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Clustering is a crucial method for deciphering data structure and producing new information. Due to its significance in revealing fundamental connections between the human brain and events, it is essential to utilize clustering for cognitive research. Dealing with noisy data caused by inaccurate synthesis from several sources or misleading data production processes is one of the most intriguing clustering difficulties. Noisy data can lead to incorrect object recognition and inference. This research aims to innovate a novel clustering approach, named Picture-Neutrosophic Trusted Safe Semi-Supervised Fuzzy Clustering (PNTS3FCM), to solve the clustering problem with noisy data using neutral and refusal degrees in the definition of Picture Fuzzy Set (PFS) and Neutrosophic Set (NS). Our contribution is to propose a new optimization model with four essential components: clustering, outlier removal, safe semi-supervised fuzzy clustering and partitioning with labeled and unlabeled data. The effectiveness and flexibility of the proposed technique are estimated and compared with the state-of-art methods, standard Picture fuzzy clustering (FC-PFS) and Confidence-weighted safe semi-supervised clustering (CS3FCM) on benchmark UCI datasets. The experimental results show that our method is better at least 10/15 datasets than the compared methods in terms of clustering quality and computational time. [ABSTRACT FROM AUTHOR]

Quadratic cost functions estimation in the linear optimal control systems governed by differential equations (DEs) or partial differential equations (PDEs) has a well-established discipline in mathematics with many interfaces to science and engineering. During its development, the impact of uncertain phenomena to objective function and the complexity of the systems to be controlled have also increased significantly. Many engineering problems like magnetohydromechanical, electromagnetical and signal analysis for the transmission and propagation of electrical signals under uncertain environment can be dealt with. In this paper, we study the optimal control problem with operating a fractional DEs and PDEs at minimum quadratic objective function in the framework of neutrosophic environment and granular computing. However, there has been no studies appeared on the neutrosophic calculus of fractional order. Hence, we will introduce some derivatives of fractional order, including the neutrosophic Riemann–Liouville fractional derivatives and neutrosophic Caputo fractional derivatives. Next, we propose a new setting of two important problems in engineering. In the first problem, we investigate the numerical and exact solutions of some neutrosophic fractional DEs and neutrosophic telegraph PDEs. In the second problem, we study the optimality conditions together with the simulation of states of a linear quadratic optimal control problem governed by neutrosophic fractional DEs and PDEs. Some key applications to DC motor model and one-link robot manipulator model are investigated to prove the effectiveness and correctness of the proposed method. • LQR problem governed by neutrosophic fractional differential equation. • Neutrosophic Riemann–Liouville and Caputo derivatives under granular computing. • Numerical neutrosophic solutions of some fractional telegraph equations. • Key applications to DC motor model and one-link robot manipulator model. [ABSTRACT FROM AUTHOR]

Abstract Besides physical consequences, obesity has negative psychological effects, thereby lowering human life quality. Major psychological consequences of this disorder includes depression, impaired body image, low self-esteem, eating disorders, stress and poor quality of life, which are correlated with age and gender. Physical interventions, mainly diet control and energy balance, have been widely applied to treat obesity; and some psychological interventions including behavioral therapy, cognitive behavioral therapy and hypnotherapy have showed some effects on obesity treatment. Other psychological therapies, such as relaxation and psychodynamic therapies, are paid less attention. This review aims to update scientific evidence regarding the mental consequences and psychological interventions for obesity. [ABSTRACT FROM AUTHOR]

Overweight and obesity (OW and OB) have been on the increase globally and posed health risks to the world’s population of all ages, including pre-born babies, children, adolescents, adults and elderly people, via their comorbid conditions. Excellent examples of comorbidities associated with obesity include cancer, cardiovascular diseases (CVD) and type 2 diabetes mellitus (T2DM). In this article, we aimed to review and update scientific evidence regarding the relationships between obesity and its common physical health consequences, including CVD, T2DM, hypertension, ischemic stroke, cancer, dyslipidemia and reproductive disorders. In addition, the economic burden of OW and OB will be discussed. Abundant evidence is found to support the associations between obesity and other diseases. In general, the odd ratios, risk ratios or hazard ratios are often higher in OW and OB people than in the normal-weight ones. However, the molecular mechanism of how OW and OB induce the development of other diseases has not been fully understood. Figures also showed that obesity and its-related disorders exert enormous pressure on the economy which is projected to increase. This review highlights the fact that obesity can lead to numerous lethal health problems; therefore, it requires a lot of economic resources to fight against this epidemic. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • We proposed a neutrosophic recommender system (NRS) based on neutrosophic set. • Algebraic operations and similarity measures of NRS were studied. • A new algorithm using the similarity measures was designed for medical diagnosis. • It was validated on the benchmark datasets in terms of MSE and computational time. • The strength of all algorithms was analyzed by ANOVA statistical tool. Abstract Medical diagnosis is a procedure for the investigation of a person’s symptoms on the basis of disease. This problem has been investigated and applied to personal healthcare systems in medicine. The relevant methods have limitations regarding neutrosophication, deneutrosophication, similarity measures, correlation coefficients, distance measure, and patients’ history. In this paper, we propose a novel neutrosophic recommender system for medical diagnosis based on algebraic neutrosophic measures. Specifically, a single-criterion neutrosophic recommender system (SC-NRS) and a multi-criteria neutrosophic recommender system (MC-NRS) accompanied by algebraic operations such as union, complement and intersection are proposed. Several types of similarity measures based on the algebraic operations and their theoretic properties are investigated. A prediction formula and a new forecast algorithm using the proposed algebraic similarity measures are designed. The proposed method is experimentally validated on some benchmark medical datasets against the relevant ones namely ICSM, DSM, CARE and CFMD. The experiments demonstrate that the proposed method has better Mean Square Error (MSE) than the other algorithms. Besides, there is no large increase in computational time taken by the proposed method and other algorithms. Experiments by various cases of parameters suggest that the MSE values remain almost the same for each dataset when randomly changing the values of parameters in all the medical datasets. Lastly, the strength of all the algorithms is analyzed through ANOVA one-way test and Kruskal-Wallis test. The proposed method has better accuracy than the related algorithms. Experimental results support the advantage and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy sets (IFSs) are successful to handle the uncertain situations of data. Distance measures of IFSs are important in the evaluation of IFSs relationships. In this paper, we analyzed the disadvantages of existing distance measures of IFSs and proposed a new distance measure called H-max of IFSs. We continued to point out some new results on intuitionistic t-norms and intuitionistic t-conorms and evaluated distance measure between two IFSs which are basically structured from these operations. Further, we combined the classification of t-representable intuitionistic fuzzy t-norms and t-conorms with the proposed distance measure to study some interesting properties. Moreover, we studied De Morgan triplets of IFSs based on the proposed distance measure. Finally, we applied the proposed distance measure to medical diagnosis problem examples and experimental validation on real-world datasets to check the applicability and effectiveness. [ABSTRACT FROM AUTHOR]

Neutrosophic set is a powerful general formal framework which generalizes the concepts of classic set, fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set, etc. Recent studies have developed systems with complex fuzzy sets, for better designing and modeling real-life applications. The single-valued complex neutrosophic set, which is an extended form of the single-valued complex fuzzy set and of the single-valued complex intuitionistic fuzzy set, presents difficulties to defining a crisp neutrosophic membership degree as in the single-valued neutrosophic set. Therefore, in this paper we propose a new notion, called interval complex neutrosophic set (ICNS), and examine its characteristics. Firstly, we define several set theoretic operations of ICNS, such as union, intersection and complement, and afterward the operational rules. Next, a decision-making procedure in ICNS and its applications to a green supplier selection are investigated. Numerical examples based on real dataset of Thuan Yen JSC, which is a small-size trading service and transportation company, illustrate the efficiency and the applicability of our approach. [ABSTRACT FROM AUTHOR]

Neutrosophic set and neutrosophic logic theory are renowned theories to deal with complex, not clearly explained and uncertain real life problems, in which classical fuzzy sets/models may fail to model properly. This paper introduces an algorithm for finding minimum spanning tree (MST) of an undirected neutrosophic weighted connected graph (abbr. UNWCG) where the arc/edge lengths are represented by a single valued neutrosophic numbers. To build the MST of UNWCG, a new algorithm based on matrix approach has been introduced. The proposed algorithm is compared to other existing methods and finally a numerical example is provided. [ABSTRACT FROM AUTHOR]

Background Computerized medical diagnosis systems from X-Ray images are of great interest to physicians for accurate decision making of possible diseases and treatments. Subclinical disease has no recognizable clinical findings, thus it is desirable to segment the dental X-Ray image into groups and then use soft computing methods to check the possibility of whether or not any disease occurs therein. Methods The current work proposed a novel framework called Dental Diagnosis System (DDS) for dental diagnosis based on the hybrid approach of segmentation, classification and decision making. It utilized the best dental image segmentation method based on semi-supervised fuzzy clustering for the segmentation task. A new graph-based clustering algorithm called APC+ for the classification task was proposed. A new decision making procedure was designed to determine the final disease from a group of diseases found from the segments. Results The proposed DDS was modeled under the real dental case of Hanoi Medical University, Vietnam including 87 dental images of five popular diseases, namely: root fracture, incluse teeth, decay, missing teeth, and resorption of periodontal bone. The DDS accuracy is 92.74% which is superior to the other methods namely fuzzy inference system (89.67%), fuzzy k-nearest neighbor (80.05%), prim spanning tree (58.46%), kruskal spanning tree (58.46%), and affinity propagation clustering (90.01%). Conclusion Empirical results established that superior performance of the DDS to other related methods the findings of the achieved results can assist dental clinicians in their professional work. [ABSTRACT FROM AUTHOR]

In this paper, we consider the sensor-energy optimization in 3D Wireless Sensor Networks (WSNs), which determines an optimal topology of sensors to prolong the network lifetime and reduce the energy expenditure. A new mathematical model for clustering in 3D WSN, considering energy consumption, constraints of communication and a 3D energy function, is presented. Using the Lagrange multiplier method, solutions of the model consisting of cluster centres and the membership matrix are computed and used in the new algorithm, called FCM-3 WSN. Experimental validation on real 3D datasets demonstrates that FCM-3 WSN outperforms the relevant methods, namely, Low-Energy Adaptive Clustering Hierarchy (LEACH), Centralized LEACH (LEACH-C), Single-hop Clustering and Energy-Efficient Protocol (SCEEP), Hybrid-Low Energy Adaptive Clustering Hierarchy (H-LEACH), K-Means and Fuzzy C-Means (FCM). [ABSTRACT FROM AUTHOR]

Geo-Demographic Analysis, which is one of the most interesting inter-disciplinary research topics between Geographic Information Systems and Data Mining, plays a very important role in policies decision, population migration and services distribution. Among some soft computing methods used for this problem, clustering is the most popular one because it has many advantages in comparison with the rests such as the fast processing time, the quality of results and the used memory space. Nonetheless, the state-of-the-art clustering algorithm namely FGWC has low clustering quality since it was constructed on the basis of traditional fuzzy sets. In this paper, we will present a novel interval type-2 fuzzy clustering algorithm deployed in an extension of the traditional fuzzy sets namely Interval Type-2 Fuzzy Sets to enhance the clustering quality of FGWC. Some additional techniques such as the interval context variable, Particle Swarm Optimization and the parallel computing are attached to speed up the algorithm. The experimental evaluation through various case studies shows that the proposed method obtains better clustering quality than some best-known ones. [ABSTRACT FROM AUTHOR]

Analyzing the relations and patterns that exist in complex data sets is an integral part of the research in complex fuzzy set theory. The main object of study in this paper is the interval-valued complex fuzzy set (IV-CFS) model. This adaptation of complex fuzzy sets can handle datasets with a time-periodic feature, and the partial ignorance that exists in the data as well as the process of assigning values for the membership functions, in addition to modeling multi-dimensional data. This paper focuses on finding the patterns and relations between complex data sets using the properties of interval-valued complex fuzzy sets (IV-CFSs). To achieve this objective, this paper establishes the concept of relations and the composition operation for IV-CFSs using the extensive properties of the Cartesian product. Some of the algebraic properties of the relations and compositions are also introduced to define the equivalence relation between IV-CFSs. The proposed method is then applied to an MCDM problem related to customers' online shopping preferences and behavior. A detailed case study of this MCDM problem is then presented through the interpretation of the results that were obtained. A brief comparison is then presented between our proposed method and other methods in literature used to analyze patterns between complex data sets. • We established the concept of relations and the composition operation for IV-CFSs. • Algebraic properties of the relations and compositions were introduced. • The method was applied to analyze customers' online shopping preferences. • Comparison was presented to analyze patterns between complex data sets. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy sets are useful for modeling uncertain data of realistic problems. In this paper, we generalize and expand the utility of complex intuitionistic fuzzy sets using the space of quaternion numbers. The proposed representation can capture composite features and convey multi-dimensional fuzzy information via the functions of real membership, imaginary membership, real non-membership, and imaginary non-membership. We analyze the order relations and logic operations of the complex intuitionistic fuzzy set theory and introduce new operations based on quaternion numbers. We also present two quaternion distance measures in algebraic and polar forms and analyze their properties. We apply the quaternion representations and measures to decision-making models. The proposed model is experimentally validated in medical diagnosis, which is an emerging application for tackling patient's symptoms and attributes of diseases. • We proposed a new concept of intuitionistic fuzzy sets based on quaternion numbers. • Several set theoretic operations and properties were provided. • Intuitionistic fuzzy distance measure via quaternion numbers was given. • A new Euclidean Quaternion Measure decision making model in polar form was given. • The method was experimentally tested on medical diagnosis benchmark datasets. [ABSTRACT FROM AUTHOR]

Mobile Ad-hoc Networks are constructed without any administration, providing the quality of service in spite of routing overhead. In MANET, it is impossible for a mobile host to contact with other hosts in a single-hop fashion. In a multi-hop scenario, packets sent by the source host are relayed by a number of intermediate hosts before reaching the destination host. Due to node mobility in MANETs, frequent path failures and route discoveries occur. Hence, RREQ (Route Request) packets have to be broadcasted for finding the route. This leads to excessive redundant retransmission of RREQ packets. This strategy induces routing overhead in MANET. In this paper, we propose a reliable routing method to obtain the Quality of Service in MANET. The bandwidth requirement is calculated using the strength of the node's signal in the established nodes. The selection of route is based on the fewer amounts of delay and strong stability. To ascertain the route more efficient than traditional broadcasting style, rebroadcast can be done with the assistance of neighbor knowledge methods. Here, NKR (Neighbor Knowledge-based Rebroadcast) algorithm and LVC (Loose Virtual Clustering) algorithm are used for routing overhead reduction in MANETs. The experimental results prove that the proposed work performs well in terms of routing overhead, network traffic and successful broadcast of data packets in the network. [ABSTRACT FROM AUTHOR]