Distance and similarity measures between intuitionistic fuzzy sets: A comparative analysis from a pattern recognition point of view

The Impact of the Intuitionistic Fuzzy Entropy-Based Weights on the Results of Subjective Quality of Life Measurement Using Intuitionistic Fuzzy Synthetic Measure

In this paper, an extended Intuitionistic Fuzzy Synthetic Measure (IFSM) with intuitionistic fuzzy (IF) entropy-based weights is presented. This method can be implemented in a ranking problem where the assessments of the criteria are expressed in the form of intuitionistic fuzzy values and the information about the importance criteria is unknown. One example of such a problem is measuring the subjective quality of life in cities. We join the debate on the determination of weights for the analysis of the quality of life problem using multi-criteria methods. To handle this problem, four different IF entropy-based weight methods were applied. Their performances were compared and analyzed based on the questionnaires from the survey concerning the quality of life in European cities. The studies show very similar weighting systems obtained by different IF entropy-based approaches, resulting in almost the same city rankings acquired through IFSM by using those weights. The differences in rankings obtained through the IFSM measure (and only by one position) concern the six cities included in the analysis. Our results support the assumption of the equal importance of the criteria in measuring this complex phenomenon.

Intuitionistic Fuzzy Modulus Similarity Measure

The concept of intuitionistic fuzzy sets (IFSs) is an expected explanation for finding the appropriate information. It originated from concept of fuzzy set (FS) theory, which extends the classical conception of a fuzzy set. This paper examines a number of widely employed similarity measures then proposes an IFSs modulus similarity measure and a weight similarity measure. Initially, the authors have discussed numerous existing similarity measures, some of which are unable to justify the axioms of being a similarity measure. Furthermore, some numerical examples are presented to compare the existing similarity measures with the proposed similarity measure. The proposed similarity measure is a practical and effective method for determining the qualitative similarity between IFSs, which do not have any paradoxical nature. In addition, the proposed similarity measure has been demonstrated practically in pattern recognition and medical diagnosis problem. Suggestions for future research comprise the conclusions of the paper.

Selection and application of building material suppliers with intuitionistic fuzzy multiple attribute decision making method

The construction industry is the basic industry of the country. With the rapid development of the economy, the construction industry has grown rapidly and the competition in the construction market has become more intense. The competition in the construction market is not only between individual enterprises, but also between the whole supply chain that provides products. Therefore, it is imperative to introduce the idea of supply chain management, strengthen the cooperation with suppliers and improve competitiveness. Supplier evaluation and selection is one of the first issues to be solved for the development of supply chain management. The selection and application of building material suppliers is a classic multiple attribute decision making (MADM). In this paper, the intuitionistic fuzzy sets (IFSs) and Hamacher operations is introduced and the induced intuitionistic fuzzy Hamacher power ordered weighted average (I-IFHPOWA) operator is built. Meanwhile, the properties of built operator are analyzed. Then, the I-IFHPOWA operator is applied to solve the MADM under IFSs. Finally, an example for building material supplier selection is utilized to proof this built model.

An Application of the Pythagorean Fuzzy Sets in the Fault Diagnosis

In this paper, a comprehensive review and critical analyses of methods based on the ordinary fuzzy set, Atanassov’s intuitionistic fuzzy set, and its extensions have been conducted to show their limitations and defects. Then, a novel similarity measure based on the generalized score function has been introduced that incorporates the significance (importance) of information, making it more intuitive to compare them. The proposed method is employed for the fault diagnosis of steam turbine generator unit under Pythagorean fuzzy environment. Ten fault types of rotating machines are established as failure patterns in nine different vibration frequency ranges, expressed in terms of Pythagorean fuzzy numbers. The superiority of the proposed method in dealing with uncertain and vague information is shown by comparing it with some existing measures in numerical examples.

On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights

In this paper, a novel Double Intuitionistic Fuzzy Synthetic Measure (DIFSM), based on intuitionistic fuzzy values for handling multi-criteria decision-making problems used to rank alternatives, is presented. In the studies, intuitionistic fuzzy sets (IFSs) represented uncertain, imprecise information or human judgment. The intuitionistic fuzzy sets can also reflect the approval, rejection, and hesitation of decision-makers. The degrees of satisfiability and non-satisfiability and uncertainty of each alternative with respect to a set of criteria are described by membership functions, non-membership functions, and hesitancy indexes, respectively. The aggregation algorithm DIFSM is inspired by Hellwig's method based on two reference points: ideal point (pattern) and anti-ideal point (anti-pattern), measuring distances between the alternative and ideal point and distance between the ideal and anti-ideal point. The proposed methods take into consideration the entropy-based weights of criteria. An illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach. Additionally, the comparative analysis results, using the DIFSM and the Intuitionistic Fuzzy TOPSIS-based framework, are presented.

Fsmpy: A Fuzzy Set Measures Python Library

This paper presents the fsmpy Python library for the implementation of any type of measures and comparisons of different types of fuzzy sets, as well as other important and useful utilities and algorithms. In this paper, we analyze the motivation behind its implementation, the design principles followed, the implemented modules of the library and its capabilities, considering intuitionistic fuzzy sets as the case study. Lastly, some examples of its application to widely used pattern recognition, medical diagnosis and image segmentation are presented.

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.

Attack-Aware IoT Network Traffic Routing Leveraging Ensemble Learning

Network Intrusion Detection Systems (NIDSs) are indispensable defensive tools against various cyberattacks. Lightweight, multipurpose, and anomaly-based detection NIDSs employ several methods to build profiles for normal and malicious behaviors. In this paper, we design, implement, and evaluate the performance of machine-learning-based NIDS in IoT networks. Specifically, we study six supervised learning methods that belong to three different classes: (1) ensemble methods, (2) neural network methods, and (3) kernel methods. To evaluate the developed NIDSs, we use the distilled-Kitsune-2018 and NSL-KDD datasets, both consisting of a contemporary real-world IoT network traffic subjected to different network attacks. Standard performance evaluation metrics from the machine-learning literature are used to evaluate the identification accuracy, error rates, and inference speed. Our empirical analysis indicates that ensemble methods provide better accuracy and lower error rates compared with neural network and kernel methods. On the other hand, neural network methods provide the highest inference speed which proves their suitability for high-bandwidth networks. We also provide a comparison with state-of-the-art solutions and show that our best results are better than any prior art by 1~20%.

Harmony Search Algorithm and Fuzzy Logic Theory: An Extensive Review from Theory to Applications

In recent years, many researchers have utilized metaheuristic optimization algorithms along with fuzzy logic theory in their studies for various purposes. The harmony search (HS) algorithm is one of the metaheuristic optimization algorithms that is widely employed in different studies along with fuzzy logic (FL) theory. FL theory is a mathematical approach to expressing uncertainty by applying the conceptualization of fuzziness in a system. This review paper presents an extensive review of published papers based on the combination of HS and FL systems. In this regard, the functional characteristics of models obtained from integration of FL and HS have been reported in various articles, and the performance of each study is investigated. The basic concept of the FL approach and its derived models are introduced to familiarize readers with the principal mechanisms of FL models. Moreover, appropriate descriptions of the primary classifications acquired from the coexistence of FL and HS methods for specific purposes are reviewed. The results show that the high efficiency of HS to improve the exploration of FL in achieving the optimal solution on the one hand, and the capability of fuzzy inference systems to provide more flexible and dynamic adaptation of the HS parameters based on human perception on the other hand, can be a powerful combination for solving optimization problems. This review paper is believed to be a useful resource for students, engineers, and professionals.

Distance-Based Knowledge Measure for Intuitionistic Fuzzy Sets with Its Application in Decision Making

Much attention has been paid to construct an applicable knowledge measure or uncertainty measure for Atanassov's intuitionistic fuzzy set (AIFS). However, many of these measures were developed from intuitionistic fuzzy entropy, which cannot really reflect the knowledge amount associated with an AIFS well. Some knowledge measures were constructed based on the distinction between an AIFS and its complementary set, which may lead to information loss in decision making. In this paper, knowledge amount of an AIFS is quantified by calculating the distance from an AIFS to the AIFS with maximum uncertainty. Axiomatic properties for the definition of knowledge measure are extended to a more general level. Then the new knowledge measure is developed based on an intuitionistic fuzzy distance measure. The properties of the proposed distance-based knowledge measure are investigated based on mathematical analysis and numerical examples. The proposed knowledge measure is finally applied to solve the multi-attribute group decision-making (MAGDM) problem with intuitionistic fuzzy information. The new MAGDM method is used to evaluate the threat level of malicious code. Experimental results in malicious code threat evaluation demonstrate the effectiveness and validity of proposed method.

Four Distances for Circular Intuitionistic Fuzzy Sets

In the paper, for the first time, four distances for Circular Intuitionistic Fuzzy Sets (C-IFSs) are defined. These sets are extensions of the standard IFS that are extensions of Zadeh’s fuzzy sets. As it is shown, the distances for the C-IFS are different than those for the standard IFSs. At the moment, they do not have analogues in fuzzy sets theory. Examples, comparing the proposed distances, are given and some ideas for further research are formulated.

Multi-attribute decision-making method based on a novel distance measure of linguistic intuitionistic fuzzy sets

Linguistic intuitionistic fuzzy sets can qualitatively rather than quantitatively express data in the form of membership degree. But quantitative tools are required to handle qualitative information. Therefore, an improved linguistic scale function, which can more accurately manifest the subjective feelings of decision-makers, is employed to deal with linguistic intuitionistic information. Subsequently, due to some commonly used distance measures do not comprehensively evaluate the information of linguistic intuitionistic fuzzy sets, an improved distance measure of linguistic intuitionistic fuzzy sets is designed. It considers the cross-evaluation information to get more realistic reasoning results. In addition, a new similarity measure defined by nonlinear Gaussian diffusion model is proposed, which can provide different response scales for different information between various schemes. The properties of these measures are also studied in detail. On this basis, a method in linguistic intuitionistic fuzzy environment is developed to handle multi-attribute decision-making problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method and the influence of the parameters is analyzed.

Representations of a Comparison Measure between Two Fuzzy Sets

This paper analyzes the representation behaviors of a comparison measure between two compared fuzzy sets. Three types of restrictions on two fuzzy sets are considered in this paper: two disjoint union fuzzy sets, two disjoint fuzzy sets and two general fuzzy sets. Differences exist among the numbers of possible representations of a comparison measure for the three types of fuzzy sets restrictions. The value of comparison measure is constant for two disjoint union fuzzy sets. There are 49 candidate representations of a comparison measure for two disjoint fuzzy sets, of which 13 candidate representations with one or two terms are obtained. For each candidate representation, a variant of the general axiomatic definition for a comparison measure is presented. Choosing the right candidate representation for a given application, we can easily and efficiently calculate and compare a comparison measure.

Similarity Measures for Learning in Lattice Based Biomimetic Neural Networks

This paper presents a novel lattice based biomimetic neural network trained by means of a similarity measure derived from a lattice positive valuation. For a wide class of pattern recognition problems, the proposed artificial neural network, implemented as a dendritic hetero-associative memory delivers high percentages of successful classification. The memory is a feedforward dendritic network whose arithmetical operations are based on lattice algebra and can be applied to real multivalued inputs. In this approach, the realization of recognition tasks, shows the inherent capability of prototype-class pattern associations in a fast and straightforward manner without need of any iterative scheme subject to issues about convergence. Using an artificially designed data set we show how the proposed trained neural net classifies a test input pattern. Application to a few typical real-world data sets illustrate the overall network classification performance using different training and testing sample subsets generated randomly.

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.

Applications of Neutrosophic Bipolar Fuzzy Sets in HOPE Foundation for Planning to Build a Children Hospital with Different Types of Similarity Measures

In this paper we provide an application of neutrosophic bipolar fuzzy sets in daily life’s problem related with HOPE foundation that is planning to build a children hospital, which is the main theme of this paper. For it we first develop the theory of neutrosophic bipolar fuzzy sets which is a generalization of bipolar fuzzy sets. After giving the definition we introduce some basic operation of neutrosophic bipolar fuzzy sets and focus on weighted aggregation operators in terms of neutrosophic bipolar fuzzy sets. We define neutrosophic bipolar fuzzy weighted averaging ( N B FWA ) and neutrosophic bipolar fuzzy ordered weighted averaging ( N B FOWA ) operators. Next we introduce different kinds of similarity measures of neutrosophic bipolar fuzzy sets. Finally as an application we give an algorithm for the multiple attribute decision making problems under the neutrosophic bipolar fuzzy environment by using the different kinds of neutrosophic bipolar fuzzy weighted/fuzzy ordered weighted aggregation operators with a numerical example related with HOPE foundation.

A distance measure between intuitionistic fuzzy sets and its application in medical diagnosis

The intuitionistic fuzzy set, as a generation of fuzzy set, can express and process uncertainty much better. Distance measures between intuitionistic fuzzy sets are used to indicate the difference degree between the information carried by intuitionistic fuzzy sets. Although some distance measures have been proposed in previous studies, they can not satisfy the axioms of distance measure, or exist counter-intuitive cases. In this paper, we give a new distance measure between intuitionistic fuzzy sets, which is based on a matrix norm and a strictly increasing (or decreasing) binary function. The new distance measure not only satisfies the axiomatic definition of distance measure, but also overcomes the counter-intuitive cases. It is proved that the new distance measure is reasonable by numerical examples. Moreover, we give the algorithms for pattern recognition and use it to solve medical diagnosis problems.

Decision Making in Medical Diagnosis via Distance Measures on Interval Valued Fuzzy Sets

The uncertain and sometimes vague, imprecise nature of medical documentation and information make the field of medical diagnosis is the most important and interesting area for applications of fuzzy set theory (FST), intuitionistic fuzzy set (IFS) and interval valued fuzzy set (IVFS). In this present study, first resemblance between IFS and IVFS has been established along with reviewed some existing distance measures for IFSs. Later, an attempt has been made to derive distance measures for IVFSs from IFSs and establish some properties on distance measures of IVFSs. Finally, medical diagnosis has been carried out and exhibits the techniques with a case study under this setting.

Super-Resolution Reconstruction from Single Image Based on Join Operation in Granular Computing

Improving the resolution of the image is convenient for people to study the local details of the image, and plays an important role in computer vision. The problem of generating a corresponding super-resolution (SR) image from a single low-resolution (LR) image is addressed via the join operation in the paper. Firstly, the LR image is partitioned into some patches, each patch is represented as the sphere granule set. Secondly, the join operation between two adjacent image patches is used to compensate the pixel value of SR image. Experimental results showed the feasibility and superiority via join operation by root mean square errors (RMSE) between the reconstructed SR image and the original image compared with bicubic interpolation and NNLasso.

Monotonic Similarity Measures of Interval-Valued Fuzzy Sets and Their Applications

A similarity measure is a measure that indicates the degree of similarity between two objects. The purpose of this work is to investigate the monotonicity properties and applications of similarity measures on interval-valued fuzzy sets. Through analyzing the intuitions of similarities, three kinds of monotonic similarity measures are defined. Furthermore, their properties and relationships with entropy and inclusion measure are investigated and discussed. Finally, some applications of the proposed monotonic similarity measures, such as pattern recognition, medical recognition, and medical diagnosis are presented.