Search results for: Fuzzy integral.

Authors: R. Uthayakumar, D. Easwaramoorthy

Abstract:

This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we analyze some results on intuitionistic fuzzy fractals in the standard intuitionistic fuzzy metric spaces with respect to the Hausdorff intuitionistic fuzzy metrics.

Keywords: Fractal Analysis, Fixed Point, Contraction, Iterated Function System, Intuitionistic Fuzzy Metric Space.

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Authors: Amit Kumar, Anila Gupta, Amarpreet Kaur

Abstract:

In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy assignment problems by representing all the parameters as triangular fuzzy numbers. The advantages of the pro-posed method are also discussed. To illustrate the proposed method a fuzzy assignment problem is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy assignment problems occurring in real life situations.

Keywords: Fuzzy assignment problem, Ranking function, Triangular fuzzy numbers.

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Authors: Shaoquan Sun, Qianqian Li

Abstract:

Based on the theory of intuitionistic fuzzy sets, the concepts of intuitionistic fuzzy subalgebras with thresholds (λ, μ) and intuitionistic fuzzy ideals with thresholds (λ, μ) of BCI-algebras are introduced and some properties of them are discussed.

Keywords: BCI-algebra, intuitionistic fuzzy set, intuitionistic fuzzy subalgebra with thresholds (λ, μ), intuitionistic fuzzy ideal with thresholds (λ, μ).

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Authors: Amit Kumar, Manjot Kaur

Abstract:

In this paper, the fuzzy linear programming formulation of fuzzy maximal flow problems are proposed and on the basis of the proposed formulation a method is proposed to find the fuzzy optimal solution of fuzzy maximal flow problems. In the proposed method all the parameters are represented by triangular fuzzy numbers. By using the proposed method the fuzzy optimal solution of fuzzy maximal flow problems can be easily obtained. To illustrate the proposed method a numerical example is solved and the obtained results are discussed.

Keywords: Fuzzy linear programming, Fuzzy maximal flow problem, Ranking function, Triangular fuzzy number

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Authors: Liu Ping

Abstract:

In this paper, for an arbitrary multiplicative functional f from the set of all upper triangular fuzzy matrices to the fuzzy algebra, we prove that there exist a multiplicative functional F and a functional G from the fuzzy algebra to the fuzzy algebra such that the image of an upper triangular fuzzy matrix under f can be represented as the product of all the images of its main diagonal elements under F and other elements under G.

Keywords: Multiplicative functional, triangular fuzzy matrix, fuzzy addition operation, fuzzy multiplication operation.

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Authors: S.K. Sardar, D. Mandal, R. Mukherjee

Abstract:

The notions of intuitionistic fuzzy h-ideal and normal intuitionistic fuzzy h-ideal in Γ-hemiring are introduced and some of the basic properties of these ideals are investigated. Cartesian product of intuitionistic fuzzy h-ideals is also defined. Finally a characterization of intuitionistic fuzzy h-ideals in terms of fuzzy relations is obtained.

Keywords: Γ-hemiring, fuzzy h-ideal, normal, cartesian product.Mathematics Subject Classification[2000] :08A72, 16Y99

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Authors: Vassilis S. Kodogiannis, John N. Lygouras

Abstract:

In this research study, an intelligent detection system to support medical diagnosis and detection of abnormal lesions by processing endoscopic images is presented. The images used in this study have been obtained using the M2A Swallowable Imaging Capsule - a patented, video color-imaging disposable capsule. Schemes have been developed to extract texture features from the fuzzy texture spectra in the chromatic and achromatic domains for a selected region of interest from each color component histogram of endoscopic images. The implementation of an advanced fuzzy inference neural network which combines fuzzy systems and artificial neural networks and the concept of fusion of multiple classifiers dedicated to specific feature parameters have been also adopted in this paper. The achieved high detection accuracy of the proposed system has provided thus an indication that such intelligent schemes could be used as a supplementary diagnostic tool in endoscopy.

Keywords: Medical imaging, Computer aided diagnosis, Endoscopy, Neuro-fuzzy networks, Fuzzy integral.

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Authors: Phongsak Phakamach

Abstract:

A DC servomotor position control system using a Fuzzy Logic Sliding mode Model Following Control or FLSMFC approach is presented. The FLSMFC structure consists of an integrator and variable structure system. The integral control is introduced into it in order to eliminated steady state error due to step and ramp command inputs and improve control precision, while the fuzzy control would maintain the insensitivity to parameter variation and disturbances. The FLSMFC strategy is implemented and applied to a position control of a DC servomotor drives. Experimental results indicated that FLSMFC system performance with respect to the sensitivity to parameter variations is greatly reduced. Also, excellent control effects and avoids the chattering phenomenon.

Keywords: Sliding mode model following control, fuzzy logic, DC servomotor.

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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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Authors: Hidehiko Okada

Abstract:

The author proposes an extension of genetic algorithm (GA) for solving fuzzy-valued optimization problems. In the proposed GA, values in the genotypes are not real numbers but fuzzy numbers. Evolutionary processes in GA are extended so that GA can handle genotype instances with fuzzy numbers. The proposed method is applied to evolving neural networks with fuzzy weights and biases. Experimental results showed that fuzzy neural networks evolved by the fuzzy GA could model hidden target fuzzy functions well despite the fact that no training data was explicitly provided.

Keywords: Evolutionary algorithm, genetic algorithm, fuzzy number, neural network, neuroevolution.

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Authors: M. Hadi Mashinchi, M. Reza Mashinchi, Siti Mariyam H. J. Shamsuddin

Abstract:

In this paper a genetic algorithms approach for solving the linear and quadratic fuzzy equations Ãx̃=B̃ and Ãx̃² + B̃x̃=C̃ , where Ã, B̃, C̃ and x̃ are fuzzy numbers is proposed by genetic algorithms. Our genetic based method initially starts with a set of random fuzzy solutions. Then in each generation of genetic algorithms, the solution candidates converge more to better fuzzy solution x̃_b . In this proposed method the final reached x̃_b is not only restricted to fuzzy triangular and it can be fuzzy number.

Keywords: Fuzzy coefficient, fuzzy equation, genetic algorithms.

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Authors: Jian Tang

Abstract:

In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semigroups. Furthermore, we introduce the notion of semiprime fuzzy ideals of ordered semigroup S and establish the relations between completely semiprime fuzzy ideals and semiprime fuzzy ideals of S. Finally, we give a characterization of prime fuzzy ideals of an ordered semigroup S and show that a nonconstant fuzzy ideal f of an ordered semigroup S is prime if and only if f is twovalued, and max{f(a), f(b)} = inf f((aSb]), ∀a, b ∈ S.

Keywords: Ordered fuzzy point, fuzzy left (right) ideal of anordered semigroup, completely semiprime fuzzy ideal, semiprimefuzzy ideal, prime fuzzy ideal.

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Authors: Hadi Sadoghi Yazdi, Tahereh Royani, Mehri Sadoghi Yazdi, Sohrab Effati

Abstract:

In this paper, a new version of support vector regression (SVR) is presented namely Fuzzy Cost SVR (FCSVR). Individual property of the FCSVR is operation over fuzzy data whereas fuzzy cost (fuzzy margin and fuzzy penalty) are maximized. This idea admits to have uncertainty in the penalty and margin terms jointly. Robustness against noise is shown in the experimental results as a property of the proposed method and superiority relative conventional SVR.

Keywords: Support vector regression, Fuzzy input, Fuzzy cost.

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Authors: Kavikumar, Azme Khamis, Young Bae Jun,

Abstract:

The purpose of the present paper is to study the concept of fuzzy bi-ideals in ternary semirings. We give some characterizations of fuzzy bi-ideals. Characterizations of regular ternary semirings are provided.

Keywords: Fuzzy ternary subsemiring, fuzzy quasi-ideal, fuzzy bi-ideal, regular ternary semiring

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Authors: N.Subramanian, U.K.Misra

Abstract:

The aim of this paper is to introduce and study a new concept of strong double χ2 (M,A, Δ) of fuzzy numbers and also some properties of the resulting sequence spaces of fuzzy numbers were examined.

Keywords: Modulus function, fuzzy number, metric space.

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Authors: A. S. Issa, S. K. Q. AL-Omari

Abstract:

In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details.

Keywords: Fourier type integral, Fourier integral, generalized quotient, Boehmian, distribution.

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Authors: R. Uthayakumar, D. Easwaramoorthy

Abstract:

The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some recent results related with Hutchinson-Barnsley operator in the metric spaces to the intuitionistic fuzzy metric spaces.

Keywords: Contraction, Iterated Function System, Hutchinson- Barnsley Operator, Intuitionistic Fuzzy Metric Space, Hausdorff Intuitionistic Fuzzy Metric.

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Authors: P. C. Saxena, D. K. Tayal

Abstract:

The join dependency provides the basis for obtaining lossless join decomposition in a classical relational schema. The existence of Join dependency shows that that the tables always represent the correct data after being joined. Since the classical relational databases cannot handle imprecise data, they were extended to fuzzy relational databases so that uncertain, ambiguous, imprecise and partially known information can also be stored in databases in a formal way. However like classical databases, the fuzzy relational databases also undergoes decomposition during normalization, the issue of joining the decomposed fuzzy relations remains intact. Our effort in the present paper is to emphasize on this issue. In this paper we define fuzzy join dependency in the framework of type-1 fuzzy relational databases & type-2 fuzzy relational databases using the concept of fuzzy equality which is defined using fuzzy functions. We use the fuzzy equi-join operator for computing the fuzzy equality of two attribute values. We also discuss the dependency preservation property on execution of this fuzzy equi- join and derive the necessary condition for the fuzzy functional dependencies to be preserved on joining the decomposed fuzzy relations. We also derive the conditions for fuzzy join dependency to exist in context of both type-1 and type-2 fuzzy relational databases. We find that unlike the classical relational databases even the existence of a trivial join dependency does not ensure lossless join decomposition in type-2 fuzzy relational databases. Finally we derive the conditions for the fuzzy equality to be non zero and the qualification of an attribute for fuzzy key.

Keywords: Fuzzy - equi join, fuzzy functions, fuzzy join dependency, type-1 fuzzy relational database, type-2 fuzzy relational database.

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Authors: Yuli Hu, Shaoquan Sun

Abstract:

The aim of this paper is to introduce the concepts of (∈, ∈∨q)-fuzzy subalgebras, (∈,∈∨q)-fuzzy ideals and (∈,∈∨q)-fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.

Keywords: BCI-algebras with operators, (∈, ∈∨q)-fuzzy subalgebras, (∈, ∈∨q)-fuzzy ideals, (∈, ∈∨q)-fuzzy quotient algebras.

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Authors: T. Pathinathan, M. Peter

Abstract:

Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: Double layered fuzzy graph, double layered non-cyclic fuzzy graph, strong, order, degree and size.

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Authors: Yuli Hu, Shaoquan Sun

Abstract:

The aim of this paper is to introduce the concepts of generalized fuzzy subalgebras, generalized fuzzy ideals and generalized fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.

Keywords: BCI-algebras with operators, generalized fuzzy subalgebras, generalized fuzzy ideals, generalized fuzzy quotient algebras.

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Authors: Chen-Yuan Chen, Wan-I Lee, Yi-Chaio Sui, Cheng-Wu Chen

Abstract:

This study focuses on the development of triangular fuzzy numbers, the revising of triangular fuzzy numbers, and the constructing of a HCFN (half-circle fuzzy number) model which can be utilized to perform more plural operations. They are further transformed for trigonometric functions and polar coordinates. From half-circle fuzzy numbers we can conceive cylindrical fuzzy numbers, which work better in algebraic operations. An example of fuzzy control is given in a simulation to show the applicability of the proposed half-circle fuzzy numbers.

Keywords: triangular fuzzy number, half-circle fuzzy numbers, predictions, polar coordinates, Lyapunov method

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Authors: Shinoj T. K, Sunil Jacob John

Abstract:

In this paper a new concept named Intuitionistic Fuzzy Multiset is introduced. The basic operations on Intuitionistic Fuzzy Multisets such as union, intersection, addition, multiplication etc. are discussed. An application of Intuitionistic Fuzzy Multiset in Medical diagnosis problem using a distance function is discussed in detail.

Keywords: Intuitionistic Fuzzy set, Multiset, Intuitionistic Fuzzy Multiset

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Authors: D.R Prince Williams

Abstract:

In this paper,we introduce a notion of fuzzy ideals in near-subtraction semigroups and study their related properties.

Keywords: subtraction algebra, subtraction semigroup, an ideal, near-subtraction semigroup, fuzzy level set, fuzzy ideal, fuzzy homomorphism.

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Authors: R. Mechgoug, A. Titaouine

Abstract:

Fuzzy systems have been successfully used for exchange rate forecasting. However, fuzzy system is very confusing and complex to be designed by an expert, as there is a large set of parameters (fuzzy knowledge base) that must be selected, it is not a simple task to select the appropriate fuzzy knowledge base for an exchange rate forecasting. The researchers often look the effect of fuzzy knowledge base on the performances of fuzzy system forecasting. This paper proposes a genetic fuzzy predictor to forecast the future value of daily US Dollar/Euro exchange rate time’s series. A range of methodologies based on a set of fuzzy predictor’s which allow the forecasting of the same time series, but with a different fuzzy partition. Each fuzzy predictor is built from two stages, where each stage is performed by a real genetic algorithm.

Keywords: Foreign exchange rate, time series forecasting, Fuzzy System, and Genetic Algorithm.

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Authors: Zoheir Tir, Rachid Abdessemed

Abstract:

This paper presents a new control scheme to control a brushless doubly fed induction generator (BDFIG) using back-to-back PWM converters for wind power generation. The proposed control scheme is a New Self-Tuning Fuzzy Proportional-Derivative Controller (NSTFPDC). The goal of BDFIG control is to achieve a similar dynamic performance to the doubly fed induction generator (DFIG), exploiting the well-known induction machine vector control philosophy. The performance of NSTFPDC controller has been investigated and compared with the two controllers, called Proportional–Integral (PI) and PD-like Fuzzy Logic controller (PD-like FLC) based BDFIG. The simulation results demonstrate the effectiveness and the robustness of the NSTFPDC controller.

Keywords: Brushless Doubly Fed Induction Generator (BDFIG), PI controller, PD-like Fuzzy Logic controller, New Self-Tuning Fuzzy Proportional-Derivative Controller (NSTFPDC), Scaling factor, back-to-back PWM converters, wind energy system.

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Authors: Jolly Puri, Shiv Prasad Yadav

Abstract:

Multi-component data envelopment analysis (MC-DEA) is a popular technique for measuring aggregate performance of the decision making units (DMUs) along with their components. However, the conventional MC-DEA is limited to crisp input and output data which may not always be available in exact form. In real life problems, data may be imprecise or fuzzy. Therefore, in this paper, we propose (i) a fuzzy MC-DEA (FMC-DEA) model in which shared and undesirable fuzzy resources are incorporated, (ii) the proposed FMC-DEA model is transformed into a pair of crisp models using α cut approach, (iii) fuzzy aggregate performance of a DMU and fuzzy efficiencies of components are defined to be fuzzy numbers, and (iv) a numerical example is illustrated to validate the proposed approach.

Keywords: Multi-component DEA, fuzzy multi-component DEA, fuzzy resources.

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Authors: Sathinee Malee, Ronnason Chinram

Abstract:

The notion of k-fuzzy ideals of semirings was introduced by Kim and Park in 1996. In 2003, Dutta and Kar introduced a notion of ternary semirings. This structure is a generalization of ternary rings and semirings. The main purpose of this paper is to introduce and study k-fuzzy ideals in ternary semirings analogous to k-fuzzy ideals in semirings considered by Kim and Park.

Keywords: k-ideals, k-fuzzy ideals, fuzzy k-ideals, ternarysemirings

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Authors: Nasser Mohamed Ramli, Mohamad Syafiq Mohamad

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Many types of controllers were applied on the continuous stirred tank reactor (CSTR) unit to control the temperature. In this research paper, Proportional-Integral-Derivative (PID) controller are compared with Fuzzy Logic controller for temperature control of CSTR. The control system for temperature non-isothermal of a CSTR will produce a stable response curve to its set point temperature. A mathematical model of a CSTR using the most general operating condition was developed through a set of differential equations into S-function using MATLAB. The reactor model and S-function are developed using m.file. After developing the S-function of CSTR model, User-Defined functions are used to link to SIMULINK file. Results that are obtained from simulation and temperature control were better when using Fuzzy logic control compared to PID control.

Keywords: CSTR, temperature, PID, fuzzy logic.

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Authors: Om Parkash, C.P.Gandhi

Abstract:

In the literature of fuzzy measures, there exist many well known parametric and non-parametric measures, each with its own merits and limitations. But our main emphasis is on applications of these measures to a variety of disciplines. To extend the scope of applications of these fuzzy measures to geometry, we need some special fuzzy measures. In this communication, we have introduced two new fuzzy measures involving trigonometric functions and simultaneously provided their applications to obtain the basic results already existing in the literature of geometry.

Keywords: Entropy, Uncertainty, Fuzzy Entropy, Concavity, Symmetry.

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