Intuitionistic Fuzzy Functions Research Articles

The Forecasting of TheNumber Tourists Arriving in Turkey with Intuitionistic Fuzzy Regression Functions Approach

The impacts of the tourism sector on countries are felt in various areas such as economy, cultural heritage and social development. Tourism contributes significantly to a country's foreign exchange earnings and positively affects the trade network. Tourists' spending boosts local economies and increases employment. These effects are particularly important for Turkey. Tourist visits can be used as a tool for regional promotion. Therefore, tourism demand forecasting is necessary to make the best use of these positive effects on Turkey's economic development and to plan tourism activities. Artificial neural network methods and fuzzy systems for time series forecasting problem are frequently used analysis methods in recent years. In this study, the time series of the total number of tourists visiting Turkey on a monthly basis is analyzed with the intuitionistic fuzzy regression functions approach, which is a generalization of the fuzzy regression functions approach. The analysis performance of the intuitionistic fuzzy regression functions approach is evaluated using fuzzy regression functions approach, multilayer perceptron artificial neural network and multiplicative neuron model artificial neural networks. As a result of the analysis, it is concluded that the intuitionistic fuzzy regression approach produces better forecasting results than both some artificial neural network models and the fuzzy regression functions approach. Since this is the first time that the intuitionistic fuzzy regression functions approach has been used in forecasting the number of tourists, the study aims to contribute to the literature and to help tourism industry employees to be more efficient and successful by providing them with the opportunity to make better future planning.

Solving Intuitionistic Fuzzy Unconstrained Optimization Problems Using Interval Newton’s Method

This research work studies the optimization of intuitionistic fuzzy valued functions in unconstrained problems. The Interval Newton's Method using an Intuitionistic approach addresses both single and multivariable optimization problems. The study incorporates a mathematical comprehension of interval intuitionistic fuzzy valued problems, as well as real-world examples to demonstrate their effectiveness. Furthermore, MATLAB code is provided to demonstrate the implementation of the Interval Newton's Method.

On Intuitionistic Fuzzy Neutrosophic Soft Ideal Topological Spaces

The purpose of this paper is to introduce the notion of intuitionistic fuzzy neutronsophic soft ideal in Intuitionistic fuzzy neutronsophic soft set theory. The concept of intuitionistic fuzzy neutrosophic soft local function is also introduced. These concepts are discussed with a view to find new intuitionistic fuzzy neutronsophic soft topologies from the original one. The basic structure, respecially a basic for such generated Intuitionistic fuzzy neutronsophic soft topologies also studied here. Finally, the notion of compatibility of intuitionistic fuzzy neutronsophic soft ideals with Intuitionistic fuzzy neutrosophic soft topologies is introduced and some equivalent conditions concerning, this topic are established here.

An adaptive categorical effect size method based on intuitionistic meta fuzzy functions

There are several categorical effect size methods in the literature. It is not clear which method performs better for a given dataset and it is a challenging task to select the correct method for a given dataset. In this sense, to overcome the questions like “Which method should we choose?” and “Which categorical effect size method is more reliable for a given dataset?”, an adaptive categorical effect size method based on intuitionistic meta fuzzy functions is introduced in the paper. Thus, the main motivation of the proposed method is to obtain more accurate outcomes by combining the results of better performing methods instead of relying on only one method. In the study, the intuitionistic fuzzy c-means clustering algorithm is adapted to meta fuzzy functions by incorporating not only membership degrees but also non-membership degrees to improve the clustering accuracy of meta fuzzy functions. Meta fuzzy functions are the linear combination of seven categorical effect size methods and the weights, which are calculated from membership grades from intuitionistic fuzzy c-means algorithm. Among the functions, the one with the lowest mean absolute percentage error is selected as the best. To evaluate the performance of the proposed method, 2 × 3, 2 × 4, and 3 × 4 contingency tables were simulated. Additionally, the performance of the proposed method is also assessed by applying it to a real-time dataset. Experimental results show that the proposed method outperforms compared to the evaluated seven categorical effect size methods in terms of mean absolute percentage error. Also, the calculated effect sizes are within the range of ±10% in terms of bias. Thus, the results verified that proposed method achieves greater reliability.

Reliability Estimation of Inverse Weibull Distribution Based on Intuitionistic Fuzzy Lifetime Data

As a commonly used model in reliability analysis, the inverse Weibull distribution (IWD) is widely applied in various scientific fields. This paper considers the reliability estimation of the IWD based on intuitionistic fuzzy lifetime data. Firstly, the related concepts of the fuzzy set theory are reviewed, and the concepts of the intuitionistic fuzzy conditional density, intuitionistic fuzzy likelihood function, and intuitionistic fuzzy conditional expectation are obtained by extension. In classical estimations, the maximum likelihood estimators of parameters and reliability are derived. Due to the nonlinearity, the EM algorithm is used to obtain the maximum likelihood estimates. In the Bayesian estimation, the gamma prior is selected, and the Bayesian estimation of the parameters and reliability is conducted under the symmetric entropy and the scale square error loss function, respectively. Since the integrals are complicated, the Lindley approximation is used to approximate the Bayesian estimates. Then, the performance of these estimators is evaluated by the Monte Carlo simulation. The simulation results show that the Bayesian estimation is more suitable than the maximum likelihood estimation for the reliability estimation. Finally, a set of real data is used to prove the effectiveness of these proposed methods. Through these methods, the reliability of the intuitive fuzzy life data is accurately estimated, which provides an important reference for the reliability analysis in the scientific field.

An improved entropy function for the intuitionistic fuzzy sets with application to cloud vendor selection

This study proposes a novel entropy function for the intuitionistic fuzzy sets to improve the existing fuzzy entropy measure. We introduce an attitude-based entropy measure by methodically calculating the experts’ attitude values through variance approach. We discuss several important properties and present an example to demonstrate the applicability and efficacy of the proposed method. An illustrative example exhibits the effectiveness of the proposed intuitionistic fuzzy entropy functions and measures. We further show the superiority of the proposed intuitionistic fuzzy entropy measures over the existing measures.

Robust intuitionistic fuzzy regression functions approaches

The fuzzy regression functions approach is a fuzzy inference system that is not rule-based and not based on expert knowledge, unlike classical fuzzy inference systems. The fuzzy regression functions approach can be defined as a fuzzy inference system based on regression analysis using the ordinary least squares method and fuzzy clustering method. As is known, the ordinary least squares method is not effective when there is an outlier in the data set. So, the fuzzy regression functions approach is affected by the outliers. Since the fuzzy regression functions approach is affected by the outlier in the data set, it is inevitable that the intuitionistic fuzzy regression functions approach, which is a generalization of the fuzzy regression functions approach, is also affected by the outliers in the data set. In this study, robust intuitionistic fuzzy regression function approaches that are not affected by the outliers in the data set are proposed. In the proposed approach, the parameter estimation is made using the robust regression-based Welsch, Bisquare, Talwar, Huber, Logistic, and Cauchy functions instead of the ordinary least squares method. The performance of the proposed method is evaluated over Bitcoin and gold time series in different years. The analysis step is carried out separately for the original case of the relevant time series and for the case where they contain outliers. As a result of the analysis, it is concluded that the proposed method gives successful forecasting results both for the case where the time series contains outliers and for the original case. According to the statistical test results, the proposed method creates a statistically significant difference compared to other methods when the data contains outliers.

Relative Density-Based Intuitionistic Fuzzy SVM for Class Imbalance Learning

The support vector machine (SVM) has been combined with the intuitionistic fuzzy set to suppress the negative impact of noises and outliers in classification. However, it has some inherent defects, resulting in the inaccurate prior distribution estimation for datasets, especially the imbalanced datasets with non-normally distributed data, further reducing the performance of the classification model for imbalance learning. To solve these problems, we propose a novel relative density-based intuitionistic fuzzy support vector machine (RIFSVM) algorithm for imbalanced learning in the presence of noise and outliers. In our proposed algorithm, the relative density, which is estimated by adopting the k-nearest-neighbor distances, is used to calculate the intuitionistic fuzzy numbers. The fuzzy values of the majority class instances are designed by multiplying the score function of the intuitionistic fuzzy number by the imbalance ratio, and the fuzzy values of minority class instances are assigned the intuitionistic fuzzy membership degree. With the help of the strong capture ability of the relative density to prior information and the strong recognition ability of the intuitionistic fuzzy score function to noises and outliers, the proposed RIFSVM not only reduces the influence of class imbalance but also suppresses the impact of noises and outliers, and further improves the classification performance. Experiments on the synthetic and public imbalanced datasets show that our approach has better performance in terms of G-Means, F-Measures, and AUC than the other class imbalance classification algorithms.

The intuitionistic fuzzy concept-oriented three-way decision model

Recently, some researchers have explored three-way decision models in the fuzzy multi-criteria environments from the perspective of criterion fuzzy concept. The main characteristics of these models include the subjective preference of decision-maker for criteria and the evaluation value information system provided by decision-maker. However, the criterion fuzzy concept only considers the decision-maker’s membership preference to each criterion, and ignores the decision-maker’s non-membership preference to each criterion. In view of this, this paper further proposes a new criterion fuzzy concept, namely the intuitionistic fuzzy concept, to express decision-maker’s preference for each criterion. At the same time, we build an intuitionistic fuzzy concept-oriented three-way decision model to solve the ranking and classification problem in the intuitionistic fuzzy multi-criteria environments with decision-maker’s preference. Firstly, based on the defined intuitionistic fuzzy concept, we construct a new intuitionistic fuzzy loss function model. Meanwhile, using intuitionistic fuzzy similarity, we propose a new conditional probability calculation method to express the correlation degree between the intuitionistic fuzzy concept and alternative’s evaluation values. Secondly, we introduce three decision-making perspectives from the membership degree and non-membership degree of expected loss to obtain the final three-way classification scheme. Moreover, by combining the thresholds of the positive and negative perspectives, we obtain the comprehensive thresholds of the comprehensive perspective, which can be used to rank all alternatives. Finally, a supplier selection problem is used to verify the feasibility and superiority of the model, and six data sets are used to verify the applicability of the model.

On Intuitionistic Fuzzy β Generalized α Normal Spaces

In this paper a new concept of generalized intuitionistic fuzzy topological space called intuitionistic fuzzy β generalized α normal space is introduced. Several characterizations of intuitionistic fuzzy β generalized α normal space, intuitionistic fuzzy strongly β generalized α normal and intuitionistic fuzzy strongly β generalized α regular spaces are studied. Moreover, the related intuitionistic fuzzy functions with intuitionistic fuzzy β generalized α normal spaces are investigated.

Intuitionistic fuzzy decision support based on EDAS and grey relational degree for historic bridges reconstruction priority

Bridge management includes all actions in the life cycle of the bridge, to ensure its safety, stability, and functionality. Numerous problems have been identified that are primarily related to the organization of planning and the role of decision-making in the reconstruction of the historic pedestrian bridges. The planning process for the reconstruction of these bridges is crucial due to increased traffic load, poor condition, or damage to bridges. Some of these bridges are part of the cultural heritage, while some are unfairly neglected. The motivation for this research arose from the need to establish the priority for the reconstruction of historic pedestrian bridges to achieve their safety, stability, functionality, and cultural preservation. For this reason, a new decision support model based on intuitionistic fuzzy group decision-making to the multi-criteria analysis is created. The model combines multi-criteria method Evaluation Based on Distance from Average Solution and grey relational degree (GRD) with intuitionistic fuzzy theory. Three relevant decision groups of experts are formed, with the knowledge and expertise in the area of research problematic, establishing criteria for the evaluation. A new approach to the consistency of criteria weights is proposed. The intuitionistic fuzzy likelihood function is developed for the aggregation of bridge evaluations. Furthermore, GRD values are calculated to determine the reconstruction priority ranking of bridge for each decision group. The final ranking is defined by integrating Integer Linear Programming (ILP) and Ant Colony Optimization (ACO), determining spatial-functional, time, and financial constraints.

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>

Weighted butterfly optimization algorithm with intuitionistic fuzzy Gaussian function based adaptive-neuro fuzzy inference system for covid-19 prediction

Covid-19 cases are increasing each day, however none of the countries successfully came up with a proper approved vaccine. Studies suggest that the virus enters the body causing a respiratory infection post contact with a disease. Measures like screening and early diagnosis contribute towards the management of COVID- 19 thereby reducing the load of health care systems. Recent studies have provided promising methods that will be applicable for the current pandemic situation. The previous system designed a various Machine Learning (ML) algorithms such as Decision Tree (DT), Random Forest (RF), XGBoost, Gradient Boosting Machine (GBM) and Support Vector Machine (SVM) for predicting COVID-19 disease with symptoms. However, it does not produce satisfactory results in terms of true positive rate. And also, better optimization methods are required to enhance the precision rate with minimum execution time. To solve this problem the proposed system designed a Weighted Butterfly Optimization Algorithm (WBOA) with Intuitionistic fuzzy Gaussian function based Adaptive-Neuro Fuzzy Inference System (IFGF-ANFIS) classifier for predicting the magnitude of COVID- 19 disease. The principle aim of this method is to design an algorithm that could predict and assess the COVID-19 parameters. Initially, the dataset regarding COVID-19 is taken as an input and preprocessed. The parameters included are age, sex, history of fever, travel history, presence of cough and lung infection. Then the optimal features are selected by using Weighted Butterfly Optimization Algorithm (WBOA) to improve the classification accuracy. Based on the selected features, an Intuitionistic fuzzy Gaussian function based Adaptive-Neuro Fuzzy Inference System (IFGF-ANFIS) classifier is utilized for classifying the people having infection possibility. The studies conducted on this proposed system indicates that it is capable of producing better results than the other systems especially in terms of accuracy, precision, recall and f-measure.

Intuitionistic Fuzzy (IF) Overlap Functions and IF-Rough Sets with Applications

Overlap function (which has symmetry and continuity) is widely used in image processing, data classification, and multi-attribute decision making problems. In recent years, theoretical research on overlap function has been extended to interval valued overlap function and lattice valued overlap function, but intuitionistic fuzzy overlap function (IF-overlap function) has not been studied. In this paper, the concept of IF-overlap function is proposed for the first time, then the generating method of IF-overlap function is given. The representable IF-overlap function is defined, and the concrete examples of representable and unrepresentable IF-overlap functions are given. Moreover, a new class of intuitionistic fuzzy rough set (IF-roght set) model is proposed by using IF-overlap function and its residual implication, which extends the IF-rough set model based on intuitionistic fuzzy triangular norm, and the basic properties of the new intuitionistic fuzzy upper and lower approximate operators are analyzed and studied. At the same time, the established IF-rough set based on IF-overlap function is applied to MCDM (multi-criteria decision-making) problems, the intuitionistic fuzzy TOPSIS method is improved. Through the comparative analysis of some cases, the new method is proved to be flexible and effective.

Subtraction and division operations on intuitionistic fuzzy sets derived from the Hamming distance

Intuitionistic fuzzy values, each characterized by a membership degree and a nonmembership degree, are the basic components of intuitionistic fuzzy sets. Arithmetic operations on intuitionistic fuzzy values/sets are of importance in practical problem solving. In this paper, the subtraction and division operations over intuitionistic fuzzy values/sets are derived from the Hamming distance between them by the optimization method. Compared with the existing operations, the developed operations are complete, that is, any two intuitionistic fuzzy values/sets can be performed by these two operations. Then, fundamental properties of the modified arithmetic operations are extensively investigated for intuitionistic fuzzy values/sets. Finally, the continuity and the derivative operation of intuitionistic fuzzy functions are introduced based on the proposed operations, which provides a novel basis for the intuitionistic fuzzy differential calculus .

Isomorphism Theorems on Intuitionistic Fuzzy Abstract Algebras

The concept of abstract algebra on intuitionistic fuzzy sets were introduced and some basic theorems were proved by authors in 2017. In this study, homomorphism between intuitionistic fuzzy abstract algebras is defined, intuitionistic fuzzy function is examined and then intuitionistic fuzzy congruence relations are defined on intuitionistic fuzzy abstract algebra. First and third isomorphism theorems on intuitionistic abstract algebras are introduced.

Integrating Kano Model, AHP, and QFD Methods for New Product Development Based on Text Mining, Intuitionistic Fuzzy Sets, and Customers Satisfaction

Online reviews are crucial to any online business that wants to increase sales on the Internet. Customer reviews have information about product attributes, customer requirements (CRs), and shopping experience; mining reviews provide the direction of decision-making for new product development and design (NPDD). Besides, the information of customer preference has vagueness and uncertainty, and the accuracy of decision-making information directly affects the success of NPDD. This paper proposed a methodology that integrates the Kano model (KM), analytic hierarchy process (AHP), and quality function deployment (QFD) methods with intuitionistic fuzzy set (IFS) to solve decision-making problems in NPDD. By the new method, the web crawler technology was first applied to e-commerce web sites to collect raw data, and the representative CRs were extracted through combining LDA model with Apriori algorithm. Second, the intuitionistic fuzzy Kano model (IFKM) is proposed to evaluate adjustment coefficient of CRs and Kano categories via customer preference membership functions. Thirdly, overall weights which contained emotional needs (ENs) and functional needs (FNs) are obtained via intuitionistic fuzzy analytic hierarchy process (IFAHP); thus, the adjusted weights are calculated from IFKM and IFAHP. Next, the intuitionistic fuzzy quality function deployment (IFQFD) is proposed to acquire engineering characteristics (ECs) of weights through combining competition benchmarks and based on technical benchmarks to make goals for a company’s NPDD. Finally, the method was applied to study vertical-configured air conditioner (VAC) as an example. The results showed that the application of text mining and IFS to improve CS is both reliable and scientific.

Intuitionistic Fuzzy Calculus Based on Einstein Operations

The intuitionistic fuzzy set (A-IFS) was introduced by Atanassov to generalize the concept of Zadeh’s fuzzy set. The basic elements of an A-IFS are the intuitionistic fuzzy numbers (IFNs). In this paper, we deal with the intuitionistic fuzzy set with the help of Einstein operations. First we introduce some operations of A-IFS, such as the Einstein sum, Einstein product, Einstein scalar multiplication and Einstein exponentiation, and redefine two new and important operation as Einstein subtraction and Einstein division. Then we investigate the limit, continuity and derivatives of intuitionistic fuzzy functions (IFFs) based on the Einstein operations. Furthermore and what is more, some infinite and definite integrals for the IFFs are discussed importantly, and an aggregation method based on the definite integral was introduced to solve some actual decision making problems, which focus on the original data and obtain better overall evaluations in information aggregation.

An adaptive forecast combination approach based on meta intuitionistic fuzzy functions

Intuitionistic meta fuzzy forecast combination functions are introduced in the paper. There are two challenges in the forecast combination literature, determining the optimum weights and the methods to combine. Although there are a few studies on determining the methods, there are numerous studies on determining the optimum weights of the forecasting methods. In this sense, the questions like “What methods should we choose in the combination?” and “What combination function or the weights should we choose for the methods” are handled in the proposed method. Thus, the first two contributions that the paper aims to propose are to obtain the optimum weights and the proper forecasting methods in combination functions by employing meta fuzzy functions (MFFs). MFFs are recently introduced for aggregating different methods on a specific topic. Although meta-analysis aims to combine the findings of different primary studies, MFFs aim to aggregate different methods based on their performances on a specific topic. Thus, forecasting is selected as the specific topic to propose a novel forecast combination approach inspired by MFFs in this study. Another contribution of the paper is to improve the performance of MFFs by employing intuitionistic fuzzy c-means. 14 meteorological datasets are used to evaluate the performance of the proposed method. Results showed that the proposed method can be a handy tool for dealing with forecasting problems. The outstanding performance of the proposed method is verified in terms of RMSE and MAPE.

Width-based distance measures on interval-valued intuitionistic fuzzy sets

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.