Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1974

Search results for: membership functions

1974 A Fuzzy Nonlinear Regression Model for Interval Type-2 Fuzzy Sets

Authors: O. Poleshchuk, E. Komarov


This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: interval type-2 fuzzy sets, fuzzy regression, weighted interval

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1973 Defuzzification of Periodic Membership Function on Circular Coordinates

Authors: Takashi Mitsuishi, Koji Saigusa


This paper presents circular polar coordinates transformation of periodic fuzzy membership function. The purpose is identification of domain of periodic membership functions in consequent part of IF-THEN rules. The proposed methods are applied to the simple color construct system.

Keywords: periodic membership function, polar coordinates transformation, defuzzification, circular coordinates

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1972 A Different Approach to Optimize Fuzzy Membership Functions with Extended FIR Filter

Authors: Jun-Ho Chung, Sung-Hyun Yoo, In-Hwan Choi, Hyun-Kook Lee, Moon-Kyu Song, Choon-Ki Ahn


The extended finite impulse response (EFIR) filter is addressed to optimize membership functions (MFs) of the fuzzy model that has strong nonlinearity. MFs are important parts of the fuzzy logic system (FLS) and, thus optimizing MFs of FLS is one of approaches to improve the performance of output. We employ the EFIR as an alternative optimization option to nonlinear fuzzy model. The performance of EFIR is demonstrated on a fuzzy cruise control via a numerical example.

Keywords: fuzzy logic system, optimization, membership function, extended FIR filter

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1971 Design of Membership Ranges for Fuzzy Logic Control of Refrigeration Cycle Driven by a Variable Speed Compressor

Authors: Changho Han, Jaemin Lee, Li Hua, Seokkwon Jeong


Design of membership function ranges in fuzzy logic control (FLC) is presented for robust control of a variable speed refrigeration system (VSRS). The criterion values of the membership function ranges can be carried out from the static experimental data, and two different values are offered to compare control performance. Some simulations and real experiments for the VSRS were conducted to verify the validity of the designed membership functions. The experimental results showed good agreement with the simulation results, and the error change rate and its sampling time strongly affected the control performance at transient state of the VSRS.

Keywords: variable speed refrigeration system, fuzzy logic control, membership function range, control performance

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1970 An Observer-Based Direct Adaptive Fuzzy Sliding Control with Adjustable Membership Functions

Authors: Alireza Gholami, Amir H. D. Markazi


In this paper, an observer-based direct adaptive fuzzy sliding mode (OAFSM) algorithm is proposed. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. The input connection matrix is used to combine the sliding surfaces of individual subsystems, and an adaptive fuzzy algorithm is used to estimate an equivalent sliding mode control input directly. The fuzzy membership functions, which were determined by time consuming try and error processes in previous works, are adjusted by adaptive algorithms. The other advantage of the proposed controller is that the input gain matrix is not limited to be diagonal, i.e. the plant could be over/under actuated provided that controllability and observability are preserved. An observer is constructed to directly estimate the state tracking error, and the nonlinear part of the observer is constructed by an adaptive fuzzy algorithm. The main advantage of the proposed observer is that, the measured outputs is not limited to the first entry of a canonical-form state vector. The closed-loop stability of the proposed method is proved using a Lyapunov-based approach. The proposed method is applied numerically on a multi-link robot manipulator, which verifies the performance of the closed-loop control. Moreover, the performance of the proposed algorithm is compared with some conventional control algorithms.

Keywords: adaptive algorithm, fuzzy systems, membership functions, observer

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1969 Influence of Telkom Membership Card Customer Perceived Value on Retaining PT. Telkom Indonesia's Customer in 2013-2014

Authors: Eka Yuliana, Siska Shabrina Julyan


The competitive environment and high customer’s churn rate in telecommunication industries lead Indonesian telecommunication companies become strive to offer products with more value. Offering product with more value can encourage customers to keep using the companies product. One of way to retain customer is give a membership card to the customers as practiced by PT. Telkom by giving Telkom Membership Card to PT. Telkom loyal customer. This study aims to determine the influence of Telkom Membership Card customer perceived value on retaining PT. Telkom Indonesia’s customer in 2013-2014 by using quantitative method with causal study. Analythical technique used in this study is Structural Equation Modelling (SEM) to test the causal relationship with 216 owner of Telkom Membership Card in Indonesia. This study conclude that: (i) Customer perceived value on Telkom Membership Card is located in fair value zone, (ii) PT. Telkom efforts in order to retain the customers is classified as good, (iii) Customer perceived value is influencing the effort to retain the customer with the probability value less than 0.05 and level of influence 69%. Based on result of this study, PT. Telkom should (i) Improve Telkom Membership Card’s promotion because not all customer of PT. Telkom have the membership card. (iia) Adding Telkom Membership Card’s benefit such as discount at various merchant (iib) Making call center for member of Telkom Membership Card (iii) PT. Telkom should be ensure availability of their service. (iv) PT. Telkom should make a priority to customer who have telkom membership card and offers a better service.For future research should be use different variables.

Keywords: customer perceived value, customer retention, marketing, relationship marketing

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1968 Membership Surface and Arithmetic Operations of Imprecise Matrix

Authors: Dhruba Das


In this paper, a method has been developed to construct the membership surfaces of row and column vectors and arithmetic operations of imprecise matrix. A matrix with imprecise elements would be called an imprecise matrix. The membership surface of imprecise vector has been already shown based on Randomness-Impreciseness Consistency Principle. The Randomness- Impreciseness Consistency Principle leads to defining a normal law of impreciseness using two different laws of randomness. In this paper, the author has shown row and column membership surfaces and arithmetic operations of imprecise matrix and demonstrated with the help of numerical example.

Keywords: imprecise number, imprecise vector, membership surface, imprecise matrix

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1967 A New Concept for Deriving the Expected Value of Fuzzy Random Variables

Authors: Liang-Hsuan Chen, Chia-Jung Chang


Fuzzy random variables have been introduced as an imprecise concept of numeric values for characterizing the imprecise knowledge. The descriptive parameters can be used to describe the primary features of a set of fuzzy random observations. In fuzzy environments, the expected values are usually represented as fuzzy-valued, interval-valued or numeric-valued descriptive parameters using various metrics. Instead of the concept of area metric that is usually adopted in the relevant studies, the numeric expected value is proposed by the concept of distance metric in this study based on two characters (fuzziness and randomness) of FRVs. Comparing with the existing measures, although the results show that the proposed numeric expected value is same with those using the different metric, if only triangular membership functions are used. However, the proposed approach has the advantages of intuitiveness and computational efficiency, when the membership functions are not triangular types. An example with three datasets is provided for verifying the proposed approach.

Keywords: fuzzy random variables, distance measure, expected value, descriptive parameters

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1966 Similarity Based Membership of Elements to Uncertain Concept in Information System

Authors: M. Kamel El-Sayed


The process of determining the degree of membership for an element to an uncertain concept has been found in many ways, using equivalence and symmetry relations in information systems. In the case of similarity, these methods did not take into account the degree of symmetry between elements. In this paper, we use a new definition for finding the membership based on the degree of symmetry. We provide an example to clarify the suggested methods and compare it with previous methods. This method opens the door to more accurate decisions in information systems.

Keywords: information system, uncertain concept, membership function, similarity relation, degree of similarity

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1965 Imprecise Vector: The Case of Subnormality

Authors: Dhruba Das


In this article, the author has put forward the actual mathematical explanation of subnormal imprecise vector. Every subnormal imprecise vector has to be defined with reference to a membership surface. The membership surface of normal imprecise vector has already defined based on Randomness-Impreciseness Consistency Principle. The Randomness- Impreciseness Consistency Principle leads to defining a normal law of impreciseness using two different laws of randomness. A normal imprecise vector is a special case of subnormal imprecise vector. Nothing however is available in the literature about the membership surface when a subnormal imprecise vector is defined. The author has shown here how to construct the membership surface of a subnormal imprecise vector.

Keywords: imprecise vector, membership surface, subnormal imprecise number, subnormal imprecise vector

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1964 Development of a Fuzzy Logic Based Model for Monitoring Child Pornography

Authors: Mariam Ismail, Kazeem Rufai, Jeremiah Balogun


A study was conducted to apply fuzzy logic to the development of a monitoring model for child pornography based on associated risk factors, which can be used by forensic experts or integrated into forensic systems for the early detection of child pornographic activities. A number of methods were adopted in the study, which includes an extensive review of related works was done in order to identify the factors that are associated with child pornography following which they were validated by an expert sex psychologist and guidance counselor, and relevant data was collected. Fuzzy membership functions were used to fuzzify the associated variables identified alongside the risk of the occurrence of child pornography based on the inference rules that were provided by the experts consulted, and the fuzzy logic expert system was simulated using the Fuzzy Logic Toolbox available in the MATLAB Software Release 2016. The results of the study showed that there were 4 categories of risk factors required for assessing the risk of a suspect committing child pornography offenses. The results of the study showed that 2 and 3 triangular membership functions were used to formulate the risk factors based on the 2 and 3 number of labels assigned, respectively. The results of the study showed that 5 fuzzy logic models were formulated such that the first 4 was used to assess the impact of each category on child pornography while the last one takes the 4 outputs from the 4 fuzzy logic models as inputs required for assessing the risk of child pornography. The following conclusion was made; there were factors that were related to personal traits, social traits, history of child pornography crimes, and self-regulatory deficiency traits by the suspects required for the assessment of the risk of child pornography crimes committed by a suspect. Using the values of the identified risk factors selected for this study, the risk of child pornography can be easily assessed from their values in order to determine the likelihood of a suspect perpetuating the crime.

Keywords: fuzzy, membership functions, pornography, risk factors

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1963 Transformation of Periodic Fuzzy Membership Function to Discrete Polygon on Circular Polar Coordinates

Authors: Takashi Mitsuishi


Fuzzy logic has gained acceptance in the recent years in the fields of social sciences and humanities such as psychology and linguistics because it can manage the fuzziness of words and human subjectivity in a logical manner. However, the major field of application of the fuzzy logic is control engineering as it is a part of the set theory and mathematical logic. Mamdani method, which is the most popular technique for approximate reasoning in the field of fuzzy control, is one of the ways to numerically represent the control afforded by human language and sensitivity and has been applied in various practical control plants. Fuzzy logic has been gradually developing as an artificial intelligence in different applications such as neural networks, expert systems, and operations research. The objects of inference vary for different application fields. Some of these include time, angle, color, symptom and medical condition whose fuzzy membership function is a periodic function. In the defuzzification stage, the domain of the membership function should be unique to obtain uniqueness its defuzzified value. However, if the domain of the periodic membership function is determined as unique, an unintuitive defuzzified value may be obtained as the inference result using the center of gravity method. Therefore, the authors propose a method of circular-polar-coordinates transformation and defuzzification of the periodic membership functions in this study. The transformation to circular polar coordinates simplifies the domain of the periodic membership function. Defuzzified value in circular polar coordinates is an argument. Furthermore, it is required that the argument is calculated from a closed plane figure which is a periodic membership function on the circular polar coordinates. If the closed plane figure is continuous with the continuity of the membership function, a significant amount of computation is required. Therefore, to simplify the practice example and significantly reduce the computational complexity, we have discretized the continuous interval and the membership function in this study. In this study, the following three methods are proposed to decide the argument from the discrete polygon which the continuous plane figure is transformed into. The first method provides an argument of a straight line passing through the origin and through the coordinate of the arithmetic mean of each coordinate of the polygon (physical center of gravity). The second one provides an argument of a straight line passing through the origin and the coordinate of the geometric center of gravity of the polygon. The third one provides an argument of a straight line passing through the origin bisecting the perimeter of the polygon (or the closed continuous plane figure).

Keywords: defuzzification, fuzzy membership function, periodic function, polar coordinates transformation

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1962 Electrical Load Estimation Using Estimated Fuzzy Linear Parameters

Authors: Bader Alkandari, Jamal Y. Madouh, Ahmad M. Alkandari, Anwar A. Alnaqi


A new formulation of fuzzy linear estimation problem is presented. It is formulated as a linear programming problem. The objective is to minimize the spread of the data points, taking into consideration the type of the membership function of the fuzzy parameters to satisfy the constraints on each measurement point and to insure that the original membership is included in the estimated membership. Different models are developed for a fuzzy triangular membership. The proposed models are applied to different examples from the area of fuzzy linear regression and finally to different examples for estimating the electrical load on a busbar. It had been found that the proposed technique is more suited for electrical load estimation, since the nature of the load is characterized by the uncertainty and vagueness.

Keywords: fuzzy regression, load estimation, fuzzy linear parameters, electrical load estimation

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1961 A New Aggregation Operator for Trapezoidal Fuzzy Numbers Based On the Geometric Means of the Left and Right Line Slopes

Authors: Manju Pandey, Nilay Khare, S. C. Shrivastava


This paper is the final in a series, which has defined two new classes of aggregation operators for triangular and trapezoidal fuzzy numbers based on the geometrical characteristics of their fuzzy membership functions. In the present paper, a new aggregation operator for trapezoidal fuzzy numbers has been defined. The new operator is based on the geometric mean of the membership lines to the left and right of the maximum possibility interval. The operator is defined and the analytical relationships have been derived. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates as well as results from the recent work of the authors on TrFN aggregates have also been computed.

Keywords: LR fuzzy number, interval fuzzy number, triangular fuzzy number, trapezoidal fuzzy number, apex angle, left apex angle, right apex angle, aggregation operator, arithmetic and geometric mean

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1960 The Behavior of The Zeros of Bargmann Analytic Functions for Multiple-Mode Systems

Authors: Muna Tabuni


The paper contains an investigation of the behavior of the Zeros of Bargmann functions for one and two-mode systems. A brief introduction to Harmonic oscillator formalism for one and two-mode is given. The Bargmann analytic representation for one and two-mode has been studied. The zeros of Bargmann analytic function for one-mode are considered. The Q Husimi functions are introduced. The Bargmann functions and the Husimi functions have the same zeros. The Bargmann functions f(z) have exactly q zeros. The evolution time of the zeros are discussed. The zeros of Bargmann analytic functions for two-mode are introduced. Various examples have been given.

Keywords: Bargmann functions, two-mode, zeros, harmonic oscillator

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1959 Some Inequalities Related with Starlike Log-Harmonic Mappings

Authors: Melike Aydoğan, Dürdane Öztürk


Let H(D) be the linear space of all analytic functions defined on the open unit disc. A log-harmonic mappings is a solution of the nonlinear elliptic partial differential equation where w(z) ∈ H(D) is second dilatation such that |w(z)| < 1 for all z ∈ D. The aim of this paper is to define some inequalities of starlike logharmonic functions of order α(0 ≤ α ≤ 1).

Keywords: starlike log-harmonic functions, univalent functions, distortion theorem

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1958 A Methodology of Using Fuzzy Logics and Data Analytics to Estimate the Life Cycle Indicators of Solar Photovoltaics

Authors: Thor Alexis Sazon, Alexander Guzman-Urbina, Yasuhiro Fukushima


This study outlines the method of how to develop a surrogate life cycle model based on fuzzy logic using three fuzzy inference methods: (1) the conventional Fuzzy Inference System (FIS), (2) the hybrid system of Data Analytics and Fuzzy Inference (DAFIS), which uses data clustering for defining the membership functions, and (3) the Adaptive-Neuro Fuzzy Inference System (ANFIS), a combination of fuzzy inference and artificial neural network. These methods were demonstrated with a case study where the Global Warming Potential (GWP) and the Levelized Cost of Energy (LCOE) of solar photovoltaic (PV) were estimated using Solar Irradiation, Module Efficiency, and Performance Ratio as inputs. The effects of using different fuzzy inference types, either Sugeno- or Mamdani-type, and of changing the number of input membership functions to the error between the calibration data and the model-generated outputs were also illustrated. The solution spaces of the three methods were consequently examined with a sensitivity analysis. ANFIS exhibited the lowest error while DAFIS gave slightly lower errors compared to FIS. Increasing the number of input membership functions helped with error reduction in some cases but, at times, resulted in the opposite. Sugeno-type models gave errors that are slightly lower than those of the Mamdani-type. While ANFIS is superior in terms of error minimization, it could generate solutions that are questionable, i.e. the negative GWP values of the Solar PV system when the inputs were all at the upper end of their range. This shows that the applicability of the ANFIS models highly depends on the range of cases at which it was calibrated. FIS and DAFIS generated more intuitive trends in the sensitivity runs. DAFIS demonstrated an optimal design point wherein increasing the input values does not improve the GWP and LCOE anymore. In the absence of data that could be used for calibration, conventional FIS presents a knowledge-based model that could be used for prediction. In the PV case study, conventional FIS generated errors that are just slightly higher than those of DAFIS. The inherent complexity of a Life Cycle study often hinders its widespread use in the industry and policy-making sectors. While the methodology does not guarantee a more accurate result compared to those generated by the Life Cycle Methodology, it does provide a relatively simpler way of generating knowledge- and data-based estimates that could be used during the initial design of a system.

Keywords: solar photovoltaic, fuzzy logic, inference system, artificial neural networks

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1957 RAFU Functions in Robotics and Automation

Authors: Alicia C. Sanchez


This paper investigates the implementation of RAFU functions (radical functions) in robotics and automation. Specifically, the main goal is to show how these functions may be useful in lane-keeping control and the lateral control of autonomous machines, vehicles, robots or the like. From the knowledge of several points of a certain route, the RAFU functions are used to achieve the lateral control purpose and maintain the lane-keeping errors within the fixed limits. The stability that these functions provide, their ease of approaching any continuous trajectory and the control of the possible error made on the approximation may be useful in practice.

Keywords: automatic navigation control, lateral control, lane-keeping control, RAFU approximation

Procedia PDF Downloads 41
1956 Subclasses of Bi-Univalent Functions Associated with Hohlov Operator

Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng


The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Keywords: analytic functions, bi-univalent functions, Hohlov operator, subordination

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1955 Prospect Theory and Activation Functions

Authors: Harpreet S. Bedi


This paper builds a correspondence between the theory of behavioral economics and the theory of artificial neural networks. The connection between these two disparate branches of knowledge is concretely constructed by designing a dictionary between prospect theory and artificial neural networks. More specifically, the activation functions in neural networks can be converted to probability weighting functions in prospect theory and vice versa. This approach leads to infinitely many activation functions and allows for their psychological interpretation in terms of risk-seeking and risk-averse behavior.

Keywords: artificial neural networks, activation functions, prospect theory, probability weighting functions

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1954 Geometric Properties of Some q-Bessel Functions

Authors: İbrahim Aktaş, Árpád Baricz


In this paper, the radii of star likeness of the Jackson and Hahn-Exton q-Bessel functions are considered, and for each of them three different normalizations is applied. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower, and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.

Keywords: bessel function, lommel function, radius of starlikeness and convexity, Struve function

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1953 Approximation of Analytic Functions of Several Variables by Linear K-Positive Operators in the Closed Domain

Authors: Tulin Coskun


We investigate the approximation of analytic functions of several variables in polydisc by the sequences of linear k-positive operators in Gadjiev sence. The approximation of analytic functions of complex variable by linear k-positive operators was tackled, and k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc were introduced in the past. Recently, very general results on convergence of the sequences of linear k-positive operators on a simply connected bounded domain within the space of analytic functions were proved. In this presentation, we extend some of these results to the approximation of analytic functions of several complex variables by sequences of linear k-positive operators.

Keywords: analytic functions, approximation of analytic functions, Linear k-positive operators, Korovkin type theorems

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1952 Unconventional Calculus Spreadsheet Functions

Authors: Chahid K. Ghaddar


The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: calculus, differential algebraic equations, solvers, spreadsheet

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1951 Study on Optimal Control Strategy of PM2.5 in Wuhan, China

Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun


In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

Keywords: grey relational degree, multiple linear regression, membership function, nonlinear programming

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1950 Artificial Intelligent Methodology for Liquid Propellant Engine Design Optimization

Authors: Hassan Naseh, Javad Roozgard


This paper represents the methodology based on Artificial Intelligent (AI) applied to Liquid Propellant Engine (LPE) optimization. The AI methodology utilized from Adaptive neural Fuzzy Inference System (ANFIS). In this methodology, the optimum objective function means to achieve maximum performance (specific impulse). The independent design variables in ANFIS modeling are combustion chamber pressure and temperature and oxidizer to fuel ratio and output of this modeling are specific impulse that can be applied with other objective functions in LPE design optimization. To this end, the LPE’s parameter has been modeled in ANFIS methodology based on generating fuzzy inference system structure by using grid partitioning, subtractive clustering and Fuzzy C-Means (FCM) clustering for both inferences (Mamdani and Sugeno) and various types of membership functions. The final comparing optimization results shown accuracy and processing run time of the Gaussian ANFIS Methodology between all methods.

Keywords: ANFIS methodology, artificial intelligent, liquid propellant engine, optimization

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1949 Fuzzy Control and Pertinence Functions

Authors: Luiz F. J. Maia


This paper presents an approach to fuzzy control, with the use of new pertinence functions, applied in the case of an inverted pendulum. Appropriate definitions of pertinence functions to fuzzy sets make possible the implementation of the controller with only one control rule, resulting in a smooth control surface. The fuzzy control system can be implemented with analog devices, affording a true real-time performance.

Keywords: control surface, fuzzy control, Inverted pendulum, pertinence functions

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1948 A New Approach for Generalized First Derivative of Nonsmooth Functions Using Optimization

Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor


In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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1947 Complex Fuzzy Evolution Equation with Nonlocal Conditions

Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli


The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups

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1946 Multi-Cluster Overlapping K-Means Extension Algorithm (MCOKE)

Authors: Said Baadel, Fadi Thabtah, Joan Lu


Clustering involves the partitioning of n objects into k clusters. Many clustering algorithms use hard-partitioning techniques where each object is assigned to one cluster. In this paper, we propose an overlapping algorithm MCOKE which allows objects to belong to one or more clusters. The algorithm is different from fuzzy clustering techniques because objects that overlap are assigned a membership value of 1 (one) as opposed to a fuzzy membership degree. The algorithm is also different from other overlapping algorithms that require a similarity threshold to be defined as a priority which can be difficult to determine by novice users.

Keywords: data mining, k-means, MCOKE, overlapping

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1945 Numerical Solution for Integro-Differential Equations by Using Quartic B-Spline Wavelet and Operational Matrices

Authors: Khosrow Maleknejad, Yaser Rostami


In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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