Intuitionistic Index Research Articles

Multiple target data-association algorithm based on Takagi–Sugeno intuitionistic fuzzy model

To solve the problem of data association in multiple target tracking in a densely cluttered environment, a multiple target data association algorithm based on Takagi–Sugeno (T-S) intuitionistic fuzzy model is proposed. In the proposed algorithm, the new multiple target T-S intuitionistic fuzzy model (MTTS-IFM) is constructed by incorporating intuitionistic fuzzy sets and intuitionistic fuzzy numbers. To identify the premise parameters for MTTS-IFM, a new intuitionistic index is defined and a modified form of the intuitionistic fuzzy C-means clustering algorithm is proposed. Furthermore, to solve the multiple target data association for the MTTS-IFM approach, the input variables of MTTS-IFM are defined using the maximum intuitionistic fuzzy entropy, and a data association approach is proposed to deal with the uncertainty between targets and measurements. Finally, simulation results show that the performance of the proposed algorithm is better than that of algorithms designed for multiple target tracking in either a clutter-free or cluttered environment. Moreover, the real-time performance was clearly better than that of the joint probabilistic data association filter (JPDAF) and slightly better than that of maximum entropy fuzzy (MEF-JPDAF), Fitzgerald-JPDAF, and a T-S intuitionistic fuzzy model (TS-FM).

Improvement of Collaborative Filtering Recommendation Algorithm Based on Intuitionistic Fuzzy Reasoning Under Missing Data

Commodity recommendation plays an essential role in the marketing field in the Internet era, and collaborative filtering, as a powerful technique of commodity recommendation, has been widely concerned in both academic studies and practical applications. Existing research on collaborative filtering often uses methods such as genetic algorithm and neural network to solve the sparsity and cold start problems while ignoring the fuzziness of users' ratings on goods or services. To solve the problems, we propose a recommendation algorithm (IFR-CF) based on intuitionistic fuzzy reasoning and collaborative filtering. In this algorithm, the characteristic coefficient in intuitionistic fuzzy reasoning is used to replace the traditional similarity coefficient to determine neighbor set, and the finite prior ordering method is used to replace traditional algorithm to recommend commodity. Two groups of data are extracted from Movielens and Jester datasets for experiments, and the MAE value generated by the recommended items is taken as the metric to verify the algorithm performance. Experimental results show that compared with the traditional algorithms, our algorithm achieves lower MAE value and higher recommendation accuracy. Meanwhile, the intuitionistic index of fuzzy set is taken into account in the calculation of the hesitation coefficient, which provides a novel solution to the problem of missing scoring data of users.

Online Visual Multiple Target Tracking by Intuitionistic Fuzzy Data Association

In this paper, a novel frame-by-frame data association algorithm based on intuitionistic fuzzy sets is proposed for online visual multiple target tracking. In the proposed algorithm, the association costs between targets and measurements are replaced by the intuitionistic fuzzy membership degrees which are obtained by a modified intuitionistic fuzzy c-means clustering algorithm. In addition, in order to mine useful information from the uncertain measurements, a new intuitionistic index is defined and the intuitionistic fuzzy point operator is applied to extract valuable information from the intuitionistic index. Experiments with challenging public datasets demonstrate that the proposed visual tracking algorithm improves tracking performance compared to other algorithms.

Threat assessment method based on intuitionistic fuzzy similarity measurement reasoning with orientation

The aim of this paper is to propose a threat assessment method based on intuitionistic fuzzy measurement reasoning with orientaion to deal with the shortcomings of the method proposed in [Ying-Jie Lei et al., Journal of Electronics and Information Technology 29(9)(2007)2077-2081] and [Dong-Feng Chen et al., Procedia Engineering 29(5)(2012)3302-3306] the ignorance of the influence of the intuitionistic index's orientation on the membership functions in the reasoning, which caused partial information loss in reasoning process. Therefore, we present a 3D expression of intuitionistic fuzzy similarity measurement, make an analysis of the constraints for intuitionistic fuzzy similarity measurement, and redefine the intuitionistic fuzzy similarity measurement. Moreover, in view of the threat assessment problem, we give the system variables of attribute function and assessment index, set up the reasoning system based on intuitionistic fuzzy similarity measurement with orientation, and design the reasoning rules, reasoning algorithms and fuzzy-resolving algorithms. Finally, through the threat assessment, some typical examples are cited to verify the validity and superiority of the method.

Intuitionistic fuzzy joint probabilistic data association filter and its application to multitarget tracking

This paper proposes a new intuitionistic fuzzy joint probabilistic data association filter for multitarget tracking in a cluttered environment. In the proposed algorithm, the joint association probabilities in JPDAF are reconstructed by utilizing intuitionistic fuzzy membership degrees of the measurements belonging to the targets. To compute the intuitionistic fuzzy membership degree, a new intuitionistic fuzzy clustering method is proposed based on intuitionistic fuzzy point operator, which can extract useful information from uncertainty information of measurement. At the same time, two new weight assignments are introduced to deal with the uncertainty of measurement, which lead to two different data association methods, IF-JPDAF1 and IF-JPDAF2. Moreover, according to the characteristic of multitarget tracking, a new intuitionistic index of intuitionistic fuzzy set is defined. Finally, experiment results show the proposed algorithms have advantages over the conventional methods (including the JPDAF, Fitzgerald's JPDAF and MEF-JPDAF) in terms of efficiency and robustness.

ENTROPY FOR INTUITIONISTIC FUZZY SETS BASED ON DISTANCE AND INTUITIONISTIC INDEX

Many researchers have put forward lots of entropy and distance measures for intuitionistic fuzzy sets (IFSs). This paper firstly reviews some basic concepts for IFSs and several widely used distance measures between IFSs. And then a series of distance measures are presented on the basis of above widely used distance measures. Based on such distance measures and intuitionistic index, a set of entropies for IFSs are proposed and proved to meet the axiomatic requirements given by Szmidt and Kacprzyk in 2001. Besides, two numerical examples are demonstrated to verify the efficiency of the proposed entropies for IFSs. Finally, the paper concludes with suggestions for future research.

Image segmentation using Atanassov’s intuitionistic fuzzy sets

The problem of segmentation in spite of all the work over the last decades, is still an important research field and also a critical preprocessing step for image processing, mostly due to the fact that finding a global optimal threshold that works well for all kind of images is indeed a very difficult task that, probably, will never be accomplished.During the past years, fuzzy logic theory has been successfully applied to image thresholding. In this paper we describe a thresholding technique using Atanassov’s intuitionistic fuzzy sets (A-IFSs). This approach uses Atanassov’s intuitionistic index values for representing the hesitance of the expert in determining whether the pixel belongs to the background or that it belongs to the object. First, we describe the general framework of this approach to bi-level thresholding. Then we present its natural extension to multilevel thresholding. This multilevel threshold methodology segments the image into several distinct regions which correspond to a background and several objects.Segmentation experimental results and comparison with Otsu’s multilevel thresholding algorithm for the calculation of two and three thresholds are presented.

A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment

The purpose of this paper is to design a new extension of the ELECTRE, known as the elimination and choice translating reality method, for multi-criteria group decision-making problems based on intuitionistic fuzzy sets. This method is widely utilized when a set of alternatives should be identified and evaluated with respect to a set of conflicting criteria by reflecting decision makers’ (DMs’) preferences. However, handling the exact data and numerical measure is difficult to be precisely focused because the DMs’ judgments are often vague in real-life decision problems and applications. A more realistic and practical approach can be to use linguistic variables expressed in intuitionistic fuzzy numbers instead of numerical data to model DMs’ judgments and to describe the inputs in the ELECTRE method. The proposed intuitionsitic fuzzy ELECTRE utilizes the truth-membership function and non-truth-membership function to indicate the degrees of satisfiability and non-satisfiability of each alternative with respect to each criterion and the relative importance of each criterion, respectively. Then, a new discordance intuitionistic index is introduced, which is extended from the concept of the fuzzy distance measure. Outranking relations are defined by pairwise comparisons and a decision graph is depicted to determine which alternative is preferable, incomparable or indifferent in the intuitionistic fuzzy environment. Finally, a comprehensive sensitivity analysis is employed to further study regarding the impact of threshold values on the final evaluation, and a comparative analysis is demonstrated with an application example in flexible manufacturing systems between the proposed ELECTRE method and the existing intuitionistic fuzzy technique for order preference by similarity to ideal solution (IF-TOPSIS) method.

An Extensional Clustering Algorithm of FCM Based on Intuitionistic Extension Index

The fuzzy C-means algorithm is an iterative algorithm in which the desired number of clusters C and the initial clustering seeds has to be pre-defined. The seeds are modified in each stage of the algorithm and for each object a degree of membership to each of the clusters is estimated. In this paper, an extensional clustering algorithm of FCM based on an intuitionistic extension index, denoted E-FCM algorithm, is proposed. For comparing the performance of the above mentioned two algorithms, the experimental results of three benchmark data sets show that the E-FCM algorithm outperforms the FCM algorithm.

The ELECTRE multicriteria analysis approach based on Atanassov’s intuitionistic fuzzy sets

In recent decades, intuitionistic fuzzy sets have been applied to many different fields; however, few current studies have used the ELECTRE method to solve multi-criteria decision-making problems with intuitionistic fuzzy information. The purpose of this paper is to develop a new method, the intuitionistic fuzzy ELECTRE method, for solving multi-criteria decision-making problems. Atanassov’s intuitionistic fuzzy set (A-IFS) characteristics are simultaneously concerned with the degree of membership, degree of non-membership, and intuitionistic index, and people can use A-IFS to describe uncertain situations in decision-making problems. We use the proposed method to rank all alternatives and determine the best alternative. The proposed method can also use imperfect or insufficient knowledge of data to deal with decision-making problems. Finally, two practical examples are given that illustrate the procedure of the proposed method.