Fuzzy Vector Research Articles

A Novel Weak Fuzzy Solution for Fuzzy Linear System

This article proposes a novel weak fuzzy solution for the fuzzy linear system. As a matter of fact, we define the right-hand side column of the fuzzy linear system as a piecewise fuzzy function to overcome the related shortcoming, which exists in the previous findings. The strong point of this proposal is that the weak fuzzy solution is always a fuzzy number vector. Two complex and non-complex linear systems under uncertainty are tested to validate the effectiveness and correctness of the presented method.

Fuzzy multivariate process capability vector

Process capability indices are numerical measures used to determine whether the process products meet the quality requirement dedicated by the customers and producers or not. When the products' quality counts on two or more correlated characteristics, multivariate process capability indices are applied. In this paper, we focus on two indices proposed by Shahriari and Abdollahzadeh (2009) and Taam et al. (1993). The traditional multivariate capability indices can't be applied if the specification limits and target value of each characteristic are presented in a linguistic form. Instead, the fuzzy set theory is used to deal with these circumstances. Here, the fuzzy formulations of the indices are developed. Furthermore, numerical examples are presented to illustrate the applicability of the proposed methods and we make a comparison between them.

A Set Covering-Based Diagnostic Expert System to Economic and Financial Applications

This paper considers the identification of problems which generate anomalies at firms through the observed symptoms on the basis of fuzzy relations and Zadeh's compositional rule of inference. A procedure for determining the fuzzy cause vector of an economic and financial diagnosis problem is proposed, which consists of the design of fuzzy relational matrix and the resolution of a system of fuzzy relational equations. An efficient algorithm for solving fuzzy relational equations in terms of the associated set covering problem is introduced. It utilizes a back-tracking method to generate each minimal covering, where no duplicate or non-minimal coverings exist. A numerical example of firms' insolvency causes diagnosis is also included.

Higher order multivariate Markov chain model for fuzzy time series

Time series analysis is often related with the discovery of patterns and prediction of features. In this paper, multivariate Markov model in fuzzy time series method to allow multi factor forecasting problem is proposed. An attempt is made to forecast global surface temperature with presence of CO2 emission. The computation is carried out using fuzzy sets and transition probability vectors. A time series model has been determined by applying Fuzzy logic. Reliability of the randomness of the forecast values have been studied by imple- menting random number simulation technique. Numerical computations have been carried out in support of theoretical findings.

Fuzzy fault-tolerant-predictive control for a class of nonlinear uncertain systems

ABSTRACTIn this paper, a fault-tolerant fuzzy model-predictive control with the integral action method for a class of nonlinear uncertain systems is proposed. Nonlinear uncertain systems subject to actuators and/or sensors faults are represented by the Takagi–Sugeno (T-S) fuzzy model. The objective is to design a stable, robust and efficient fault-tolerant controller based on a T-S fuzzy observer with measurable premise variables. The proposed T-S fuzzy observer estimates state vector and faults. Based on Lyapunov theory, the trajectory tracking performances and the closed-loop system stability are analysed. The gains of the fuzzy observer and the pre-stabilized control law are obtained by solving linear matrix inequalities. Simulation results illustrate the robustness of the proposed controller with respect to uncertainties on an academic mathematical system.

Enhanced Fuzzy Rule with Modified Particle Swarm Optimization Based Handoff Algorithm in Wireless Mobile Communication Network

In wireless communication handoff plays a pivotal role. It is responsible for providing seamless communication between Base Stations (BSs) while user progresses from one cell to another cell. An exact handoff decisionis very hard because at the cell boundary Mobile Terminal (MT) understandings signal from serving BS as well as from neighboring BSs. In this situation MT fluctuates between BSs because of which unnecessary handoffs occur and degrade the signal excellence, which is not acceptable. As an attempt in this way, an Enhanced Fuzzy Rule (EFR) based controller is developed in this paper to reduce the number of unnecessary handoffs. Here, some parameters are considered such as Power Level, Bandwidth, and Cost along with the velocity of the Mobile Terminal (MT) are considered here for the design of the Handoff algorithm. The Membership Functions (MFs) for each of the parameter are determined and corresponding Membership Degrees are evaluated from their concerned MFs. The optimized fuzzification of the parameters is carried out by developing the appropriate weight vector. The weight vector is optimized using Modified Particle Swarm Optimization (MPSO) algorithm. Experimental results show that the proposed algorithms attained best performance compared to existing Thresholded RSS algorithm, fuzzy vertical handoff decision vector.

The Study on the (<i>L,M</i>)-Fuzzy Independent Set Systems

Independent sets play an important role in matroid theory. In this paper, the definitions of pre-independent fuzzy set system and independent fuzzy set system in L-fuzzy setting are presented. Independent M-fuzzifying set system is introduced and some of its properties are discussed. Further independent (L,M)-fuzzy set system is given and some of its properties are obtained. The relations of these independent set systems in the setting of fuzzy vector spaces and fuzzy graphs are showed.

Minimal Solution of Complex Fuzzy Linear Systems

This paper investigates the complex fuzzy linear equation Cz~=w~ in which C is a crisp complex matrix and w~ is an arbitrary LR complex fuzzy vector. The complex fuzzy linear system is converted to equivalent high order fuzzy linear system Gx~=b~. A new numerical procedure for calculating the complex fuzzy solution is designed and a sufficient condition for the existence of strong complex fuzzy solution is derived in detail. Some examples are given to illustrate the proposed method.

Design and real time implementation of type-2 fuzzy vector control for DFIG based wind generators

Doubly fed induction generator is very sensitive to voltage variations in the grid, which pose limitation for wind power plants during the grid integrated operation. Handling the uncertainity in wind speed and grid faults is a major challenge to fulfill the modern grid code requirements. This paper proposes a new control strategy for Rotor side converter using Interval type-2 fuzzy sets which can model and handle uncertainties in the system parameters. The presence of third dimension in the membership function, offers an additional degree of freedom in the design of the controller to counter the effects of fluctuations in wind speed and low voltage during severe grid fault conditions. A 2 MW DFIG connected to the grid is modelled in simulation software RSCAD and interfaced with Real time digital simulator (RTDS) to perform the simulations in real-time. The RTDS platform is considered by many research laboratories as real-time testing module for controller prototyping and also for hardware in the loop (HIL) applications. The controller performance is evaluated in HIL configuration, by performing the real-time simulations under various parameter uncertainties. The proposed controller can improve the low voltage ride through capability of DFIG compared to that of PI and type-1 fuzzy controller.

Research on the Multiple Attribute Decision Making Model of Intelligent Information Processing with Intuitionistic Fuzzy Information

In this paper, we shall investigate the multiple attribute decision making model of intelligent information pro- cessing with intuitionistic fuzzy information. Firstly, it introduces the concept of intuitionistic fuzzy sets and fuzzy num- ber directly and sorting method, and the concept of intuitionistic fuzzy vector product. Secondly, puts forward the intui- tionistic fuzzy set method of intuitionistic fuzzy transform, the Multiple Attribute Decision Making Model of Intelligent Information Processing with Intuitionistic Fuzzy Information. Finally, take soccer robot motion control as intelligent in- formation processing example, sets up intelligent multiple attribute decision making model processing Intuitionistic Fuzzy Information with the fuzzy matrix, to study the feasibility of the application model in the real environment.

M-Preconditioner for Solving Fuzzy Linear Systems

An M-preconditioner is provided for solving fuzzy linear systems whose coefficient matrices are crisp M-matrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the M-preconditioned conjugate gradient (MPCG) method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

Theory of Fuzzy Sets: Construction of Membership Surfaces of Normal Fuzzy Vectors

Fuzzy vectors have been studied almost since the beginning of the theory of fuzzy sets. However, just as a fuzzy number has to be defined with reference to a membership function, every fuzzy vector too has to be defined with reference to a membership surface. Nothing however is available in the literature about the membership surface when a fuzzy vector is defined. In this article, using the Randomness-Fuzziness Consistency Principle, it would be shown how to construct the membership surface of a normal fuzzy vector.

English

In this paper, a two-stage fuzzy random programming for a management problem in terms of water resources allocation having fuzzy random variable coefficients and decision vector of random variables is studied. The first results show the fact that a fuzzy pseudorandom optimal solution of a two-stage fuzzy random programming may be resolved into a two of pseudorandom optimal solutions of relative two-stage random programmings. The subsequent results present a method that a fuzzy pseudorandom optimal solution of two-stage fuzzy random programming is structured by a two of pseudorandom optimal solutions of a relative two two-stage random programmings. A numerical example was given to clarify the obtained results. Key words: Two-stage programming, fuzzy parameters, water resources management, interval analysis, fuzzy random variable, fuzzy approach

Solutions of fuzzy LR algebraic linear systems using linear programs

Using linear programs, we give the necessary and sufficient conditions for the solvability of a fuzzy LR algebraic linear system. Fuzzy LR algebraic linear systems are linear systems with LR fuzzy coefficient matrix and an LR fuzzy vector as the right-hand side. We consider an approximate solution when the fuzzy LR algebraic linear system lacks a solution. Also, we propose a linear programming problem to compute a solution or an approximate solution of a fuzzy LR algebraic linear system. Finally, by numerical examples, we show the suitability of our proposed approximate solution in comparison with another proposed approximate solution.

Bounded and Semi Bounded Inverse Theorems in Fuzzy Normed Spaces

In this paper, the author introduces the notion of the complete fuzzy norm on a linear space. And the author considers some relations between the fuzzy completeness and ordinary completeness on a linear space, moreover a new form of fuzzy compact spaces, namely b-compact spaces, b-closed space is introduced. Some characterization of their properties is obtained. Also some basic properties for linear operators between fuzzy normed spaces are further studied. The notions of fuzzy vector spaces and fuzzy topological vector spaces were introduced in Katsaras and Liu (1977). These ideas were modified by Katsaras (1981), and in (1984) Katsaras defined the fuzzy norm on a vector space. In (1991) Krishna and Sarma discussed the generation of a fuzzy vector topology from an ordinary vector topology on vector spaces. Also Krishna and Sarma (1992) observed the convergence of sequence of fuzzy points. Rhie et al. (1997) Introduced the notion of fuzzy a-Cauchy sequence of fuzzy points and fuzzy completeness.

Generalized convexity in fuzzy vector optimization through a linear ordering

In this article we study efficiency and weakly efficiency in fuzzy vector optimization. After formulating the problem, we introduce two new concepts of generalized convexity for fuzzy vector mappings based on the generalized Hukuhara differentiability, pseudoinvexity-I and pseudoinvexity-II. We prove that pseudoinvexity is the necessary and sufficient condition for a stationary point to be a solution of a fuzzy vector optimization problem. We give conditions to insure that a fuzzy vector mapping is invex and pseudoinvex (I and II). Moreover, we present some examples to illustrate the results. Lastly, we use these results to study the class of problems which have uncertainty and inaccuracies in the objective function coefficients of mathematical programming models.

FUZZY VECTOR EQUILIBRIUM PROBLEM

In the present paper, we introduce and study a fuzzy vector equi- librium problem and prove some existence results with and without convexity assumptions by using some particular forms of results of Kim and Lee (W.K. Kim and K.H. Lee, Generalized fuzzy games and fuzzy equilibria, Fuzzy Sets and Systems, 122 (2001), 293-301) and Tarafdar (E. Tarafdar, Fixed point theorems in H-spaces and equilibrium points of abstract economies, J. Aust. Math. Soc.(Series A), 53(1992), 252-260). An example is also constructed in support of fuzzy vector equilibrium problem.

A novel approach to streamline RE process for multi-agent systems

The intensification of ubiquitous computing has revitalised distributed multi-agent systems. Business and product requirements often change as development proceeds, making a straight-line path to requirement engineering (RE) impracticable. To cope up with the adaptability in the requirements, this work offers a novel evolutionary approach to revolutionise RE process for MAS. The proposed framework bridges the gap between users and developers by facilitating user-oriented view using user story cards and developer-oriented view using agent cards. To address inter-agent coordination issues, this work presents bilateral concepts-type of dependency and degree of dependency that assist the developers in reducing the trivial dependencies and thereby unnecessary communication overheads. An integrated approach for requirements prioritisation enables a large number of stakeholders to resolve their conflicts in deciding which agents are viable to achieve. In addition, a fuzzy traceability vector model and a coding scheme to specify the requirements of agents are the distinguished features of this work.

基于AHP-FCE的遥感卫星系统覆盖效能评估

针对遥感卫星系统的顶层设计与合理规划，建立科学的卫星系统覆盖能力评估模型具有重要意义。为此，建立了层次化的覆盖效能评估指标体系，采用层次分析法(AHP)设计指标权重；提出了一种新的覆盖特性仿真计算流程,基于模糊综合评判法(FCE)计算了评估指标的单因素模糊向量；最终提出了一个完整的基于AHP-FCE方法的遥感卫星系统覆盖效能评估技术流程，以多颗国内外典型遥感卫星进行了评估实验，验证了方法的有效性。 It is significant to establish a scientific coverage capability assessment model in the top-level de-signing and rational planning of remote sensing satellite system. The paper established a hierar-chical index system of coverage effectiveness evaluation, and the analytic hierarchy process (AHP) was used in index weights designing. Then, a new simulation computing process of coverage feature was proposed, and the fuzzy vector of index was calculated based on fuzzy comprehensive evaluation (FCE). Finally the paper put forward a complete effectiveness evaluation process of remote sensing satellite system based on AHP-FCE. Evaluation experiment using the typical do-mestic and foreign remote sensing satellites verified the effectiveness of the method.

Approximate solution of fuzzy differential equations under generalized differentiability

In this paper, an approach for approximating the fuzzy linear system of differential equations under generalized differentiability is presented, because under this interpretation, we may obtain solutions which have a decreasing length of their support. In several applications the behavior of these solutions better reflects the behavior of some real-world systems. Also, we investigate a necessary and sufficient conditions for the solution vector to be a fuzzy vector.