Advances in Fuzzy Systems The latest articles from Hindawi © 2018 , Hindawi Limited . All rights reserved. Aumann Fuzzy Improper Integral and Its Application to Solve Fuzzy Integro-Differential Equations by Laplace Transform Method Mon, 01 Jan 2018 10:09:54 +0000 We introduce the Aumann fuzzy improper integral to define the convolution product of a fuzzy mapping and a crisp function in this paper. The Laplace convolution formula is proved in this case and used to solve fuzzy integro-differential equations with kernel of convolution type. Then, we report and correct an error in the article by Salahshour et al. dealing with the same topic. Elhassan Eljaoui, Said Melliani, and L. Saadia Chadli Copyright © 2018 Elhassan Eljaoui et al. All rights reserved. FCM-Type Fuzzy Coclustering for Three-Mode Cooccurrence Data: 3FCCM and 3Fuzzy CoDoK Mon, 18 Dec 2017 08:54:17 +0000 Cocluster structure analysis is a basic technique for revealing intrinsic structural information from cooccurrence data among objects and items, in which coclusters are composed of mutually familiar pairs of objects and items. In many real applications, it is also the case that we have not only cooccurrence information among objects and items but also intrinsic relation among items and other ingredients. For example, in food preference analysis, users’ preferences on foods should be found considering not only user-food cooccurrences but also the implicit relation among users and cooking ingredients. In this paper, two FCM-type fuzzy coclustering models, that is, FCCM and Fuzzy CoDoK, are extended for revealing intrinsic cocluster structures from three-mode cooccurrence data, where the aggregation degree of three elements in each cocluster is maximized through iterative updating of three types of fuzzy memberships for objects, items, and ingredients. The characteristic features of the proposed methods are demonstrated through a numerical experiment. Katsuhiro Honda, Yurina Suzuki, Seiki Ubukata, and Akira Notsu Copyright © 2017 Katsuhiro Honda et al. All rights reserved. Mobility Load Balancing in Cellular System with Multicriteria Handoff Algorithm Wed, 29 Nov 2017 07:52:18 +0000 Efficient traffic load balancing algorithm is very important to serve more mobile users in the cellular networks. This paper is based on mobility load balancing handoff algorithm using fuzzy logic. The rank of the serving and the neighboring Base Transceiver Stations (BTSs) are calculated every half second with the help of measurement report from the two-ray propagation model. This algorithm is able to balance load of the BTS by handing off some ongoing calls on BTS’s edge of highly loaded BTS to move to overlapping underloaded BTS, such that the coverage area of loaded BTS virtually shrunk towards BTS center of a loaded sector. In case of low load scenarios, the coverage area of a BTS is presumed to be virtually widened to cover up to the partial serving area of neighboring BTS. This helps a highly loaded neighboring BTS or failed BTS due to power or transmission. Simulation shows that new call blocking and handoff blocking using the proposed algorithm are enhanced notably. Solomon T. Girma and Abinet G. Abebe Copyright © 2017 Solomon T. Girma and Abinet G. Abebe. All rights reserved. A New Type-2 Soft Set: Type-2 Soft Graphs and Their Applications Wed, 18 Oct 2017 00:00:00 +0000 The correspondence between a vertex and its neighbors has an essential role in the structure of a graph. Type-2 soft sets are also based on the correspondence of primary parameters and underlying parameters. In this study, we present an application of type-2 soft sets in graph theory. We introduce vertex-neighbors based type-2 soft sets over (set of all vertices of a graph) and (set of all edges of a graph). Moreover, we introduce some type-2 soft operations in graphs by presenting several examples to demonstrate these new concepts. Finally, we describe an application of type-2 soft graphs in communication networks and present procedure as an algorithm. Khizar Hayat, Muhammad Irfan Ali, Bing-Yuan Cao, and Xiao-Peng Yang Copyright © 2017 Khizar Hayat et al. All rights reserved. Morphism of -Polar Fuzzy Graph Wed, 23 Aug 2017 00:00:00 +0000 The main purpose of this paper is to introduce the notion of -polar -morphism on -polar fuzzy graphs. The action of -polar -morphism on -polar fuzzy graphs is studied. Some elegant theorems on weak and coweak isomorphism are obtained. Also, some properties of highly irregular, edge regular, and totally edge regular -polar fuzzy graphs are studied. Ch. Ramprasad, P. L. N. Varma, S. Satyanarayana, and N. Srinivasarao Copyright © 2017 Ch. Ramprasad et al. All rights reserved. Vertex Degrees and Isomorphic Properties in Complement of an -Polar Fuzzy Graph Tue, 22 Aug 2017 06:19:20 +0000 Computational intelligence and computer science rely on graph theory to solve combinatorial problems. Normal product and tensor product of an -polar fuzzy graph have been introduced in this article. Degrees of vertices in various product graphs, like Cartesian product, composition, tensor product, and normal product, have been computed. Complement and -complement of an -polar fuzzy graph are defined and some properties are studied. An application of an -polar fuzzy graph is also presented in this article. Ch. Ramprasad, P. L. N. Varma, S. Satyanarayana, and N. Srinivasarao Copyright © 2017 Ch. Ramprasad et al. All rights reserved. A Fuzzy Simulation Model for Military Vehicle Mobility Assessment Mon, 07 Aug 2017 00:00:00 +0000 There has been increasing interest in improving the mobility of ground vehicles. The interest is greater in predicting the mobility for military vehicles. In this paper, authors review various definitions of mobility. Based on this review, a new definition of mobility called fuzzy mobility is given. An algorithm for fuzzy mobility assessment is described with the help of fuzzy rules. The simulation is carried out and its implementation, testing, and validation strategies are discussed. Aby K. George, Harpreet Singh, Macam S. Dattathreya, and Thomas J. Meitzler Copyright © 2017 Aby K. George et al. All rights reserved. Enhanced Decision Support Systems in Intensive Care Unit Based on Intuitionistic Fuzzy Sets Sun, 21 May 2017 00:00:00 +0000 In areas of medical diagnosis and decision-making, several uncertainty and ambiguity shrouded situations are most often imposed. In this regard, one may well assume that intuitionistic fuzzy sets (IFS) should stand as a potent technique useful for demystifying associated with the real healthcare decision-making situations. To this end, we are developing a prototype model helpful for detecting the patients risk degree in Intensive Care Unit (ICU). Based on the intuitionistic fuzzy sets, dubbed Medical Intuitionistic Fuzzy Expert Decision Support System (MIFEDSS), the shown work has its origins in the Modified Early Warning Score (MEWS) standard. It is worth noting that the proposed prototype effectiveness validation is associated through a real case study test at the Polyclinic ESSALEMA cited in Sfax, Tunisia. This paper does actually provide some practical initial results concerning the system as carried out in real life situations. Indeed, the proposed system turns out to prove that the MIFEDSS does actually display an imposing capability for an established handily ICU related uncertainty issues. The performance of the prototypes is compared with the MEWS standard which exposed that the IFS application appears to perform highly better in deferring accuracy than the expert MEWS score with higher degrees of sensitivity and specificity being recorded. Hanen Jemal, Zied Kechaou, and Mounir Ben Ayed Copyright © 2017 Hanen Jemal et al. All rights reserved. Color Image Segmentation Using Fuzzy C-Regression Model Sun, 16 Apr 2017 00:00:00 +0000 Image segmentation is one important process in image analysis and computer vision and is a valuable tool that can be applied in fields of image processing, health care, remote sensing, and traffic image detection. Given the lack of prior knowledge of the ground truth, unsupervised learning techniques like clustering have been largely adopted. Fuzzy clustering has been widely studied and successfully applied in image segmentation. In situations such as limited spatial resolution, poor contrast, overlapping intensities, and noise and intensity inhomogeneities, fuzzy clustering can retain much more information than the hard clustering technique. Most fuzzy clustering algorithms have originated from fuzzy c-means (FCM) and have been successfully applied in image segmentation. However, the cluster prototype of the FCM method is hyperspherical or hyperellipsoidal. FCM may not provide the accurate partition in situations where data consists of arbitrary shapes. Therefore, a Fuzzy C-Regression Model (FCRM) using spatial information has been proposed whose prototype is hyperplaned and can be either linear or nonlinear allowing for better cluster partitioning. Thus, this paper implements FCRM and applies the algorithm to color segmentation using Berkeley’s segmentation database. The results show that FCRM obtains more accurate results compared to other fuzzy clustering algorithms. Min Chen and Simone A. Ludwig Copyright © 2017 Min Chen and Simone A. Ludwig. All rights reserved. An Extension of the Fuzzy Possibilistic Clustering Algorithm Using Type-2 Fuzzy Logic Techniques Tue, 31 Jan 2017 06:41:09 +0000 In this work an extension of the Fuzzy Possibilistic C-Means (FPCM) algorithm using Type-2 Fuzzy Logic Techniques is presented, and this is done in order to improve the efficiency of FPCM algorithm. With the purpose of observing the performance of the proposal against the Interval Type-2 Fuzzy C-Means algorithm, several experiments were made using both algorithms with well-known datasets, such as Wine, WDBC, Iris Flower, Ionosphere, Abalone, and Cover type. In addition some experiments were performed using another set of test images to observe the behavior of both of the above-mentioned algorithms in image preprocessing. Some comparisons are performed between the proposed algorithm and the Interval Type-2 Fuzzy C-Means (IT2FCM) algorithm to observe if the proposed approach has better performance than this algorithm. Elid Rubio, Oscar Castillo, Fevrier Valdez, Patricia Melin, Claudia I. Gonzalez, and Gabriela Martinez Copyright © 2017 Elid Rubio et al. All rights reserved. Position Control of the Single Spherical Wheel Mobile Robot by Using the Fuzzy Sliding Mode Controller Thu, 12 Jan 2017 13:38:31 +0000 A spherical wheel robot or Ballbot—a robot that balances on an actuated spherical ball—is a new and recent type of robot in the popular area of mobile robotics. This paper focuses on the modeling and control of such a robot. We apply the Lagrangian method to derive the governing dynamic equations of the system. We also describe a novel Fuzzy Sliding Mode Controller (FSMC) implemented to control a spherical wheel mobile robot. The nonlinear nature of the equations makes the controller nontrivial. We compare the performance of four different fuzzy controllers: (a) regulation with one signal, (b) regulation and position control with one signal, (c) regulation and position control with two signals, and (d) FSMC for regulation and position control with two signals. The system is evaluated in a realistic simulation and the robot parameters are chosen based on a LEGO platform, so the designed controllers have the ability to be implemented on real hardware. Hamed Navabi, Soroush Sadeghnejad, Sepehr Ramezani, and Jacky Baltes Copyright © 2017 Hamed Navabi et al. All rights reserved. Forefront of Fuzzy Logic in Data Mining: Theory, Algorithms, and Applications Thu, 29 Dec 2016 09:33:19 +0000 Gözde Ulutagay, Ronald Yager, Bernard De Baets, and Tofigh Allahviranloo Copyright © 2016 Gözde Ulutagay et al. All rights reserved. Cardinal Basis Piecewise Hermite Interpolation on Fuzzy Data Thu, 29 Dec 2016 09:15:28 +0000 A numerical method along with explicit construction to interpolation of fuzzy data through the extension principle results by widely used fuzzy-valued piecewise Hermite polynomial in general case based on the cardinal basis functions, which satisfy a vanishing property on the successive intervals, has been introduced here. We have provided a numerical method in full detail using the linear space notions for calculating the presented method. In order to illustrate the method in computational examples, we take recourse to three prime cases: linear, cubic, and quintic. H. Vosoughi and S. Abbasbandy Copyright © 2016 H. Vosoughi and S. Abbasbandy. All rights reserved. Minimal Solution of Complex Fuzzy Linear Systems Mon, 26 Dec 2016 08:48:18 +0000 This paper investigates the complex fuzzy linear equation in which is a crisp complex matrix and is an arbitrary LR complex fuzzy vector. The complex fuzzy linear system is converted to equivalent high order fuzzy linear system . A new numerical procedure for calculating the complex fuzzy solution is designed and a sufficient condition for the existence of strong complex fuzzy solution is derived in detail. Some examples are given to illustrate the proposed method. Xiaobin Guo and Ke Zhang Copyright © 2016 Xiaobin Guo and Ke Zhang. All rights reserved. Fuzzy Logic versus Classical Logic: An Example in Multiplicative Ideal Theory Thu, 15 Dec 2016 14:10:00 +0000 We discuss a fuzzy result by displaying an example that shows how a classical argument fails to work when one passes from classical logic to fuzzy logic. Precisely, we present an example to show that, in the fuzzy context, the fact that the supremum is naturally used in lieu of the union can alter an argument that may work in the classical context. Olivier A. Heubo-Kwegna Copyright © 2016 Olivier A. Heubo-Kwegna. All rights reserved. A New Method for Defuzzification and Ranking of Fuzzy Numbers Based on the Statistical Beta Distribution Wed, 16 Nov 2016 13:06:16 +0000 Granular computing is an emerging computing theory and paradigm that deals with the processing of information granules, which are defined as a number of information entities grouped together due to their similarity, physical adjacency, or indistinguishability. In most aspects of human reasoning, these granules have an uncertain formation, so the concept of granularity of fuzzy information could be of special interest for the applications where fuzzy sets must be converted to crisp sets to avoid uncertainty. This paper proposes a novel method of defuzzification based on the mean value of statistical Beta distribution and an algorithm for ranking fuzzy numbers based on the crisp number ranking system on R. The proposed method is quite easy to use, but the main reason for following this approach is the equality of left spread, right spread, and mode of Beta distribution with their corresponding values in fuzzy numbers within interval, in addition to the fact that the resulting method can satisfy all reasonable properties of fuzzy quantity ordering defined by Wang et al. The algorithm is illustrated through several numerical examples and it is then compared with some of the other methods provided by literature. A. Rahmani, F. Hosseinzadeh Lotfi, M. Rostamy-Malkhalifeh, and T. Allahviranloo Copyright © 2016 A. Rahmani et al. All rights reserved. Number Based Fuzzy Inference System for Dynamic Plant Control Tue, 08 Nov 2016 07:43:54 +0000 Frequently the reliabilities of the linguistic values of the variables in the rule base are becoming important in the modeling of fuzzy systems. Taking into consideration the reliability degree of the fuzzy values of variables of the rules the design of inference mechanism acquires importance. For this purpose, Z number based fuzzy rules that include constraint and reliability degrees of information are constructed. Fuzzy rule interpolation is presented for designing of an inference engine of fuzzy rule-based system. The mathematical background of the fuzzy inference system based on interpolative mechanism is developed. Based on interpolative inference process Z number based fuzzy controller for control of dynamic plant has been designed. The transient response characteristic of designed controller is compared with the transient response characteristic of the conventional fuzzy controller. The obtained comparative results demonstrate the suitability of designed system in control of dynamic plants. Rahib H. Abiyev Copyright © 2016 Rahib H. Abiyev. All rights reserved. An Image Segmentation by BFV and TLBO Mon, 07 Nov 2016 14:19:16 +0000 This paper presents the establishing of a biconvex fuzzy variational (BFV) method with teaching learning based optimization (TLBO) for geometric image segmentation (GIS). Firstly, a biconvex object function is adopted to process GIS. Then, TLBO is introduced to maximally optimize the length penalty item (LPI), which will be changed under teaching and learner phase of TLBO, making the LPI closer to the target boundary. Afterward, the LPI can be adjusted based on fitness function, namely, the evaluation standards of image quality. Finally, the LP is combined item with the numerical order to get better results. Different GIS strategies are compared with various fitness functions in terms of accuracy. Simulations show that the presented method is more effective in this area. Mohammad Heidari Copyright © 2016 Mohammad Heidari. All rights reserved. A Novel Method for Optimal Solution of Fuzzy Chance Constraint Single-Period Inventory Model Sun, 06 Nov 2016 12:50:48 +0000 A method is proposed for solving single-period inventory fuzzy probabilistic model (SPIFPM) with fuzzy demand and fuzzy storage space under a chance constraint. Our objective is to maximize the total profit for both overstock and understock situations, where the demand for each product in the objective function is considered as a fuzzy random variable (FRV) and with the available storage space area , which is also a FRV under normal distribution and exponential distribution. Initially we used the weighted sum method to consider both overstock and understock situations. Then the fuzziness of the model is removed by ranking function method and the randomness of the model is removed by chance constrained programming problem, which is a deterministic nonlinear programming problem (NLPP) model. Finally this NLPP is solved by using LINGO software. To validate and to demonstrate the results of the proposed model, numerical examples are given. Anuradha Sahoo and J. K. Dash Copyright © 2016 Anuradha Sahoo and J. K. Dash. All rights reserved. Fuzzy Aspect Based Opinion Classification System for Mining Tourist Reviews Mon, 31 Oct 2016 08:12:01 +0000 Due to the large amount of opinions available on the websites, tourists are often overwhelmed with information and find it extremely difficult to use the available information to make a decision about the tourist places to visit. A number of opinion mining methods have been proposed in the past to identify and classify an opinion into positive or negative. Recently, aspect based opinion mining has been introduced which targets the various aspects present in the opinion text. A number of existing aspect based opinion classification methods are available in the literature but very limited research work has targeted the automatic aspect identification and extraction of implicit, infrequent, and coreferential aspects. Aspect based classification suffers from the presence of irrelevant sentences in a typical user review. Such sentences make the data noisy and degrade the classification accuracy of the machine learning algorithms. This paper presents a fuzzy aspect based opinion classification system which efficiently extracts aspects from user opinions and perform near to accurate classification. We conducted experiments on real world datasets to evaluate the effectiveness of our proposed system. Experimental results prove that the proposed system not only is effective in aspect extraction but also improves the classification accuracy. Muhammad Afzaal, Muhammad Usman, A. C. M. Fong, Simon Fong, and Yan Zhuang Copyright © 2016 Muhammad Afzaal et al. All rights reserved. Fuzzy Rules for Ant Based Clustering Algorithm Thu, 27 Oct 2016 15:58:24 +0000 This paper provides a new intelligent technique for semisupervised data clustering problem that combines the Ant System (AS) algorithm with the fuzzy -means (FCM) clustering algorithm. Our proposed approach, called F-ASClass algorithm, is a distributed algorithm inspired by foraging behavior observed in ant colonyT. The ability of ants to find the shortest path forms the basis of our proposed approach. In the first step, several colonies of cooperating entities, called artificial ants, are used to find shortest paths in a complete graph that we called graph-data. The number of colonies used in F-ASClass is equal to the number of clusters in dataset. Hence, the partition matrix of dataset founded by artificial ants is given in the second step, to the fuzzy -means technique in order to assign unclassified objects generated in the first step. The proposed approach is tested on artificial and real datasets, and its performance is compared with those of -means, -medoid, and FCM algorithms. Experimental section shows that F-ASClass performs better according to the error rate classification, accuracy, and separation index. Amira Hamdi, Nicolas Monmarché, Mohamed Slimane, and Adel M. Alimi Copyright © 2016 Amira Hamdi et al. All rights reserved. Robust FCM Algorithm with Local and Gray Information for Image Segmentation Thu, 20 Oct 2016 09:33:41 +0000 The FCM (fuzzy -mean) algorithm has been extended and modified in many ways in order to solve the image segmentation problem. However, almost all the extensions require the adjustment of at least one parameter that depends on the image itself. To overcome this problem and provide a robust fuzzy clustering algorithm that is fully free of the empirical parameters and noise type-independent, we propose a new factor that includes the local spatial and the gray level information. Actually, this work provides three extensions of the FCM algorithm that proved their efficiency on synthetic and real images. Hanane Barrah, Abdeljabbar Cherkaoui, and Driss Sarsri Copyright © 2016 Hanane Barrah et al. All rights reserved. Fuzzy Constrained Probabilistic Inventory Models Depending on Trapezoidal Fuzzy Numbers Thu, 22 Sep 2016 07:35:08 +0000 We discussed two different cases of the probabilistic continuous review mixture shortage inventory model with varying and constrained expected order cost, when the lead time demand follows some different continuous distributions. The first case is when the total cost components are considered to be crisp values, and the other case is when the costs are considered as trapezoidal fuzzy number. Also, some special cases are deduced. To investigate the proposed model in the crisp case and the fuzzy case, illustrative numerical example is added. From the numerical results we will conclude that Uniform distribution is the best distribution to get the exact solutions, and the exact solutions for fuzzy models are considered more practical and close to the reality of life and get minimum expected total cost less than the crisp models. Mona F. El-Wakeel and Kholood O. Al-yazidi Copyright © 2016 Mona F. El-Wakeel and Kholood O. Al-yazidi. All rights reserved. Understanding Open Source Software Evolution Using Fuzzy Data Mining Algorithm for Time Series Data Wed, 14 Sep 2016 08:42:55 +0000 Source code management systems (such as Concurrent Versions System (CVS), Subversion, and git) record changes to code repositories of open source software projects. This study explores a fuzzy data mining algorithm for time series data to generate the association rules for evaluating the existing trend and regularity in the evolution of open source software project. The idea to choose fuzzy data mining algorithm for time series data is due to the stochastic nature of the open source software development process. Commit activity of an open source project indicates the activeness of its development community. An active development community is a strong contributor to the success of an open source project. Therefore commit activity analysis along with the trend and regularity analysis for commit activity of open source software project acts as an important indicator to the project managers and analyst regarding the evolutionary prospects of the project in the future. Munish Saini, Sandeep Mehmi, and Kuljit Kaur Chahal Copyright © 2016 Munish Saini et al. All rights reserved. Object Boundary Detection Using Active Contour Model via Multiswarm PSO with Fuzzy-Rule Based Adaptation of Inertia Factor Sun, 04 Sep 2016 07:56:12 +0000 Active contour models, colloquially known as snakes, are quite popular for several applications such as object boundary detection, image segmentation, object tracking, and classification via energy minimization. While energy minimization may be accomplished using traditional optimization methods, approaches based on nature-inspired evolutionary algorithms have been developed in recent years. One such evolutionary algorithm that has been used extensively in active contours is the particle swarm optimization (PSO). However, conventional PSO converges slowly and gets trapped in local minimum easily which results in inaccurate detection of concavities in the object boundary. This is taken care of by using proposed multiswarm PSO in which a swarm is set for every control point in the snake and then all the swarms search for their best points simultaneously through information sharing among them. The performance of the multiswarm PSO-based search process is further enhanced by using dynamic adaptation of the inertia factor. In this paper, we propose using a set of fuzzy rules to adjust the inertia weight on the basis of the current normalized snake energy and the current value of inertia. Experimental results demonstrate the effectiveness of the proposed method compared to conventional approaches. Ajay Khunteta and D. Ghosh Copyright © 2016 Ajay Khunteta and D. Ghosh. All rights reserved. Fuzzy Pheromone Potential Fields for Virtual Pedestrian Simulation Sun, 21 Aug 2016 07:02:42 +0000 The study of collective movement of pedestrians is crucial in various situations, such as evacuation of buildings, stadiums, or external events like concerts or public events. In such situations and under panic conditions, several incidents and disasters may arise, resulting in loss of human lives. Hence, the study and modeling of the pedestrians behavior are imperative in both normal and panic situations. In a previous work, we developed a microscopic model for pedestrian movement based on the algorithm of Ant Colonies and the principles of cellular automata. We took advantage of a fuzzy model to better reflect the uncertainty and vagueness of the perception of space to pedestrians, especially to represent the desirability or blurred visibility of virtual pedestrians. This paper uses the mechanism of artificial potential fields. Said fields provide virtual pedestrians with better visibility of their surroundings and its various components (goals and obstacles). The predictions provided by the first-order traffic flow theory are confirmed by the results of the simulation. The advantage of this model lies in the combination of benefits provided by the model of ants and artificial potential fields in a fuzzy modeling, to better understand the perceptions of pedestrians. Meriem Mandar and Azedine Boulmakoul Copyright © 2016 Meriem Mandar and Azedine Boulmakoul. All rights reserved. A Similarity Classifier with Bonferroni Mean Operators Tue, 26 Jul 2016 10:03:46 +0000 A similarity classifier based on Bonferroni mean based operators is introduced. The new Bonferroni mean based variant of the similarity classifier is also extended to cover a new Bonferroni-OWA variant. The new Bonferroni-OWA based similarity classifier raises the question of how to accomplish the weighting needed and for this reason we also examine a number of linguistic quantifiers for weight generation. The new proposed similarity classifier variants are tested on four real world medical research related data sets. The results are compared with results from two previously presented similarity classifiers, one based on the generalized mean and another based on an arithmetic mean operator. The results show that comparatively better classification accuracy can be reached with the proposed new similarity classifier variants. Onesfole Kurama, Pasi Luukka, and Mikael Collan Copyright © 2016 Onesfole Kurama et al. All rights reserved. An Improved Fuzzy Based Missing Value Estimation in DNA Microarray Validated by Gene Ranking Mon, 18 Jul 2016 14:17:37 +0000 Most of the gene expression data analysis algorithms require the entire gene expression matrix without any missing values. Hence, it is necessary to devise methods which would impute missing data values accurately. There exist a number of imputation algorithms to estimate those missing values. This work starts with a microarray dataset containing multiple missing values. We first apply the modified version of the fuzzy theory based existing method LRFDVImpute to impute multiple missing values of time series gene expression data and then validate the result of imputation by genetic algorithm (GA) based gene ranking methodology along with some regular statistical validation techniques, like RMSE method. Gene ranking, as far as our knowledge, has not been used yet to validate the result of missing value estimation. Firstly, the proposed method has been tested on the very popular Spellman dataset and results show that error margins have been drastically reduced compared to some previous works, which indirectly validates the statistical significance of the proposed method. Then it has been applied on four other 2-class benchmark datasets, like Colorectal Cancer tumours dataset (GDS4382), Breast Cancer dataset (GSE349-350), Prostate Cancer dataset, and DLBCL-FL (Leukaemia) for both missing value estimation and ranking the genes, and the results show that the proposed method can reach 100% classification accuracy with very few dominant genes, which indirectly validates the biological significance of the proposed method. Sujay Saha, Anupam Ghosh, Dibyendu Bikash Seal, and Kashi Nath Dey Copyright © 2016 Sujay Saha et al. All rights reserved. An Exhaustive Study of Possibility Measures of Interval-Valued Intuitionistic Fuzzy Sets and Application to Multicriteria Decision Making Tue, 12 Jul 2016 07:08:20 +0000 This work is interested in showing the importance of possibility theory in multicriteria decision making (MCDM). Thus, we apply some possibility measures from literature to the MCDM method using interval-valued intuitionistic fuzzy sets (IVIFSs). These measures are applied to a decision matrix after being transformed with aggregation operators. The results are compared between each other and concluding remarks are drawn. Fatma Dammak, Leila Baccour, and Adel M. Alimi Copyright © 2016 Fatma Dammak et al. All rights reserved. A Semi-Supervised Framework for MMMs-Induced Fuzzy Co-Clustering with Virtual Samples Thu, 23 Jun 2016 13:32:41 +0000 Although the goal of clustering is to reveal structural information from unlabeled datasets, in cases with partial structural supervisions, semi-supervised clustering is expected to improve partition quality. However, in many real applications, it may cause additional costs to provide an enough amount of supervised objects with class labels. A virtual sample approach is a practical technique for improving classification quality in semi-supervised learning, in which additional virtual samples are generated from supervised objects. In this research, the virtual sample approach is adopted in semi-supervised fuzzy co-clustering, where the goal is to reveal object-item pairwise cluster structures from cooccurrence information among them. Several experimental results demonstrate the characteristics of the proposed approach. Daiji Tanaka, Katsuhiro Honda, Seiki Ubukata, and Akira Notsu Copyright © 2016 Daiji Tanaka et al. All rights reserved.