that the proposed method provides better result in comparison with the existing methods in terms of qualitative and higher score of image quantity measurement metrics such as SSIM (0.83), FQI (0.85), and IFQI (0.88).

A region-adaptive non-local denoising algorithm for low-dose computed tomography images.

Low-dose computed tomography (LDCT) can effectively reduce radiation exposure in patients. However, with such dose reductions, large increases in speckled noise and streak artifacts occur, resulting in seriously degraded reconstructed images. The non-local means (NLM) method has shown potential for improving the quality of LDCT images. In the NLM method, similar blocks are obtained using fixed directions over a fixed range. However, the denoising performance of this method is limited. In this paper, a region-adaptive NLM method is proposed for LDCT image denoising. In the proposed method, pixels are classified into different regions according to the edge information of the image. Based on the classification results, the adaptive searching window, block size and filter smoothing parameter could be modified in different regions. Furthermore, the candidate pixels in the searching window could be filtered based on the classification results. In addition, the filter parameter could be adjusted adaptively based on intuitionistic fuzzy divergence (IFD). The experimental results showed that the proposed method performed better in LDCT image denoising than several of the related denoising methods in terms of numerical results and visual quality.

A fuzzy edge detector driven telegraph total variation model for image despeckling

<p style='text-indent:20px;'>Speckle noise suppression is a challenging and crucial pre-processing stage for higher-level image analysis. In this work, a new attempt has been made using telegraph total variation equation and fuzzy set theory for image despeckling. The intuitionistic fuzzy divergence function has been used to distinguish between edges and noise. To the best of the authors' knowledge, most of the studies on the multiplicative speckle noise removal process focus only on diffusion-based filters, and little attention has been paid to the study of fuzzy set theory. The proposed approach enjoys the benefits of both telegraph total variation equation and fuzzy edge detector, which is robust to noise and preserves image structural details. Moreover, we establish the existence and uniqueness of weak solutions of a regularized version of the present system using the Schauder fixed point theorem. With the proposed technique, despeckling is carried out on natural, real synthetic aperture radar, and real ultrasound images. The experimental results computed by the suggested method are reported, which are found better in terms of noise elimination and detail/edge preservation, concerning the existing approaches.</p>

New Generalized Intuitionistic Fuzzy Divergence Measure with Applications to Multi-Attribute Decision Making and Pattern Recognition

Background: The notion of fuzzy set was introduced by Zadeh. After that, many researchers extended the concept of fuzzy sets in different ways. Atanassov introduced the concept of intuitionistic fuzzy sets as an extension of fuzzy sets. This concept is applied in many fields such as bio-informatics, image processing, decision making, feature selection, pattern recognition, etc. Objectives: The prime objective of this paper is to introduce a new generalized intuitionistic fuzzy divergence measure with proof of its validity and discussions on its elegant properties. Applications of the proposed divergence measure in multi-attribute decision making and pattern recognition are also discussed with some numerical illustrations. Further, the proposed divergence measure is compared with other methods for solving MADM and pattern recognition problems which exist in the literature. Methods: The divergence measure method is used to measure the divergence between two given sets. In addition, the results of the other existing measures are also given to compare with the proposed measure. Results: It was observed that the proposed divergence measure found much better results in comparison with the other existing methods. Conclusion: A new divergence measure for intuitionistic fuzzy sets is introduced with some of its properties. Applications of the proposed divergence measure to pattern recognition and MADM are illustrated through examples. The comparison of the proposed method with the existing methods shows the legacy of the results of the proposed method. It is concluded that the proposed divergence measure is effective for solving real-world problems related to MADM and pattern recognition.

Novel Generalized Divergence Measure on Intuitionistic Fuzzy Sets and Its Application

In the present paper, we introduce a new parametric fuzzy divergence measure on intuitionistic fuzzy sets. Some properties of the proposed measure are also being studied. In addition, the application of the intuitionistic fuzzy divergence measure in decision making and consequently choosing the best medicines and treatment for the patients has also been discussed. There are some diseases for which vaccine is not available. In that case, we have devised a method to choose the best treatment for the patients based on the results of clinical trials.

A novel EDAS approach on intuitionistic fuzzy set for assessment of health-care waste disposal technology using new parametric divergence measures

Nowadays, health-care waste management is a challenging issue for both the public and government sectors because it contains infectious, radioactive, or hazardous waste. Selecting a suitable method for health-care waste disposal is known as a complex decision-making problem due to the existence of several multiple criteria that may in conflict with each other. In this paper, we propose a novel method called evaluation based on distance from average solution framework based on parametric divergence measures with the context of intuitionistic fuzzy sets to evaluate and rank the health-care waste disposal alternative. To do this, first, novel parametric intuitionistic fuzzy divergence measures are developed, and various desired properties have also been examined. Second, the decision experts are evaluated, and the criteria weights are computed by developed parametric divergence measure method. Third, the preference order of the alternatives is illustrated by the developed framework. The proposed framework is based on the positive and negative distances from the average solution. Moreover, the health-care waste disposal alternative selection problem is considered to elucidate the applicability of the proposed framework. Four health-care waste disposal alternatives, including incineration, steam sterilization, microwave and landfill disposal, are considered in this study. The health-care waste disposal alternatives considered in this study include. The outcome illustrates that, the steam sterilization was the highest appraisal score (0.7025) and therefore, it should be chosen as the most suitable health-care waste disposal method in this study. Also, a comparison with existing approaches is shown to illustrate the validity and practicability of the developed framework.

A novel entropy and divergence measures with multi-criteria service quality assessment using interval-valued intuitionistic fuzzy TODIM method

Interval-valued intuitionistic fuzzy sets (IVIFSs) are proven to be the fastest growing research area and are more flexible way to handle the uncertainty. Information measures play vital role in the study of uncertain information; therefore, number of new interval-valued intuitionistic fuzzy divergence and entropy measures have been proposed in the literature and applied for different purposes. Recently, multi-criteria decision-making (MCDM) methods with IVIFSs have broadly studied by researchers and practitioners in various fields. In this paper, firstly surveys of IVIF-divergence and entropy measures are conducted and then demonstrated some counter-intuitive cases. Then, novel divergence and entropy measures are originated for IVIFSs to avoid the shortcomings of previous measures. Later on, systematic reviews of Portuguese for Interactive Multi-criteria Decision Making (TODIM) method are presented with recent fuzzy developments. Based on classical TODIM method, a new approach for MCDM is introduced under IVIF environment which considers the bounded rationality of decision makers. In the present method, the proposed entropy measure is utilized to compute the weight vector of the criteria, and the proposed divergence measure is applied in the calculation of dominance degrees. To illustrate the effectiveness of the present approach, a decision-making problem of vehicle insurance companies is presented where the evaluation values of the alternatives are given in terms of IVIF numbers. Comparison with some existing methods shows the applicability and consistency of the present method.

On intuitionistic fuzzy order-α divergence and entropy measures with MABAC method for multiple attribute group decision-making

The development of information measures associated with fuzzy and intuitionistic fuzzy sets is an important research area from the past few decades. Divergence and entropy are two significant information measures in the intuitionistic fuzzy set (IFS) theory, which have gained wider attention from researchers due to their extensive applications in different areas. In the literature, the existing information measures for IFSs have some drawbacks, which make them irrelevant to use in application areas. In order to obtain more robust and flexible information measures for IFSs, the present work develops and studies some parametric information measures under the intuitionistic fuzzy environment. First, the paper reviews the existing intuitionistic fuzzy divergence measures in detail with their shortcomings and then proposes four new order-α divergence measures between two IFSs. It is worth mentioning that the developed divergence measures satisfy several elegant mathematical properties. Second, we define four new entropy measures called order-α intuitionistic fuzzy entropy measures in order to quantify the fuzziness associated with an IFS. We prove basic and advanced properties of the order-α intuitionistic fuzzy entropy measures for justifying their validity. The paper shows that the introduced measures include various existing fuzzy and intuitionistic fuzzy information measures as their special cases. Further, utilizing the conventional multi-attributive border approximation area comparison (MABAC) model, we develop an intuitionistic fuzzy MABAC method to solve real-life multiple attribute group decision-making problems. Finally, the proposed method is demonstrated by using a practical application of personnel selection.

Jensen-Tsalli’s Intuitionistic Fuzzy Divergence Measure and Its Applications in Medical Analysis and Pattern Recognition

Vagueness in scientific studies poses a challenge. Intuitionistic Fuzzy Set (IFS) theory has emerged as a powerful and flexible tool to counter such challenge. So, there is a need to develop such measures which can not only measure the vagueness but also quantify the differences in underlying IFSs. The aim of this communication is to introduce one such divergence measure called Intuitionistic Fuzzy Jensen-Tsalli Divergence measure in the settings of IFS theory. The presence of parameters makes the proposed divergence measure flexible and competent for applications. Besides discussing some of its major properties, the findings are applied in pattern recognition problem and in medical diagnosis of some diseases with same set of symptoms. The performance of the proposed measure is genuinely compared with some other existing measures in literature through numerical examples based on medical diagnosis and pattern recognition.

Multi-attribute decision making based on novel generalized parametric exponential intuitionistic fuzzy divergence measure

In this work, the main theme is to investigate a novel generalized parametric exponential intuitionistic fuzzy divergence measure along with the study of its detailed properties for its authenticity. The applications of this newly developed generalized intuitionistic fuzzy divergence measure have been provided to multi-attribute decision making (MADM). Numerical verification has been illustrated to demonstrate the proposed method for solving multi-attribute decision making problem under fuzzy environment.

Intuitionistic fuzzy divergence measure-based ELECTRE method for performance of cellular mobile telephone service providers

In India, Telecom sector has been enduring a massive growth for over two and half decades in the bandwidth, preference of services and depth of penetration in urban, semi-urban and rural areas. Exploring the service providers or selecting the best cellular mobile telephone service providers (CMTSPs/TSPs) according to operational performance parameter can help to achieve the goal of telecom service provider selection (TSPS). Here, this assessment generally comprises various TSPs alternatives and different operational performance criteria; therefore, TSPS could be considered as a multi-criteria decision-making (MCDM) problem. The analytical data have been taken from the Telecom Regulatory Authority of India (TRAI), Jan–Mar 2017. Most of the data vary from 1 month to another. Thus, these small ranges of variation in the data are incorporated with the intuitionistic fuzzy numbers (IFNs). In this paper, we develop an outranking method, intuitionistic fuzzy ELECTRE (IF-ELECTRE), for MCDM problems. Proposed method is based on divergence measure, operators of IFNs, some modifications of classical ELECTRE method. In the MCDM, the criterion weight determination is a vital issue for the accuracy of evaluation results. In the process of calculation of criterion weight, concordance and discordance values, we propose new Jensen–Shannon divergence (JS-divergence) for IFSs to overcome the shortcoming of the existing ones and demonstrate different elegant properties of the proposed one. Since the uncertainty is an inevitable feature of MCDM problems, the proposed method can be a valuable tool for decision-making in an uncertain atmosphere to determine the partial-preference outranking order. To express the strength and reasonableness of the proposed method in the real-world MCDM problems, a TSPS problem is implemented. Using the proposed framework, a decision expert can make a strategy to improve the performance by benchmarking operational parameters. Finally, a comparison is discussed between the results of the proposed method and the existing ones for validating the proposed method. This analysis shows that the proposed method is efficient and well consistent with the other methods.

Exponential Jensen intuitionistic fuzzy divergence measure with applications in medical investigation and pattern recognition

The need of suitable divergence measures arises as they play an important role in the problems related to discrimination and inferences. This communication is intended to introduce one such exponential divergence measure based on well-known exponential entropy introduced by Pal and Pal and its validation. Further, this idea has been generalized to introduce a new exponential divergence measure for intuitionistic fuzzy sets. Besides establishing its validity, some of its major properties are also studied. In addition to this, applications of proposed divergence measure for IFSs are given in medical investigation and pattern recognition.

Optimal TOU tariff design using robust intuitionistic fuzzy divergence based thresholding

This paper proposes a robust midterm framework to determine optimal time-of-use (TOU) electricity pricing for retailers using intuitionistic fuzzy divergence based thresholding. It will analyze load profile and perform a comprehensive evaluation of load violation and uncertainty as well by exponential intuitionistic fuzzy entropy. The key advantage is that the proposed method will handle uncertain behavior of load and wholesale price with membership and non-membership functions. In the proposed algorithm client response to the retailer prices and the competition among rival retailers have been explicitly taken into account. The proposed scheme can be applied to several pricing policies where the peak-to-average ratio (PAR) will be decreased. The model is implemented on a realistic case in which the superior performance of the proposed method is demonstrated.

Intuitionistic fuzzy divergence measure-based multi-criteria decision-making method

Divergence measure is a significant tool for evaluating the amount of discrimination for IFSs. Since then it has acquired concentration for their applications in different areas. In this paper, we utilize the conception of Jensen–Shannon divergence to propose new measures called Jensen-exponential divergence for measuring the discrimination between intuitionistic fuzzy sets (IFSs) and demonstrate some very elegant properties, which show its strength for applications point of view. Next, a multi-criteria decision-making (MCDM) problem for IFSs that describes information about options with respect to criteria is studied. A technique that employs the relative comparisons for IFSs (that uses all the constraints, viz. membership, non-membership and hesitancy degrees) based on the advantage and disadvantage scores of the options with respect to criterion, where criterion weights are completely unknown, is used. In addition, the score functions are applied to evaluate the strength and worst scores leading to the satisfaction degree of the options. A multi-objective optimization model for optimal weights of the criterion that maximizes the satisfaction degree of each option is constructed. Energy resources play an important role in the social and economic development of the countries. Due to the industrialization, population growth and urbanization, the demand of energy is increasing gradually and this requires the selection of most suitable energy resource for economic development of the countries. The proposed MCDM method is presented to choose the most appropriate energy alternative among set of renewable energy alternatives. In this real case study, the decision makers provide their opinions in terms of linguistic variables because it is tricky to portray exact numerical values during the evaluation of energy alternatives. Finally, a comprehensive comparison is prepared to express the effectiveness of the technique over the existing techniques for the IF MCDM problems.

New Divergence and Entropy Measures for Intuitionistic Fuzzy Sets on Edge Detection

Edges of the image play an important role in the field of digital image processing and computer vision. The edges reduce the amount of data, extract useful information from the image and preserve significant structural properties of an input image. Further, these edges can be used for object and facial expression detection. In this paper, we will propose new intuitionistic fuzzy divergence and entropy measures with its proof of validity for intuitionistic fuzzy sets. A new and significant technique has been developed for edge detection. To check the robustness of the proposed method, obtained results are compared with Canny, Sobel and Chaira methods. Finally, mean square error (MSE) and peak signal-to-noise ratio (PSNR) have been calculated and PSNR values of proposed method are always equal or greater than the PSNR values of existing methods. The detected edges of the various sample images are found to be true, smooth and sharpen.

Edge Detection Method for Latent Fingerprint Images Using Intuitionistic Type-2 Fuzzy Entropy

Abstract A latent fingerprint is an interesting issue because of it has attained from crime places and moreover contained a low quality image, less number of features and unwanted noises. It is necessity to extract the original image with exact boundary from the surface for further processing such as authentication, identification and matching. In this work, a new distance measure has been proposed for latent fingerprint edge detection using Intuitionistic Type-2 Fuzzy Entropy (IT2FE) and a comprehensible definition is made for Intuitionistic Type-2 Fuzzy Sets (IT2FS). IT2FS takes into account of uncertainty in the form of membership function which is also termed as Intuitionistic Type-2 Fuzzy Divergence (IT2FD). The experiment is conducted with public domain fingerprint databases such as FVC-2004 and IIIT-latent fingerprint. The edge detection is carried out with the proposed method and the results are discovered better regarding existing method.