The traditional Choquet aggregation operators and generalized OWA operator are generally suitable for aggregating the information taking the form of numerical values, and yet they will fail in dealing with triangularfuzzy information. Moti- vated by the ideal of Choquet integral  and generalized OWA operator  , in this paper, we propose a generalized tri- angular fuzzycorrelatedaveraging (GTFCA) operator, whose prominent characteristic is that they cannot only consider the importance of the elements or their ordered positions, but also reﬂect the correlations of the elements or their ordered posi- tions and study some desirable properties of the GTFCA operator, such as commutativity, idempotency and monotonicity. We have applied the GTFCA operator to multipleattributedecisionmaking problems with triangularfuzzy information. Fi- nally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. In the future, we shall continue working in the extension and application of the developed operators to other domains. Acknowledgments
Motivated by the ideas of NWBM, GNWBM, IFNWBM, and GIFNWBM operators proposed by Zhou and He , this paper is to propose the Normalized Weighted GBM (NWGBM) and the Gen- eralized NWGBM (GNWGBM), the 2-Dimensional Uncertain Linguistic NWGBM (2DULNWGBM) and the 2-Dimensional Uncertain Linguistic Generalized NWGBM (2DULGNWGBM). Based on these opera- tors, the MADM approach with 2DULVs is developed. The rest of this study is organized as follows. Section 2 briey reviews some basic concepts. Section 3 develops the Normalized Weighted Geometric Bonfer- roni Mean (NWGBM) and the Generalized Normalized Weighted Geometric Bonferroni Mean (GNWGBM). Section 4 introduces 2DULVs. In Section 5, we propose 2-Dimensional Uncertain Linguistic NWGBM (2DULNWGBM) and 2-Dimensional Uncertain Lin- guistic GNWGBM (2DULGNWGBM). In Section 6, we use the 2DULGNWGBM operator for the MADM problems and give the decisionmaking steps. Sec- tion 7 gives an example to show the eectiveness of the proposed method. Finally, Section 8 gives some conclusions.
The IVHFS, which allows the membership degree of an element to a set represented by several possible interval values, can be considered as a powerful tool to express un- certain information in the group decision-making process. But it cannot handle indeter- minate and inconsistent information, while the INS gives us an additional possibility to represent uncertainty, imprecise, incomplete, and inconsistent information which exists in real world and would be more suitable to handle indeterminate information and incon- sistent information. However, existing SVNSs and INSs cannot allow truth-membership degrees, indeterminacy-membership degrees and falsity-membership degrees of an ele- ment to a set represented by several possible values or interval values, and then existing correlation coeﬃcients for SVNSs and INSs cannot also handle this hesitant problem. To solve this problem, it is very necessary to introduce the concept of interval neutrosophic hesitant fuzzy sets (INHFSs), which permit truth-membership degrees, indeterminacy- membership degrees, and falsity-membership degrees of an element to a given set to have a few diﬀerent interval values. Hence, the INHFS encompasses fuzzy set, IFS, IVIFS, SVNS, INS, HFS, DHFS, and IVHFS as special cases of the INHFS. The purposes of this paper are: (1) to propose the concept of INHFSs based on the combination of INSs and IVHFSs and some basic operations of INHFSs, (2) to develop some correlation co- eﬃcients between INHFSs and to investigate their properties and the relation between the correlation coeﬃcients and some similarity measures, and (3) to establish a multi- ple attributedecisionmaking method based on the correlation coeﬃcients under interval neutrosophic hesitant fuzzy environment. The proposed decisionmaking method based on the correlation coeﬃcients can avoid complex information aggregation and can directly utilize the derived correlation coeﬃcients to calculate the correlation degrees between alternatives and the ideal alternative for the ranking order of the alternatives.
Atanassov introduced the concept of intuitionistic fuzzy set which is a generalization concept of fuzzy set. Rough sets [17-18]was originally proposed by Pawlak and is an extension of crisp set theory for the study of intelligent system characterized by inexact, uncertain or insufficient information. It is a useful tool for dealing with uncertainty or imprecision information. Rough sets have successfully found its application indifferent fields such as artificial intelligence, pattern recognition, medical diagnosis[25-27], data mining[13-14,
Atanassov [1,2] introduced the concept of intuitionistic fuzzy set(IFS) characterized by a membership function and a non-membership function, which is a generalization of the concept of fuzzy set  whose basic component is only a membership function. The intuitionistic fuzzy set has received more and more attention since its appearance. Later, Atanassov and Gargov[4-5] further introduced the interval-valued intuitionistic fuzzy set (IVIFS), which is a generalization of the IFS. The fundamental characteristic of the IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. Xu proposed the interval-valued intuitionistic fuzzy weighted averaging (IVIFWA) operato, the interval-valued intuitionistic fuzzy ordered weighted averaging (IVIFOWA) operator and the interval-valued intuitionistic fuzzy hybrid aggregation (IVIFHA) operator and gave an application of the IVIFHA operator to multipleattribute group decisionmaking with interval- valued intuitionistic fuzzy information. Wei and Zhaoinvestigated some multipleattribute group decisionmaking (MAGDM) problems in which both the attribute weights and the expert weights are usually correlative, attribute values take the form of intuitionistic fuzzy values or interval-valued intuitionistic fuzzy values and developed the induced intuitionistic fuzzycorrelatedaveraging (I-IFCA) operator and some desirable properties of the I-IFCA operators are studied, such as commutativity, idempotency and monotonicity. Yu et al.
Management Science (MS) /operations Research (OR) is an old and famous field that deals with making decisions. Data mining (DM) can be defined as the process of extracting important and useful information from large sets of data (Abello et al., 2002). According to Han and Kamber (2001), some of the most important functions of data mining include concept description (characterization and discrimination), association, classification, clustering, and prediction. In addition, DM is an interdisciplinary field that combines artificial intelligence, database management, data visualization, machine learning, mathematic algorithms, and statistics (Tsai, 2012). Recently, there has been an increasing interest in the integration of OR and DM (Meisel & Mattfeld, 2010; Corne et al., 2012). For instance, data mining can be helpful in many OR application areas and can be used in a complementary way to optimization method to identify constraints and reduce the search space (Olafsson et al., 2008).
The proposed model related to the Self- Organizing Map algorithm, a testing data set with the one-dimensional vectors and An Odds Ratio coefficient is performed in the Cloudera parallel network environment with the configuration as follows: This Cloudera system includes 9 nodes (9 servers). The configuration of each server in the Cloudera system is: Intel® Server Board S1200V3RPS, Intel® Pentium® Processor G3220 (3M Cache, 3.00 GHz), 2GB CC3-10600 ECC 1333 MHz LP Unbuffered DIMMs. The operating system of each server in the 9 servers is: Cloudera. All 9 nodes have the same configuration information. The Java language is used in programming the application of the proposed model related to the Odds Ratio similarity coefficient of the clustering technologies in the Cloudera
Geraldin B. Dela Cruz et al.  described about "hybrid data mining method which is based on PCA-GA. Both the classifiers are used as fitness function in GA and also in data mining classification process in which performance is increased". Lao H Saal et al.  has described about "BioArray Software Environment (BASE) and presented the web customizable bioinformatics solution named as Bio Array Software Environment which is used for the management and analysis of major areas of microarray experimentation". Brenner et al.  mainly discussed about "Gene expression analysis by massively parallel signature sequencing (MPSS) on micro bead arrays, which provides unprecedented depth of analysis by allowing application of powerful statistical •
Finally, we found a solution and proposed malware analytics visualization method that comprised of descriptive, diagnostic, predictive and prescriptive. The application of proposed malware analytics visualization method is currently under development stage and in future we plan to implement the application and optimize the existing method to allow for greater productivity on fewer resources with better accuracy. This study is significant and the proposed visualization method will be able to effectively perform the malware pattern analysis and predict future attacks.
Each of these elements of the Candidate Consulting Objects should be analysed and re- conceptualised to the latent BITA process structure in SAM to obtain an alignment framework. This framework is defined by four strategic change centres: business strategy, IT strategy, business infrastructure, and IT infrastructure. The concepts of strategic adjustment as construct and functional integration developed by  are re-conceptualised as the options of an IT consultancy that act as connectors of the interactions between IT/business components. Therefore, once the initial constructs have been defined as a result of the application of the methodological framework in IT consulting, it prescribes three actions within this adaptation flow: align the IT pre-diagnosis, establish relevance to diagnostic classes, and align the subsystems of IT consulting (Figure 5).
Vagueness in the scientific studies presents a challenging dimension. Intuitionistic fuzzy set theory has emerged as a tool for its characterization. There is need to associate measures which can measure vagueness and differences in the underlying characterizing IFSs. In the present paper we introduce an information theoretic divergence measure, called intuitionistic fuzzy Jensen-Rényi divergence. It is a difference measure in the setting of intuitionistic fuzzy set theory, involving parameters that provide flexibility and choice. The strength of the new measure lies in its properties and applications. An approach to multiple-attributedecisionmaking based on intuitionistic fuzzy Jensen-Rényi divergence is proposed. A numerical example illustrates the application of the new measure and the role of various parameters therein to multipleattribute decisionmaking problem formulated in terms of intuitionistic fuzzy sets.
Root CA establishes roles and responsibilities using these considered factors: business process, IS architecture and IT infrastructure. Business process describes interaction among certification practice participants. Business process in Root CA can be more complex depends on how INPKI grows in the future; accordingly Root CA will consider its necessary personnel later. IS architecture hints how Root CA’s business process cascaded into processed data/information and related application, include specialized application to maintain its certificate and Sub-CA’s certificate. IT infrastructure covers appropriate technology in INPKI deployment. Through comparison with other root CA and review WebTrust best-practice, Root CA in INPKI should establish these following roles (Prov. 5.2.1): system administrator, operator, registration officer, and auditor. As information
This paper proposed a new method of the MADM problems based on the TFLHHA operator. The new method can deal with the MADM problems where the decisionmaking information takes the form of the TFL Vs directly, and makes the computation process of the TFL Vs easily without the loss of the information. This method is easy to use and understand, and it enriched and developed the theory and method of the MADM, This method can solve these MADM problems where the attribute values take the form of the fuzzy linguistic variables, such as fuzzy linguistic variables, the uncertain fuzzy linguistic variables, the triangularfuzzy linguistic variables, the trapezoid fuzzy linguistic variables, and the mixed fuzzy linguistic variables, if we can transform these fuzzy linguistic variables into the trapezoid fuzzy linguistic variables. But this method can only solve the MADM problem under the linguistic context. So it is the limitation of this paper. In the future, we will apply this method to solve the real-life MADM problems in the linguistic context, and we will continued working in the decisionmaking method of the MADM problems with the TFL V .
(NLP) solution procedure by considering triangularfuzzy numbers. Liu and Zeng  proposes a new TOPSIS method to deal with the fuzzymultipleattribute group decisionmaking problem based on the expected value operator of the trapezoidal fuzzy number when the fuzzydecision matrixes and the weights of the decision attributes and decision makers are all given by the trapezoidal fuzzy number. Tsaur et al.  convert the fuzzy MCDM problem into a crisp one via centroid defuzzification and then solve the non-fuzzy MCDM problem by the TOPSIS method. Chu and Lin  changed the fuzzy MCDM problem into a crisp one. Differing from the others, they first derive the membership functions of all the weighted ratings in a weighted normalized decision matrix and then convert them to crisp values by defuzzifying and then use TOPSIS method to solve this problem.
Abstract. An Interval-Valued Trapezoidal Intuitionistic Fuzzy Number (IVTrIFN) is a special case of an Intuitionistic Fuzzy Set (IFS), which is dened on a real number set. From a geometric viewpoint, the expectation and expectant score of an IVTrIFN are dened using the notion of a barycenter, and a new method is developed to rank IVTrIFNs. Hereby, some generalized aggregation operators of IVTrIFNs are dened, including the generalized ordered weighted averagingoperator and the generalized hybrid weighted averagingoperator, which are employed to solve multi-attribute group decisionmaking problems. Using the weighted average operator of IVTrIFNs, the attribute values of alternatives are integrated into the individual comprehensive ratings, which are further aggregated into the collective one by the generalized hybrid weighted averagingoperator of IVTrIFNs. The ranking orders of alternatives are then generated according to the expectation and expectant score of the collective comprehensive ratings of alternatives. A numerical example is examined to demonstrate the applicability and implementation process of the decision method proposed in this paper.
The second type is the aggregation operators of TIFN. Zhang and Liu  dened the concepts of TIFN in which the membership and the non-membership degrees are denoted by triangularfuzzy number. Then, the weighted geometric averagingoperator and the weighted arithmetic average operator are presented and used for the decision-making area. Robinson and EC  investigated Triangular Intuitionistic Fuzzy Ordered Weighted Averaging (TIFOWA) operator and the Triangular Intuitionistic Fuzzy Hybrid Aggregation (TIFHA) operator. Chen and Li  developed a new distance measure between two TIFNs to aid in determining attribute weights, and they presented the Weighted Arithmetic Averagingoperator on TIFNs (TIFN-WAA), and then proposed a dynamic MADM model with TIFNs. Wang et al.  proposed new arithmetic operations and logic operators for TIFNs and applied them to fault analysis of a printed circuit board assembly system. Yu and Xu  dened the concepts of Intuitionistic Multiplicative TriangularFuzzy (IMTF) set and intuitionistic multiplicative tri- angular fuzzy number, and then discussed their opera- tional laws and some desirable properties. Based on the operational laws, they developed a series of aggregation operators for IMTF information. Combining the fuzzy measure and Choquet integral, Wan and Dong  dened the TIF Choquet integral aggregation operator and investigated some desirable properties for this operator.
Abstract. With respect to the interval neutrosophic Multi-AttributeDecision-Making (MADM) problems, the MADM method is developed based on some interval neutrosophic aggregation operators. Firstly, the Induced Generalized Interval Neutrosophic Hybrid Arithmetic Averaging (IGINHAA) operator and the Induced Generalized Interval Neutro- sophic Hybrid Geometric Mean (IGINHGM) operator are proposed, which can weight all the input arguments and their ordered positions. Further, regarding the situation where the input elements are interdependent, the Induced Generalized Interval Neutrosophic Shapley Hybrid Arithmetic Averaging (IGINSHAA) operator and the Induced Generalized Interval Neutrosophic Shapley Hybrid Geometric Mean (IGINSHGM) operator are proposed, which are extensions of IGINHAA and IGINHGM operators, respectively, and some properties of these given operators are investigated. Furthermore, the interval neutrosophic cross entropy, which is an extension of single-valued neutrosophic cross entropy, is dened, and the models based on the interval neutrosophic cross entropy and generalized Shapley function are respectively constructed to determine the optimal fuzzy measures on the attribute and ordered sets. Finally, an approach to interval neutrosophic MADM with interactive conditions and incomplete known weight information is proposed based on these given operators, and a practical example is shown to verify the practicality and feasibility of the new approach.
The application of TIFN in MCDM is based on its ability to express decision information in several dimensions and to reflect the assessment information in a more holistic manner . Several research efforts have been made in the advancement of TIFN over the past few years. Among them, we can mention the characterization of membership and non-membership degrees in intuitionistic fuzzy sets (IFS) using the triangularfuzzy numbers by Shu et al. . Chen and Li  developed a new distance measurement between two TIFNs for determining attribute weights, as well as weighted arithmetic averaging (TIFN-WAA) operators on TIFNs. Zhang and Nan  developed a methodology for ranking TIFNs by considering the concept of a TIFN as a special case of the IFN. Wan et al. , using the TIFN, extended the classical VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method for solving multi-attributes group decision-making (MAGDM) problems, while Li et al.  investigated the arithmetic operations and cut sets over TIFNs, and defined the values and ambiguities of the membership degree and non-membership degree for the TIFNs, as well as the value index and ambiguity index.
The research on the evolution law of the opinions can help the decision makers (DMs) improve the decision-making efficiency, predict the trend of events and make the right decision. These opinions are always described by one number, which is inaccurate and incomplete. To solve such a problem, in this paper, the hesitant fuzzy DeGroot (HF-DeGroot) opinion dynamics model is proposed. In order to simulate the transformation of hesitant fuzzy opinions, we introduced the multiplications for real matrix and hesitant fuzzy matrix. Then three kinds of transformation matrices with the consideration of the similarity degree, self-confidence degree and authority degree are constructed based on the hesitant fuzzy data and the consensus condition for the model is discussed as well. Furthermore, the HF-DeGroot opinion dynamics decision-making method is proposed from a prediction perspective and is applied to the emergency decision for the public health events. Finally, the effectiveness, feasibility and practicability of this method are shown by the comparison and simulation results.
attacker cannot obtain any meaningful connection between the plain-audio and cipher-audio. Therefore; the proposed method dealt with this kind of attack and tried to make it infeasible by making the chaining series of plaintext at the diffusion stage. As a result, all the resulting cipher will be changed even if only one bit of the original audio data had been changed. Also, the effectiveness of the IRV value which change with every run time, thus the resulting cipher audio will be different every execution time even if the same plain audio and secrete key have been used, i.e. the chosen plaintext attack will be infeasible. Figure 7 shows different execution process for same audio file. The figure indicates that for each encryption process, the resulting cipher-audio will be different.