Search results for: fuzzy multiplication operation.

Authors: M. Umabharathi, S. Vijayabaskar

Abstract:

Evolutionary Fuzzy PID Speed Controller for Permanent Magnet Synchronous Motor (PMSM) is developed to achieve the Speed control of PMSM in Closed Loop operation and to deal with the existence of transients. Consider a Fuzzy PID control design problem, based on common control Engineering Knowledge. If the transient error is big, that Good transient performance can be obtained by increasing the P and I gains and decreasing the D gains. To autotune the control parameters of the Fuzzy PID controller, the Evolutionary Algorithms (EA) are developed. EA based Fuzzy PID controller provides better speed control and guarantees the closed loop stability. The Evolutionary Fuzzy PID controller can be implemented in real time Applications without any concern about instabilities that leads to system failure or damage.

Keywords: Evolutionary Algorithm (EA), Fuzzy system, Genetic Algorithm (GA), Membership, Permanent Magnet Synchronous Motor (PMSM).

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Authors: Shaoquan Sun, Chunxiang Liu

Abstract:

In this paper, we extend the fuzzy subrings with operators to the (λ, μ)-fuzzy subrings with operators. And the concepts of the (λ, μ)-fuzzy subring with operators and (λ, μ)-fuzzy quotient ring with operators are gived, while their elementary properties are discussed.

Keywords: Fuzzy subring with operators, (λ, μ)-fuzzy subring with operators, (λ, μ)-fuzzy quotient ring with operators.

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Authors: Behrouz Fathi-Vajargah, Sara Ghasemalipour

Abstract:

This paper studies a random fuzzy queueing system that the interarrival times of customers arriving at the server and the service times are independent and identically distributed random fuzzy variables. We match the random fuzzy queueing system with the random fuzzy alternating renewal process and we do not use from α-pessimistic and α-optimistic values to estimate the average chance of the event ”random fuzzy queueing system is busy at time t”, we employ the fuzzy simulation method in practical applications. Some theorem is proved and finally we solve a numerical example with fuzzy simulation method.

Keywords: Random fuzzy variables, Fuzzy simulation, Queueing system, Interarrival times.

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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: Pilar Rey-del-Castillo, Jesús Cardeñosa

Abstract:

There are many situations where input feature vectors are incomplete and methods to tackle the problem have been studied for a long time. A commonly used procedure is to replace each missing value with an imputation. This paper presents a method to perform categorical missing data imputation from numerical and categorical variables. The imputations are based on Simpson-s fuzzy min-max neural networks where the input variables for learning and classification are just numerical. The proposed method extends the input to categorical variables by introducing new fuzzy sets, a new operation and a new architecture. The procedure is tested and compared with others using opinion poll data.

Keywords: Classifier, imputation techniques, fuzzy systems, fuzzy min-max neural networks.

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Authors: Aqeel S. Jaber, Abu Zaharin Ahmad, Ahmed N. Abdalla

Abstract:

The artificial intelligent controller in power system plays as most important rule for many applications such as system operation and its control specially Load Frequency Controller (LFC). The main objective of LFC is to keep the frequency and tie-line power close to their decidable bounds in case of disturbance. In this paper, parallel fuzzy PI adaptive with conventional PD technique for Load Frequency Control system was proposed. PSO optimization method used to optimize both of scale fuzzy PI and tuning of PD. Two equal interconnected power system areas were used as a test system. Simulation results show the effectiveness of the proposed controller compared with different PID and classical fuzzy PI controllers in terms of speed response and damping frequency.

Keywords: Load frequency control, PSO, fuzzy control.

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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: 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: 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: Ágnes Vathy-Fogarassy, Balázs Feil, János Abonyi

Abstract:

Most of fuzzy clustering algorithms have some discrepancies, e.g. they are not able to detect clusters with convex shapes, the number of the clusters should be a priori known, they suffer from numerical problems, like sensitiveness to the initialization, etc. This paper studies the synergistic combination of the hierarchical and graph theoretic minimal spanning tree based clustering algorithm with the partitional Gath-Geva fuzzy clustering algorithm. The aim of this hybridization is to increase the robustness and consistency of the clustering results and to decrease the number of the heuristically defined parameters of these algorithms to decrease the influence of the user on the clustering results. For the analysis of the resulted fuzzy clusters a new fuzzy similarity measure based tool has been presented. The calculated similarities of the clusters can be used for the hierarchical clustering of the resulted fuzzy clusters, which information is useful for cluster merging and for the visualization of the clustering results. As the examples used for the illustration of the operation of the new algorithm will show, the proposed algorithm can detect clusters from data with arbitrary shape and does not suffer from the numerical problems of the classical Gath-Geva fuzzy clustering algorithm.

Keywords: Clustering, fuzzy clustering, minimal spanning tree, cluster validity, fuzzy similarity.

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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. Tarafdar Haque, S. Najafi

Abstract:

Improving the reactive power and voltage profile of a distribution substation is investigated in this paper. The purpose is to properly determination of the shunt capacitors on/off status and suitable tap changer (TC) position of a substation transformer. In addition, the limitation of secondary bus voltage, the maximum allowable number of switching operation in a day for on load tap changer and on/off status of capacitors are taken into account. To achieve these goals, an artificial neural network (ANN) is designed to provide preliminary scheduling. Input of ANN is active and reactive powers of transformer and its primary and secondary bus voltages. The output of ANN is capacitors on/off status and TC position. The preliminary schedule is further refined by fuzzy dynamic programming in order to reach the final schedule. The operation of proposed method in Q/V improving is compared with the results obtained by operator operation in a distribution substation.

Keywords: Neuro-fuzzy, Dynamic programming, Reactive power, Voltage profile.

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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: 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: Amarunnishad T.M., Govindan V.K., Abraham T. Mathew

Abstract:

An image compression method has been developed using fuzzy edge image utilizing the basic Block Truncation Coding (BTC) algorithm. The fuzzy edge image has been validated with classical edge detectors on the basis of the results of the well-known Canny edge detector prior to applying to the proposed method. The bit plane generated by the conventional BTC method is replaced with the fuzzy bit plane generated by the logical OR operation between the fuzzy edge image and the corresponding conventional BTC bit plane. The input image is encoded with the block mean and standard deviation and the fuzzy bit plane. The proposed method has been tested with test images of 8 bits/pixel and size 512×512 and found to be superior with better Peak Signal to Noise Ratio (PSNR) when compared to the conventional BTC, and adaptive bit plane selection BTC (ABTC) methods. The raggedness and jagged appearance, and the ringing artifacts at sharp edges are greatly reduced in reconstructed images by the proposed method with the fuzzy bit plane.

Keywords: Image compression, Edge detection, Ground truth image, Peak signal to noise ratio

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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: 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: 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: 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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