Search results for: recursive algebra

Authors: Fenglong Guo, Dingcheng Wang

Abstract:

This paper studies ruin probabilities in two discrete-time risk models with premiums, claims and rates of interest modelled by three autoregressive moving average processes. Generalized Lundberg inequalities for ruin probabilities are derived by using recursive technique. A numerical example is given to illustrate the applications of these probability inequalities.

Keywords: Lundberg inequality, NWUC, Renewal recursive technique, Ruin probability

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Authors: Miloje S. Radenkovic, Tamal Bose

Abstract:

This paper presents the convergence analysis of a prediction based blind equalizer for IIR channels. Predictor parameters are estimated by using the recursive least squares algorithm. It is shown that the prediction error converges almost surely (a.s.) toward a scalar multiple of the unknown input symbol sequence. It is also proved that the convergence rate of the parameter estimation error is of the same order as that in the iterated logarithm law.

Keywords: Adaptive blind equalizer, Recursive leastsquares, Adaptive Filtering, Convergence analysis.

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Authors: Nahid-Al-Masood, Jubaer Ahmed, Amina Hasan Abedin, S. R. Deeba, Faeza Hafiz, Mahmuda Begum

Abstract:

An electric utility-s main concern is to plan, design, operate and maintain its power supply to provide an acceptable level of reliability to its users. This clearly requires that standards of reliability be specified and used in all three sectors of the power system, i.e., generation, transmission and distribution. That is why reliability of a power system is always a major concern to power system planners. This paper presents the reliability analysis of Bangladesh Power System (BPS). Reliability index, loss of load probability (LOLP) of BPS is evaluated using recursive algorithm and considering no de-rated states of generators. BPS has sixty one generators and a total installed capacity of 5275 MW. The maximum demand of BPS is about 5000 MW. The relevant data of the generators and hourly load profiles are collected from the National Load Dispatch Center (NLDC) of Bangladesh and reliability index 'LOLP' is assessed for the period of last ten years.

Keywords: Recursive algorithm, LOLP, forced outage rate, cumulative probability.

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Authors: Alexander Y. Vaninsky

Abstract:

The paper compares the treatment of fractions in a typical undergraduate college curriculum and in abstract algebra textbooks. It stresses that the main difference is that the undergraduate curriculum treats equivalent fractions as equal, and this treatment eventually leads to paradoxes and impairs the students- ability to perceive ratios, proportions, radicals and rational exponents adequately. The paper suggests a simplified version of rigorous theory of fractions suitable for regular college curriculum.

Keywords: Fractions, mathematics curriculum, mathematics education, teacher preparation

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Authors: Ikbal Zammouri, Béchir Ayeb

Abstract:

In this paper, we propose a new method to describe fractal shapes using parametric l-systems. First we introduce scaling factors in the production rules of the parametric l-systems grammars. Then we decorticate these grammars with scaling factors using turtle algebra to show the mathematical relation between l-systems and iterated function systems (IFS). We demonstrate that with specific values of the scaling factors, we find the exact relationship established by Prusinkiewicz and Hammel between l-systems and IFS.

Keywords: Fractal shapes, IFS, parametric l-systems, turtlealgebra.

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Authors: Areej M. Abduldaim, Nadia M. G. Al-Saidi

Abstract:

Algebra is one of the important fields of mathematics. It concerns with the study and manipulation of mathematical symbols. It also concerns with the study of abstractions such as groups, rings, and fields. Due to the development of these abstractions, it is extended to consider other structures, such as vectors, matrices, and polynomials, which are non-numerical objects. Computer algebra is the implementation of algebraic methods as algorithms and computer programs. Recently, many algebraic cryptosystem protocols are based on non-commutative algebraic structures, such as authentication, key exchange, and encryption-decryption processes are adopted. Cryptography is the science that aimed at sending the information through public channels in such a way that only an authorized recipient can read it. Ring theory is the most attractive category of algebra in the area of cryptography. In this paper, we employ the algebraic structure called skew -Armendariz rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is established and illustrated through numerical example, and its soundness and completeness are proved.

Keywords: Cryptosystem, identification, skew π-Armendariz rings, skew polynomial rings, zero knowledge protocol.

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Authors: Hong Son Hoang, Remy Baraille

Abstract:

The (sub)-optimal soolution of linear filtering problem with correlated noises is considered. The special recursive form of the class of filters and criteria for selecting the best estimator are the essential elements of the design method. The properties of the proposed filter are studied. In particular, for Markovian observation noise, the approximate filter becomes an optimal Gevers-Kailath filter subject to a special choice of the parameter in the class of given linear recursive filters.

Keywords: Linear dynamical system, filtering, minimum meansquare filter, correlated noise

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Authors: M.Asif, M.R.Arshad, P.A.Wilson

Abstract:

In this paper, a simple active contour based visual tracking algorithm is presented for outdoor AGV application which is currently under development at the USM robotic research group (URRG) lab. The presented algorithm is computationally low cost and able to track road boundaries in an image sequence and can easily be implemented on available low cost hardware. The proposed algorithm used an active shape modeling using the B-spline deformable template and recursive curve fitting method to track the current orientation of the road.

Keywords: Active contour, B-spline, recursive curve fitting.

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Authors: Richard Elling Moe

Abstract:

Computer languages are usually lumped together into broad -paradigms-, leaving us in want of a finer classification of kinds of language. Theories distinguishing between -genuine differences- in language has been called for, and we propose that such differences can be observed through a notion of expressive mode. We outline this concept, propose how it could be operationalized and indicate a possible context for the development of a corresponding theory. Finally we consider a possible application in connection with evaluation of language revision. We illustrate this with a case, investigating possible revisions of the relational algebra in order to overcome weaknesses of the division operator in connection with universal queries.

Keywords: Expressive mode, Computer language species, Evaluation of revision, Relational algebra, Universal database queries

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Authors: Mona Taheri

Abstract:

In this study, we examine multiple algebras and algebraic structures derived from them and by stating a theory on multiple algebras; we will show that the theory of multiple algebras is a natural extension of the theory of universal algebras. Also, we will treat equivalence relations on multiple algebras, for which the quotient constructed modulo them is a universal algebra and will study the basic relation and the fundamental algebra in question. In this study, by stating the characteristic theorem of multiple algebras, we show that the theory of multiple algebras is a natural extension of the theory of universal algebras.

Keywords: multiple algebras , universal algebras

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Authors: Ping He, Heng-You Lan, Gong-Quan Tan

Abstract:

The multidelays linear control systems described by difference differential equations are often studied in modern control theory. In this paper, the delay-independent stabilization algebraic criteria and the theorem of delay-independent stabilization for linear systems with multiple time-delays are established by using the Lyapunov functional and the Riccati algebra matrix equation in the matrix theory. An illustrative example and the simulation result, show that the approach to linear systems with multiple time-delays is effective.

Keywords: Linear system, Delay-independent stabilization, Lyapunovfunctional, Riccati algebra matrix equation.

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Authors: Hsun Su, Yuan-Kang Shih, Shin-Shin Kao

Abstract:

Many well-known interconnection networks, such as kary n-cubes, recursive circulant graphs, generalized recursive circulant graphs, circulant graphs and so on, are shown to belong to the family of cycle composition networks. Recently, various studies about mutually independent hamiltonian cycles, abbreviated as MIHC-s, on interconnection networks are published. In this paper, using an improved construction method, we obtain MIHC-s on cycle composition networks with a much weaker condition than the known result. In fact, we established the existence of MIHC-s in the cycle composition networks and the result is optimal in the sense that the number of MIHC-s we constructed is maximal.

Keywords: Hamiltonian cycle, k-ary n-cube, cycle composition networks, mutually independent.

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Authors: Mona Taheri

Abstract:

The purpose of this research is to study the concepts of multiple Cartesian product, variety of multiple algebras and to present some examples. In the theory of multiple algebras, like other theories, deriving new things and concepts from the things and concepts available in the context is important. For example, the first were obtained from the quotient of a group modulo the equivalence relation defined by a subgroup of it. Gratzer showed that every multiple algebra can be obtained from the quotient of a universal algebra modulo a given equivalence relation. The purpose of this study is examination of multiple algebras and basic relations defined on them as well as introduction to some algebraic structures derived from multiple algebras. Among the structures obtained from multiple algebras, this article studies submultiple algebras, quotients of multiple algebras and the Cartesian product of multiple algebras.

Keywords: hypergroup, multiple algebras

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Authors: Alina Mirza, Sumrin M. Kabir, Shahzad A. Sheikh

Abstract:

The Orthogonal Frequency Division Multiplexing (OFDM) with high data rate, high spectral efficiency and its ability to mitigate the effects of multipath makes them most suitable in wireless application. Impulsive noise distorts the OFDM transmission and therefore methods must be investigated to suppress this noise. In this paper, a State Space Recursive Least Square (SSRLS) algorithm based adaptive impulsive noise suppressor for OFDM communication system is proposed. And a comparison with another adaptive algorithm is conducted. The state space model-dependent recursive parameters of proposed scheme enables to achieve steady state mean squared error (MSE), low bit error rate (BER), and faster convergence than that of some of existing algorithm.

Keywords: OFDM, Impulsive Noise, SSRLS, BER.

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Authors: Anosh Arshad Sundhu, Francesco Giordano, Giacomo Della Croce, Maurizio Arnone

Abstract:

Digital Twin (DT) is a technology that generates a virtual representation of a physical system or process, enabling real-time monitoring, analysis, and simulation. DT of an Electrical Distribution System (EDS) can perform online analysis by integrating the static and real-time data in order to show the current grid status and predictions about the future status to the Distribution System Operator (DSO), producers and consumers. DT technology for EDS also offers the opportunity to DSO to test hypothetical scenarios. This paper discusses the development of a DT of an EDS by Smart Grid Controller (SGC) application, which is developed using open-source libraries and languages. The developed application can be integrated with Supervisory Control and Data Acquisition System (SCADA) of any EDS for creating the DT. The paper shows the performance of developed tools inside the application, tested on real EDS for grid observability, Smart Recursive Load Flow (SRLF) calculation and state estimation of loads in MV feeders.

Keywords: Digital Twin, Distribution System Operator, Electrical Distribution System, Smart Grid Controller, Supervisory Control and Data Acquisition System, Smart Recursive Load Flow.

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Authors: Hadi Sadoghi Yazdi, Mehri Sadoghi Yazdi, Mohammad Reza Mohammadi

Abstract:

This paper is concerned with studying the forgetting factor of the recursive least square (RLS). A new dynamic forgetting factor (DFF) for RLS algorithm is presented. The proposed DFF-RLS is compared to other methods. Better performance at convergence and tracking of noisy chirp sinusoid is achieved. The control of the forgetting factor at DFF-RLS is based on the gradient of inverse correlation matrix. Compared with the gradient of mean square error algorithm, the proposed approach provides faster tracking and smaller mean square error. In low signal-to-noise ratios, the performance of the proposed method is superior to other approaches.

Keywords: Forgetting factor, RLS, Inverse correlation matrix, human motion analysis.

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Authors: Jyh-Da Wei, Hsin-Chen Tsai

Abstract:

This work presents a novel means of extracting fixedlength parameters from voice signals, such that words can be recognized in linear time. The power and the zero crossing rate are first calculated segment by segment from a voice signal; by doing so, two feature sequences are generated. We then construct an FIR system across these two sequences. The parameters of this FIR system, used as the input of a multilayer proceptron recognizer, can be derived by recursive LSE (least-square estimation), implying that the complexity of overall process is linear to the signal size. In the second part of this work, we introduce a weighting factor λ to emphasize recent input; therefore, we can further recognize continuous speech signals. Experiments employ the voice signals of numbers, from zero to nine, spoken in Mandarin Chinese. The proposed method is verified to recognize voice signals efficiently and accurately.

Keywords: Speech Recognition, FIR system, Recursive LSE, Multilayer Perceptron

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Authors: Benedetto Manganelli, Beniamino Murgante

Abstract:

The distinction among urban, periurban and rural areas represents a classical example of uncertainty in land classification. Satellite images, geostatistical analysis and all kinds of spatial data are very useful in urban sprawl studies, but it is important to define precise rules in combining great amounts of data to build complex knowledge about territory. Rough Set theory may be a useful method to employ in this field. It represents a different mathematical approach to uncertainty by capturing the indiscernibility. Two different phenomena can be indiscernible in some contexts and classified in the same way when combining available information about them. This approach has been applied in a case of study, comparing the results achieved with both Map Algebra technique and Spatial Rough Set. The study case area, Potenza Province, is particularly suitable for the application of this theory, because it includes 100 municipalities with different number of inhabitants and morphologic features.

Keywords: Land Classification, Map Algebra, Periurban Fringe, Rough Set, Urban Planning, Urban Sprawl.

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Authors: Yeqing Guan, Fen Yang

Abstract:

To learn about China-s future energy demand, this paper first proposed GM(1,1) model group based on recursive solutions of parameters estimation, setting up a general solving-algorithm of the model group. This method avoided the problems occurred on the past researches that remodeling, loss of information and large amount of calculation. This paper established respectively all-data-GM(1,1), metabolic GM(1,1) and new information GM (1,1)model according to the historical data of energy consumption in China in the year 2005-2010 and the added data of 2011, then modeling, simulating and comparison of accuracies we got the optimal models and to predict. Results showed that the total energy demand of China will be 37.2221 billion tons of equivalent coal in 2012 and 39.7973 billion tons of equivalent coal in 2013, which are as the same as the overall planning of energy demand in The 12th Five-Year Plan.

Keywords: energy demands, GM(1, 1) model group, least square estimation, prediction

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Authors: Ethar H. Khalil, Bahaa I. Kazem

Abstract:

In this work a software simulation model has been proposed for two driven wheels mobile robot path planning; that can navigate in dynamic environment with static distributed obstacles. The work involves utilizing Bezier curve method in a proposed N order matrix form; for engineering the mobile robot path. The Bezier curve drawbacks in this field have been diagnosed. Two directions: Up and Right function has been proposed; Probability Recursive Function (PRF) to overcome those drawbacks. PRF functionality has been developed through a proposed; obstacle detection function, optimization function which has the capability of prediction the optimum path without comparison between all feasible paths, and N order Bezier curve function that ensures the drawing of the obtained path. The simulation results that have been taken showed; the mobile robot travels successfully from starting point and reaching its goal point. All obstacles that are located in its way have been avoided. This navigation is being done successfully using the proposed PRF techniques.

Keywords: Mobile robot, path planning, Bezier curve.

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Authors: Mingtao Ding, Zheng Tian, Haixia Xu

Abstract:

The batch nature limits the standard kernel principal component analysis (KPCA) methods in numerous applications, especially for dynamic or large-scale data. In this paper, an efficient adaptive approach is presented for online extraction of the kernel principal components (KPC). The contribution of this paper may be divided into two parts. First, kernel covariance matrix is correctly updated to adapt to the changing characteristics of data. Second, KPC are recursively formulated to overcome the batch nature of standard KPCA.This formulation is derived from the recursive eigen-decomposition of kernel covariance matrix and indicates the KPC variation caused by the new data. The proposed method not only alleviates sub-optimality of the KPCA method for non-stationary data, but also maintains constant update speed and memory usage as the data-size increases. Experiments for simulation data and real applications demonstrate that our approach yields improvements in terms of both computational speed and approximation accuracy.

Keywords: adaptive method, kernel principal component analysis, online extraction, recursive algorithm

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Authors: Mutuku Muvengei, John Kihiu

Abstract:

This paper focuses on the development of bond graph dynamic model of the mechanical dynamics of an excavating mechanism previously designed to be used with small tractors, which are fabricated in the Engineering Workshops of Jomo Kenyatta University of Agriculture and Technology. To develop a mechanical dynamics model of the manipulator, forward recursive equations similar to those applied in iterative Newton-Euler method were used to obtain kinematic relationships between the time rates of joint variables and the generalized cartesian velocities for the centroids of the links. Representing the obtained kinematic relationships in bondgraphic form, while considering the link weights and momenta as the elements led to a detailed bond graph model of the manipulator. The bond graph method was found to reduce significantly the number of recursive computations performed on a 3 DOF manipulator for a mechanical dynamic model to result, hence indicating that bond graph method is more computationally efficient than the Newton-Euler method in developing dynamic models of 3 DOF planar manipulators. The model was verified by comparing the joint torque expressions of a two link planar manipulator to those obtained using Newton- Euler and Lagrangian methods as analyzed in robotic textbooks. The expressions were found to agree indicating that the model captures the aspects of rigid body dynamics of the manipulator. Based on the model developed, actuator sizing and valve sizing methodologies were developed and used to obtain the optimal sizes of the pistons and spool valve ports respectively. It was found that using the pump with the sized flow rate capacity, the engine of the tractor is able to power the excavating mechanism in digging a sandy-loom soil.

Keywords: Actuators, bond graphs, inverse dynamics, recursive equations, quintic polynomial trajectory.

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Authors: Xun Ge, Jingju Qian

Abstract:

To investigate some relations between higher mathe¬matics scores in Chinese graduate student entrance examination and calculus (resp. linear algebra, probability statistics) scores in subject's completion examination of Chinese university, we select 20 students as a sample, take higher mathematics score as a decision attribute and take calculus score, linear algebra score, probability statistics score as condition attributes. In this paper, we are based on rough-set theory (Rough-set theory is a logic-mathematical method proposed by Z. Pawlak. In recent years, this theory has been widely implemented in the many fields of natural science and societal science.) to investigate importance of condition attributes with respective to decision attribute and strength of condition attributes supporting decision attribute. Results of this investigation will be helpful for university students to raise higher mathematics scores in Chinese graduate student entrance examination.

Keywords: Rough set, higher mathematics scores, decision attribute, condition attribute.

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Authors: N. Mahendran, R. Madhuranthi

Abstract:

Wireless sensor networks (WSNs), are constantly in demand to process information more rapidly with less energy and area cost. Presently, processor based solutions have difficult to achieve high processing speed with low-power consumption. This paper presents a simple and accurate data processing scheme for low power wireless sensor node, based on reduced number of processing element (PE). The presented model provides a simple recursive structure (SRS) to process the sampled data in the wireless sensor environment and to reduce the power consumption in wireless sensor node. Based on this model, to process the incoming samples and produce a smaller amount of data sufficient to reconstruct the original signal. The ModelSim simulator used to simulate SRS structure. Functional simulation is carried out for the validation of the presented architecture. Xilinx Power Estimator (XPE) tool is used to measure the power consumption. The experimental results show the average power consumption of 91 mW; this is 42% improvement compared to the folded tree architecture.

Keywords: Power consumption, energy efficiency, low power WSN node, recursive structure, sleep/wake scheduling.

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Authors: Cheng Zhang, James Marco, Walid Allafi, Truong Q. Dinh, W. D. Widanage

Abstract:

Equivalent circuit models (ECMs) are widely used in battery management systems in electric vehicles and other battery energy storage systems. The battery dynamics and the model parameters vary under different working conditions, such as different temperature and state of charge (SOC) levels, and therefore online parameter identification can improve the modelling accuracy. This paper presents a way of online ECM parameter identification using a continuous time (CT) estimation method. The CT estimation method has several advantages over discrete time (DT) estimation methods for ECM parameter identification due to the widely separated battery dynamic modes and fast sampling. The presented method can be used for online SOC estimation. Test data are collected using a lithium ion cell, and the experimental results show that the presented CT method achieves better modelling accuracy compared with the conventional DT recursive least square method. The effectiveness of the presented method for online SOC estimation is also verified on test data.

Keywords: Equivalent circuit model, continuous time domain estimation, linear integral filter method, parameter and SOC estimation, recursive least square.

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Authors: J. Ritonja

Abstract:

Available commercial applications of power system stabilizers assure optimal damping of synchronous generator’s oscillations only in a small part of operating range. Parameters of the power system stabilizer are usually tuned for the selected operating point. Extensive variations of the synchronous generator’s operation result in changed dynamic characteristics. This is the reason that the power system stabilizer tuned for the nominal operating point does not satisfy preferred damping in the overall operation area. The small-signal stability and the transient stability of the synchronous generators have represented an attractive problem for testing different concepts of the modern control theory. Of all the methods, the adaptive control has proved to be the most suitable for the design of the power system stabilizers. The adaptive control has been used in order to assure the optimal damping through the entire synchronous generator’s operating range. The use of the adaptive control is possible because the loading variations and consequently the variations of the synchronous generator’s dynamic characteristics are, in most cases, essentially slower than the adaptation mechanism. The paper shows the development and the application of the self-tuning power system stabilizer based on recursive least square identification method and linear quadratic regulator. Identification method is used to calculate the parameters of the Heffron-Phillips model of the synchronous generator. On the basis of the calculated parameters of the synchronous generator’s mathematical model, the synthesis of the linear quadratic regulator is carried-out. The identification and the synthesis are implemented on-line. In this way, the self-tuning power system stabilizer adapts to the different operating conditions. A purpose of this paper is to contribute to development of the more effective power system stabilizers, which would replace currently used linear stabilizers. The presented self-tuning power system stabilizer makes the tuning of the controller parameters easier and assures damping improvement in the complete operating range. The results of simulations and experiments show essential improvement of the synchronous generator’s damping and power system stability.

Keywords: Adaptive control, linear quadratic regulator, power system stabilizer, recursive least square identification.

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Authors: G. Ramana Murthy, C. Senthilpari, P. Velrajkumar, Lim Tien Sze

Abstract:

In this paper, a design methodology to implement low-power and high-speed 2nd order recursive digital Infinite Impulse Response (IIR) filter has been proposed. Since IIR filters suffer from a large number of constant multiplications, the proposed method replaces the constant multiplications by using addition/subtraction and shift operations. The proposed new 6T adder cell is used as the Carry-Save Adder (CSA) to implement addition/subtraction operations in the design of recursive section IIR filter to reduce the propagation delay. Furthermore, high-level algorithms designed for the optimization of the number of CSA blocks are used to reduce the complexity of the IIR filter. The DSCH3 tool is used to generate the schematic of the proposed 6T CSA based shift-adds architecture design and it is analyzed by using Microwind CAD tool to synthesize low-complexity and high-speed IIR filters. The proposed design outperforms in terms of power, propagation delay, area and throughput when compared with MUX-12T, MCIT-7T based CSA adder filter design. It is observed from the experimental results that the proposed 6T based design method can find better IIR filter designs in terms of power and delay than those obtained by using efficient general multipliers.

Keywords: CSA Full Adder, Delay unit, IIR filter, Low-Power, PDP, Parametric Analysis, Propagation Delay, Throughput, VLSI.

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Authors: Xun Ge

Abstract:

Recently, X. Ge and J. Qian investigated some relations between higher mathematics scores and calculus scores (resp. linear algebra scores, probability statistics scores) for Chinese university students. Based on rough-set theory, they established an information system S = (U,CuD,V, f). In this information system, higher mathematics score was taken as a decision attribute and calculus score, linear algebra score, probability statistics score were taken as condition attributes. They investigated importance of each condition attribute with respective to decision attribute and strength of each condition attribute supporting decision attribute. In this paper, we give further investigations for this issue. Based on the above information system S = (U, CU D, V, f), we analyze the decision rules between condition and decision granules. For each x E U, we obtain support (resp. strength, certainty factor, coverage factor) of the decision rule C —>x D, where C —>x D is the decision rule induced by x in S = (U, CU D, V, f). Results of this paper gives new analysis of on higher mathematics scores for Chinese university students, which can further lead Chinese university students to raise higher mathematics scores in Chinese graduate student entrance examination.

Keywords: Rough set, support, strength, certainty factor, coverage factor.

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Authors: A. Nasiri Pour, B. Rostami Tabar, A.Rahimzadeh

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Accurate demand forecasting is one of the most key issues in inventory management of spare parts. The problem of modeling future consumption becomes especially difficult for lumpy patterns, which characterized by intervals in which there is no demand and, periods with actual demand occurrences with large variation in demand levels. However, many of the forecasting methods may perform poorly when demand for an item is lumpy. In this study based on the characteristic of lumpy demand patterns of spare parts a hybrid forecasting approach has been developed, which use a multi-layered perceptron neural network and a traditional recursive method for forecasting future demands. In the described approach the multi-layered perceptron are adapted to forecast occurrences of non-zero demands, and then a conventional recursive method is used to estimate the quantity of non-zero demands. In order to evaluate the performance of the proposed approach, their forecasts were compared to those obtained by using Syntetos & Boylan approximation, recently employed multi-layered perceptron neural network, generalized regression neural network and elman recurrent neural network in this area. The models were applied to forecast future demand of spare parts of Arak Petrochemical Company in Iran, using 30 types of real data sets. The results indicate that the forecasts obtained by using our proposed mode are superior to those obtained by using other methods.

Keywords: Lumpy Demand, Neural Network, Forecasting, Hybrid Approach.

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Authors: Shaoquan Sun, Qianqian Li

Abstract:

The aim of this paper is to introduce the notions of intuitionistic T-S fuzzy subalgebras and intuitionistic T-S fuzzy ideals in BCI-algebras, and then to investigate their basic properties.

Keywords: BCI-algebra, intuitionistic T-S fuzzy subalgebra, intuitionistic T-S fuzzy ideal, norm intersection, direct product, epimorphism, isomorphism.

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