Search results for: uncertain volatility.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 226

Search results for: uncertain volatility.

136 Degradation Model of Optical Characteristics of Zno-Pigmented White Paint by Electron Radiation

Authors: Tian Hai, Yang Shengsheng, Jr., Wang Yi

Abstract:

Based on an analysis of the mechanism of degradation of optical characteristics of the ZnO-pigmented white paint by electron irradiation, a model of single molecular color centers is built. An equation that explains the relationship between the changes of variation of the ZnO-pigmented white paint-s spectrum absorptance and electron fluence is derived. The uncertain parameters in the equation can be calculated using the curve fitting by experimental data. The result indicates that the model can be applied to predict the degradation of optical characteristics of ZnO-pigmented white paint by electron radiation.

Keywords: ZnO-pigmented white pain, effects of electron radiation, optical characteristics degradation, prediction model.

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135 Empirical Analyses of Determinants of D.J.S.I.US Mean Returns

Authors: Nikolaos Sariannidis, Grigoris Giannarakis, Nikolaos Litinas, Nikos Kartalis

Abstract:

This study investigates the relationship between 10 year bond value, Yen/U.S dollar exchange rate, non-farm payrolls (all employs) and crude oil to U.S. Dow Jones Sustainability Index. A GARCH model is used to test these relationships for the period January 1st 1999 to January 31st 2008 using monthly data. Results show that an increase of the 10 year bond and non farm payrolls (all employs) lead to an increase of the D.J.S.I returns. On the contrary the volatility of the Yen/U.S dollar exchange rates as well as the increase of crude oil returns has negative effects on the U.S D.J.S.I returns. This study aims at assisting investors to understand the influences certain macroeconomic indicators have on the companies- stock returns as reported by the D.J.S.I.

Keywords: Bond value, Corporate Social Responsibility, Crudeoil, D.J.S.I United States, Exchange rate, GARCH, Non-farmpayrolls.

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134 Analyzing the Effects of Adding Bitcoin to Portfolio

Authors: Shashwat Gangwal

Abstract:

This paper analyses the effect of adding Bitcoin, to the portfolio (stocks, bonds, Baltic index, MXEF, gold, real estate and crude oil) of an international investor by using daily data available from 2nd of July, 2010 to 2nd of August, 2016. We conclude that adding Bitcoin to portfolio, over the course of the considered period, always yielded a higher Sharpe ratio. This means that Bitcoin’s returns offset its high volatility. This paper, recognizing the fact that Bitcoin is a relatively new asset class, gives the readers a basic idea about the working of the virtual currency, the increasing number developments in the financial industry revolving around it, its unique features and the detailed look into its continuously growing acceptance across different fronts (Banks, Merchants and Countries) globally. We also construct optimal portfolios to reflect the highly lucrative and largely unexplored opportunities associated with investment in Bitcoin.

Keywords: Portfolio management, Bitcoin, optimization, Sharpe ratio.

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133 The Application of Learning Systems to Support Decision for Stakeholder and Infrastructures Managers Based On Crowdsourcing

Authors: Alfonso Bastías, Álvaro González

Abstract:

The actual grow of the infrastructure in develop country require sophisticate ways manage the operation and control the quality served. This research wants to concentrate in the operation of this infrastructure beyond the construction. The infrastructure-s operation involves an uncertain environment, where unexpected variables are present every day and everywhere. Decision makers need to make right decisions with right information/data analyzed most in real time. To adequately support their decisions and decrease any negative impact and collateral effect, they need to use computational tools called decision support systems (DSS), but now the main source of information came from common users thought an extensive crowdsourcing

Keywords: Crowdsourcing, Learning Systems, Decision Support Systems, Infrastructure, Construction.

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132 Multivalued Knowledge-Base based on Multivalued Datalog

Authors: Agnes Achs

Abstract:

The basic aim of our study is to give a possible model for handling uncertain information. This model is worked out in the framework of DATALOG. The concept of multivalued knowledgebase will be defined as a quadruple of any background knowledge; a deduction mechanism; a connecting algorithm, and a function set of the program, which help us to determine the uncertainty levels of the results. At first the concept of fuzzy Datalog will be summarized, then its extensions for intuitionistic- and interval-valued fuzzy logic is given and the concept of bipolar fuzzy Datalog is introduced. Based on these extensions the concept of multivalued knowledge-base will be defined. This knowledge-base can be a possible background of a future agent-model.

Keywords: Fuzzy-, intuitionistic-, bipolar datalog, multivalued knowledge-base

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131 Strategy Analysis and Creation by Simulation in the General Game

Authors: Gábor Szűcs, Gábor Neszveda, Xin Fang

Abstract:

In this paper the General Game problem is described. In this problem the competition or cooperation dilemma occurs as the two basic types of strategies. The strategy possibilities have been analyzed for finding winning strategy in uncertain situations (no information about the number of players and their strategy types). The winning strategy is missing, but a good solution can be found by simulation by varying the ratio of the two types of strategies. This new method has been used in a real contest with human players, where the created strategies by simulation have reached very good ranks. This construction can be applied in other real social games as well.

Keywords: competition, cooperation, finding good strategy, General Game

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130 H-Infinity Controller Design for the Switched Reluctance Machine

Authors: Siwar Fadhel, Imen Bahri, Man Zhang

Abstract:

The switched reluctance machine (SRM) has undeniable qualities in terms of low cost and mechanical robustness. However, its highly nonlinear character and its uncertain parameters justify the development of complicated controls. In this paper, authors present the design of a robust H-infinity current controller for an 8/6 SRM with taking into account the nonlinearity of the SRM and with rejection of disturbances. The electromagnetic torque is indirectly regulated through the current controller. To show the performances of this control, a robustness analysis is performed by comparing the H-infinity and PI controller simulation results. This comparison demonstrates better performances for the presented controller. The effectiveness and robustness of the presented controller are also demonstrated by experimental tests.

Keywords: Current regulation, experimentation, robust H-infinity control, switched reluctance machine.

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129 The Relationship between the Disposition Effect and Herding Behavior: Evidence from Taiwan’s Information Technology Stocks

Authors: Chih-Hsiang Chang

Abstract:

This study aims to explore the relationship between the disposition effect and herding behavior of investors trading Taiwanese information technology stocks. This study differs from previous literature in two aspects. First, in contrast with the earlier studies that focused on investigating investors’ herding behavior, this study explores the possibility that the disposition effect drives investors’ herding behavior. Additionally, it takes an in-depth look at the interdependence between the disposition effect and herding behavior of investors, including lead-lag relationship and volatility transmission effect. Empirical results show that investors trading Taiwan’s information technology stocks exhibit pronounced herding behavior and that the disposition effect has a great impact on their herding behavior.

Keywords: Herding behavior, Disposition effect, Behavioral finance.

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128 Robust H8 Fuzzy Control Design for Nonlinear Two-Time Scale System with Markovian Jumps based on LMI Approach

Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

Abstract:

This paper examines the problem of designing a robust H8 state-feedback controller for a class of nonlinear two-time scale systems with Markovian Jumps described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear two-time scale systems to have an H8 performance are derived. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard nonlinear two-time scale systems. A numerical example is provided to illustrate the design developed in this paper.

Keywords: TS fuzzy, Markovian jumps, LMI, two-time scale systems.

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127 A Modified Fuzzy C-Means Algorithm for Natural Data Exploration

Authors: Binu Thomas, Raju G., Sonam Wangmo

Abstract:

In Data mining, Fuzzy clustering algorithms have demonstrated advantage over crisp clustering algorithms in dealing with the challenges posed by large collections of vague and uncertain natural data. This paper reviews concept of fuzzy logic and fuzzy clustering. The classical fuzzy c-means algorithm is presented and its limitations are highlighted. Based on the study of the fuzzy c-means algorithm and its extensions, we propose a modification to the cmeans algorithm to overcome the limitations of it in calculating the new cluster centers and in finding the membership values with natural data. The efficiency of the new modified method is demonstrated on real data collected for Bhutan-s Gross National Happiness (GNH) program.

Keywords: Adaptive fuzzy clustering, clustering, fuzzy logic, fuzzy clustering, c-means.

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126 Cut Flower Production: A Source of Incremental Income for the Marginal Farmers of the State of West Bengal in India

Authors: Ruma Bhattacharyya

Abstract:

The basic objective of this paper is to measure and compare the profitability of investments made by the small and marginal farmers of the state of West Bengal in floriculture shifting from the traditional cultivation of paddy. A comparison of IRR is made to establish the fact that cultivation of flowers yield higher returns farmers whose land size is so small that viability of paddy cultivation is raising a question mark. A detailed study of the price behavior of the flower crop has been carried out in which the factors leading to the volatility of the price and the dispersion of the range have also been discussed. Finally the incremental incomes of the farmers have been calculated with the help of imputed income from paddy cultivation and the reported income from the selected flowers. The study shows that the farmers stand gainers if they opt for flower cultivation.

Keywords: Bazar Samity, Floriculture, Marginal Farmers.

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125 Design of Permanent Sensor Fault Tolerance Algorithms by Sliding Mode Observer for Smart Hybrid Powerpack

Authors: Sungsik Jo, Hyeonwoo Kim, Iksu Choi, Hunmo Kim

Abstract:

In the SHP, LVDT sensor is for detecting the length changes of the EHA output, and the thrust of the EHA is controlled by the pressure sensor. Sensor is possible to cause hardware fault by internal problem or external disturbance. The EHA of SHP is able to be uncontrollable due to control by feedback from uncertain information, on this paper; the sliding mode observer algorithm estimates the original sensor output information in permanent sensor fault. The proposed algorithm shows performance to recovery fault of disconnection and short circuit basically, also the algorithm detect various of sensor fault mode.

Keywords: Smart Hybrid Powerpack (SHP), Electro Hydraulic Actuator (EHA), Permanent Sensor fault tolerance, Sliding mode observer (SMO), Graphic User Interface (GUI).

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124 Augmented Lyapunov Approach to Robust Stability of Discrete-time Stochastic Neural Networks with Time-varying Delays

Authors: Shu Lü, Shouming Zhong, Zixin Liu

Abstract:

In this paper, the robust exponential stability problem of discrete-time uncertain stochastic neural networks with timevarying delays is investigated. By introducing a new augmented Lyapunov function, some delay-dependent stable results are obtained in terms of linear matrix inequality (LMI) technique. Compared with some existing results in the literature, the conservatism of the new criteria is reduced notably. Three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed method.

Keywords: Robust exponential stability, delay-dependent stability, discrete-time neural networks, stochastic, time-varying delays.

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123 An efficient Activity Network Reduction Algorithm based on the Label Correcting Tracing Algorithm

Authors: Weng Ming Chu

Abstract:

When faced with stochastic networks with an uncertain duration for their activities, the securing of network completion time becomes problematical, not only because of the non-identical pdf of duration for each node, but also because of the interdependence of network paths. As evidenced by Adlakha & Kulkarni [1], many methods and algorithms have been put forward in attempt to resolve this issue, but most have encountered this same large-size network problem. Therefore, in this research, we focus on network reduction through a Series/Parallel combined mechanism. Our suggested algorithm, named the Activity Network Reduction Algorithm (ANRA), can efficiently transfer a large-size network into an S/P Irreducible Network (SPIN). SPIN can enhance stochastic network analysis, as well as serve as the judgment of symmetry for the Graph Theory.

Keywords: Series/Parallel network, Stochastic network, Network reduction, Interdictive Graph, Complexity Index.

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122 Mind Your Product-Market Strategy on Selecting Marketing Inputs: An Uncertainty Approach in Indian Context

Authors: Susmita Ghosh, Bhaskar Bhowmick

Abstract:

Market is an important factor for start-ups to look into during decision-making in product development and related areas. Emerging country markets are more uncertain in terms of information availability and institutional supports. The literature review of market uncertainty reveals the need for identifying factors representing the market uncertainty. This paper identifies factors for market uncertainty using Exploratory Factor Analysis (EFA) and confirmed the number of factor retention using an alternative factor retention criterion ‘Parallel Analysis’. 500 entrepreneurs, engaged in start-ups from all over India participated in the study. This paper concludes with the factor structure of ‘market uncertainty’ having dimensions of uncertainty in industry orientation, uncertainty in customer orientation and uncertainty in marketing orientation.

Keywords: Uncertainty, market, orientation, competitor, demand.

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121 Probabilistic Simulation of Triaxial Undrained Cyclic Behavior of Soils

Authors: Arezoo Sadrinezhad, Kallol Sett, S. I. Hariharan

Abstract:

In this paper, a probabilistic framework based on Fokker-Planck-Kolmogorov (FPK) approach has been applied to simulate triaxial cyclic constitutive behavior of uncertain soils. The framework builds upon previous work of the writers, and it has been extended for cyclic probabilistic simulation of triaxial undrained behavior of soils. von Mises elastic-perfectly plastic material model is considered. It is shown that by using probabilistic framework, some of the most important aspects of soil behavior under cyclic loading can be captured even with a simple elastic-perfectly plastic constitutive model.

Keywords: Elasto-plasticity, uncertainty, soils, Fokker-Planck equation, Fourier Spectral method, Finite Difference method.

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120 Definable Subsets in Covering Approximation Spaces

Authors: Xun Ge, Zhaowen Li

Abstract:

Covering approximation spaces is a class of important generalization of approximation spaces. For a subset X of a covering approximation space (U, C), is X definable or rough? The answer of this question is uncertain, which depends on covering approximation operators endowed on (U, C). Note that there are many various covering approximation operators, which can be endowed on covering approximation spaces. This paper investigates covering approximation spaces endowed ten covering approximation operators respectively, and establishes some relations among definable subsets, inner definable subsets and outer definable subsets in covering approximation spaces, which deepens some results on definable subsets in approximation spaces.

Keywords: Covering approximation space, covering approximation operator, definable subset, inner definable subset, outer definable subset.

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119 Reachable Set Bounding Estimation for Distributed Delay Systems with Disturbances

Authors: Li Xu, Shouming Zhong

Abstract:

The reachable set bounding estimation for distributed delay systems with disturbances is a new problem. In this paper,we consider this problem subject to not only time varying delay and polytopic uncertainties but also distributed delay systems which is not studied fully untill now. we can obtain improved non-ellipsoidal reachable set estimation for neural networks with time-varying delay by the maximal Lyapunov-Krasovskii fuctional which is constructed as the pointwise maximum of a family of Lyapunov-Krasovskii fuctionals corresponds to vertexes of uncertain polytope.On the other hand,matrix inequalities containing only one scalar and Matlabs LMI Toolbox is utilized to give a non-ellipsoidal description of the reachable set.finally,numerical examples are given to illustrate the existing results.

Keywords: Reachable set, Distributed delay, Lyapunov-Krasovskii function, Polytopic uncertainties.

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118 Improving Sales through Inventory Reduction: A Retail Chain Case Study

Authors: M. G. Mattos, J. E. Pécora Jr, T. A. Briso

Abstract:

Today's challenging business environment, with unpredictable demand and volatility, requires a supply chain strategy that handles uncertainty and risks in the right way. Even though inventory models have been previously explored, this paper seeks to apply these concepts on a practical situation. This study involves the inventory replenishment problem, applying techniques that are mainly based on mathematical assumptions and modeling. The primary goal is to improve the retailer’s supply chain processes taking store differences when setting the various target stock levels. Through inventory review policy, picking piece implementation and minimum exposure definition, we were able not only to promote the inventory reduction as well as improve sales results. The inventory management theory from literature review was then tested on a single case study regarding a particular department in one of the largest Latam retail chains.

Keywords: Inventory, distribution, retail, risk, safety stock, sales, uncertainty.

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117 Reliability-Based Topology Optimization Based on Evolutionary Structural Optimization

Authors: Sang-Rak Kim, Jea-Yong Park, Won-Goo Lee, Jin-Shik Yu, Seog-Young Han

Abstract:

This paper presents a Reliability-Based Topology Optimization (RBTO) based on Evolutionary Structural Optimization (ESO). An actual design involves uncertain conditions such as material property, operational load and dimensional variation. Deterministic Topology Optimization (DTO) is obtained without considering of the uncertainties related to the uncertainty parameters. However, RBTO involves evaluation of probabilistic constraints, which can be done in two different ways, the reliability index approach (RIA) and the performance measure approach (PMA). Limit state function is approximated using Monte Carlo Simulation and Central Composite Design for reliability analysis. ESO, one of the topology optimization techniques, is adopted for topology optimization. Numerical examples are presented to compare the DTO with RBTO.

Keywords: Evolutionary Structural Optimization, PerformanceMeasure Approach, Reliability-Based Topology Optimization, Reliability Index Approach.

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116 Logistic Changeability - Application of a Methodological Framework for Designing Logistic Changeability

Authors: Sebastian Bertsch

Abstract:

In the past decades, the environment of production companies showed a permanent increase in dynamic and volatility in the form of demand fluctuations, new technologies or global crises. As a reaction to these new requirements, changeability of production systems came into attention. A changeable production system can adapt to these changes quickly and with little effort. Even though demand for changeable production exists for some time, the practical application is still insufficient.

To overcome this deficit, a three year research project at the Department of Production Systems and Logistics at the Leibniz University of Hanover/ Germany was initiated. As a result of this project, different concepts have been developed to design production changeable. An excerpt of the results will be presented in this paper. An eight step procedure will be presented to design the changeability of production logistics. This procedure has been applied at a German manufacturer of high demanding weighing machines. The developed procedure, their application in industry, as well as the major results of the application will be presented.

Keywords: Changeability, Change Drivers, Production Logistics.

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115 Constructing a Fuzzy Net Present Value Method to Evaluating the BOT Sport Facilities

Authors: Huei-Fu Lu

Abstract:

This paper is to develop a fuzzy net present value (FNPV) method by taking vague cash flow and imprecise required rate of return into account for evaluating the value of the Build-Operate-Transfer (BOT) sport facilities. In order to clearly manifest a more realistic capital budgeting model based on the classical net present value (NPV) method, some uncertain financial elements in NPV formula will be fuzzified as triangular fuzzy numbers. Through the conscientious manipulation of fuzzy set theory, we will find that the proposed FNPV model is a more explicit extension of classical (crisp) model and could be more practicable for the financial managers to capture the essence of capital budgeting of sport facilities than non-fuzzy model.

Keywords: Fuzzy sets; Capital budgeting, Sport facility, Net present value (NPV), Build-Operate-Transfer (BOT) scheme

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114 Using Adaptive Pole Placement Control Strategy for Active Steering Safety System

Authors: Hadi Adibi-Asl, Alireza Doosthosseini, Amir Taghavipour

Abstract:

This paper studies the design of an adaptive control strategy to tune an active steering system for better drivability and maneuverability. In the first step, adaptive control strategy is applied to estimate the uncertain parameters on-line (e.g. cornering stiffness), then the estimated parameters are fed into the pole placement controller to generate corrective feedback gain to improve the steering system dynamic’s characteristics. The simulations are evaluated for three types of road conditions (dry, wet, and icy), and the performance of the adaptive pole placement control (APPC) are compared with pole placement control (PPC) and a passive system. The results show that the APPC strategy significantly improves the yaw rate and side slip angle of a bicycle plant model.

Keywords: Adaptive control, active steering, pole placement, vehicle dynamics.

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113 Solid Waste Management in Steel Industry - Challenges and Opportunities

Authors: Sushovan Sarkar, Debabrata Mazumder

Abstract:

Solid waste management in steel industry is broadly classified in “4 Rs” i.e. reduce, reuse, recycle and restore the materials. Reuse and recycling the entire solid waste generated in the process of steel making is a viable solution in targeting a clean, green and zero waste technology leading to sustainable development of the steel industry. Solid waste management has gained importance in steel industry in view of its uncertainty, volatility and speculation due to world competitive standards, rising input costs, scarcity of raw materials and solid waste generated like in other sectors. The challenges that the steel Industry faces today are the requirement of a sustainable development by meeting the needs of our present generation without compromising the ability of future generations. Technologies are developed not only for gainful utilization of solid wastes in manufacture of conventional products but also for conversion of same in to completely new products.

Keywords: Reuse, recycle, solid waste, sustainable development.

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112 Using Fuzzy Numbers in Heavy Aggregation Operators

Authors: José M. Merigó, Montserrat Casanovas

Abstract:

We consider different types of aggregation operators such as the heavy ordered weighted averaging (HOWA) operator and the fuzzy ordered weighted averaging (FOWA) operator. We introduce a new extension of the OWA operator called the fuzzy heavy ordered weighted averaging (FHOWA) operator. The main characteristic of this aggregation operator is that it deals with uncertain information represented in the form of fuzzy numbers (FN) in the HOWA operator. We develop the basic concepts of this operator and study some of its properties. We also develop a wide range of families of FHOWA operators such as the fuzzy push up allocation, the fuzzy push down allocation, the fuzzy median allocation and the fuzzy uniform allocation.

Keywords: Aggregation operators, Fuzzy numbers, Fuzzy OWAoperator, Heavy OWA operator.

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111 A Single-Period Inventory Problem with Resalable Returns: A Fuzzy Stochastic Approach

Authors: Oshmita Dey, Debjani Chakraborty

Abstract:

In this paper, a single period inventory model with resalable returns has been analyzed in an imprecise and uncertain mixed environment. Demand has been introduced as a fuzzy random variable. In this model, a single order is placed before the start of the selling season. The customer, for a full refund, may return purchased products within a certain time interval. Returned products are resalable, provided they arrive back before the end of the selling season and are found to be undamaged. Products remaining at the end of the season are salvaged. All demands not met directly are lost. The probabilities that a sold product is returned and that a returned product is resalable, both imprecise in a real situation, have been assumed to be fuzzy in nature.

Keywords: Fuzzy random variable, Modified graded meanintegration, Internet mail order, Inventory.

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110 Managing, Sustaining, and Future Proofing the Business of Educational Provision Following Large-Scale Disaster and Disruption

Authors: Judy Yarwood, Lesley Seaton, Philippa Seaton

Abstract:

A catastrophic earthquake measuring 6.3 on the Richter scale struck the Christchurch, New Zealand Central Business District on February 22, 2012, abruptly disrupting the business of teaching and learning at Christchurch Polytechnic Institute of Technology. This paper presents the findings from a study undertaken about the complexity of delivering an educational programme in the face of this traumatic natural event. Nine interconnected themes emerged from this multiple method study: communication, decision making, leader- and follower-ship, balancing personal and professional responsibilities, taking action, preparedness and thinking ahead, all within a disruptive and uncertain context. Sustainable responses that maximise business continuity, and provide solutions to practical challenges, are among the study-s recommendations.

Keywords: Business continuity, earthquake, education, sustainability

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109 The Intuitionistic Fuzzy Ordered Weighted Averaging-Weighted Average Operator and its Application in Financial Decision Making

Authors: Shouzhen Zeng

Abstract:

We present a new intuitionistic fuzzy aggregation operator called the intuitionistic fuzzy ordered weighted averaging-weighted average (IFOWAWA) operator. The main advantage of the IFOWAWA operator is that it unifies the OWA operator with the WA in the same formulation considering the degree of importance that each concept has in the aggregation. Moreover, it is able to deal with an uncertain environment that can be assessed with intuitionistic fuzzy numbers. We study some of its main properties and we see that it has a lot of particular cases such as the intuitionistic fuzzy weighted average (IFWA) and the intuitionistic fuzzy OWA (IFOWA) operator. Finally, we study the applicability of the new approach on a financial decision making problem concerning the selection of financial strategies.

Keywords: Intuitionistic fuzzy numbers, Weighted average, OWA operator, Financial decision making

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108 FAT based Adaptive Impedance Control for Unknown Environment Position

Authors: N. Z. Azlan, H. Yamaura

Abstract:

This paper presents the Function Approximation Technique (FAT) based adaptive impedance control for a robotic finger. The force based impedance control is developed so that the robotic finger tracks the desired force while following the reference position trajectory, under unknown environment position and uncertainties in finger parameters. The control strategy is divided into two phases, which are the free and contact phases. Force error feedback is utilized in updating the uncertain environment position during contact phase. Computer simulations results are presented to demonstrate the effectiveness of the proposed technique.

Keywords: Adaptive impedance control, force based impedance control, force control, Function Approximation Technique (FAT), unknown environment position.

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107 Node Insertion in Coalescence Hidden-Variable Fractal Interpolation Surface

Authors: Srijanani Anurag Prasad

Abstract:

The Coalescence Hidden-variable Fractal Interpolation Surface (CHFIS) was built by combining interpolation data from the Iterated Function System (IFS). The interpolation data in a CHFIS comprise a row and/or column of uncertain values when a single point is entered. Alternatively, a row and/or column of additional points are placed in the given interpolation data to demonstrate the node added CHFIS. There are three techniques for inserting new points that correspond to the row and/or column of nodes inserted, and each method is further classified into four types based on the values of the inserted nodes. As a result, numerous forms of node insertion can be found in a CHFIS.

Keywords: Fractal, interpolation, iterated function system, coalescence, node insertion, knot insertion.

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