A new method for solving linear multi-objective transportation problems with fuzzy parameters

There are several methods in the literature for solving transportation problems by representing the parameters as normal fuzzy numbers. Chiang [J. Chiang, The optimal solution of the transportation problem with fuzzy demand and fuzzy product, J. Inform. Sci. Eng. 21 (2005) 439-451] pointed out that it is better to represent the parameters as (λ, ρ) interval-valued fuzzy numbers instead of normal fuzzy numbers and proposed a method to find the optimal solution of single objective transportation problems by representing the availability and demand as (λ, ρ) interval-valued fuzzy numbers. In this paper, the shortcomings of the existing method are pointed out and to overcome these shortcomings, a new method is proposed to find solution of a linear multi-objective transportation problem by representing all the parameters as (λ, ρ) interval-valued fuzzy numbers. To illustrate the proposed method a numerical example is solved. The advantages of the proposed method over existing method are also discussed.     

Simulation and evaluation of dual fully fuzzy linear systems by fuzzy neural network

In this paper, a novel hybrid method based on fuzzy neural network for approximate solution of fuzzy linear systems of the form Ax = Bx + d, where A and B are two square matrices of fuzzy coefficients, x and d are two fuzzy number vectors, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate solution, a simple and fast algorithm from the cost function of the fuzzy neural network is proposed. Finally, we illustrate our approach by some numerical examples.     

E2: A new logic model for MVL relations

A new logic model is presented in this paper for subsets of Rⁿ × R^m known as n-input m-output r-valued multiple-valued logic (MVL) relations, where n, m >0 and r >1 are integers, and R = {0,1, … , r − 1} is an enumeration of the finite ordered set E = {e₀, e₁,…, e_r−1}. The model, called E2 systems (or shortly E2), represents an extension of an existing generalized cube representation for MVL relations called set functions. E2 systems consist of two components: logic implication (LI) systems, and logic equivalence (LE) systems. Some properties of the E2 systems are presented, and applying the model in cell-based combinatorial MVL circuit synthesis is discussed.     

A new auto-switched chaotic system and its FPGA implementation

This paper presents a 3D chaotic system which is constructed by an auto-switched numerical resolution of multiple three dimensional continuous chaotic systems. The designed chaotic system provides complex chaotic attractors and can change its behaviors automatically via a chaotic switching-rule. Some complex dynamical behaviors are investigated and analyzed. The originality of the proposed architecture is that allows to solve the problem of the finite precision due to the digital implementation while provides a good trade-off between high security, performance and hardware resources (low power and cost). Hardware digital implementation and FPGA circuit experimental results demonstrate a promising technique can be applied in efficient embedded ciphering communication systems. Moreover, the proposed chaotic system should be very useful for the consideration of reducing negative influence of dynamical degradation in real-time embedded applications.     

一类模糊逻辑系统幺半群与同态映射

首先利用代数中幺半群的概念给出了模糊逻辑系统专业领域的概念, 建立专业领域概念的目的是为了规范模糊逻辑系统中语言变量的取值范围, 从而将模糊逻辑系统看作是某个笛卡儿乘积幺半群的有限子集. 然后利用这个笛卡儿乘积幺半群的乘积运算构造了模糊逻辑系统幺半群. 最后, 在一定的约定条件下证明了通常使用的一类Mamdani形模糊逻辑系统的输出可以看作是从模糊逻辑系统幺半群到连续函数域的同态映射.     

Reliability evaluation of multi-state systems under cost consideration

A more practical and desirable performance index of multi-state systems is the two-terminal reliability for level (d, c) (2TR_d,c), defined as the probability that d units of flow can be transmitted from the source node to the sink node with the total cost less than or equal to c. In this article, a simple algorithm is developed to calculate 2TR_d,c in terms of (d, c)-MPs. Two major advantages of the proposed algorithm include: (1) as of now, it is the only algorithm that searches for (d, c)-MPs without requiring all minimal paths (MPs) and the procedure of transforming feasible solutions; (2) it is more practical and efficient in solving (d, c)-MP problem in contrast to the best-known method. An example is provided to illustrate the generation of (d, c)-MPs by using the presented algorithm, and 2TR_d,c is thus evaluated. Furthermore, the computational experiments are conducted to verify the performance of the presented algorithm.     

Adaptive fuzzy tracking control for the chaotic permanent magnet synchronous motor drive system via backstepping

An adaptive fuzzy control method is developed to suppress chaos in the permanent magnet synchronous motor drive system via backstepping technology. Fuzzy logic systems are used to approximate unknown nonlinearities and an adaptive backstepping technique is employed to construct controllers. Compared with the conventional backstepping, the designed fuzzy controllers’ structure is very simple. The simulation results indicate that the proposed control scheme can suppress the chaos of PMSM drive systems and track the reference signal successfully even under the parameter uncertainties.     

Hardware Implementation of Fuzzy PID Controllers

For traditional hardware implementation of fuzzy PID controllers, it is large at computation and bad in real-time performance, so, a kind of PID control algorithm, whose gain parameters could be tuned by their fuzzy system, was selected as studying example for a novel idea of hardware implementation. In this paper, authors presented hardware network of memory address mapping to implement fuzzy PID control algorithm, and designed the corresponding hardware system. The idea actually realizes fusion of hardware and intelligent algorithm. The implementation effectively simplified hardware circuits, the whole controller is very simple without CPU. Meanwhile, it is very easy to use, only connecting the sensor/transducer, the driver and the actuator is OK. The controller is very rapid in response, it need only two A/D conversion periods for outputting a required control signal. So the implementation could meet real-time performance effectively.     

Indirect adaptive fuzzy observer and controller design based on interval type-2 T-S fuzzy model

This paper presents the design scheme of the indirect adaptive fuzzy observer and controller based on the interval type-2 (IT2) T-S fuzzy model. The nonlinear systems can be well approximated by IT2 T-S fuzzy model, in which the fuzzy rules’ antecedents are interval type-2 fuzzy sets and consequents are linear state equations. The proposed IT2 T-S fuzzy model is a combination of IT2 fuzzy system and T-S fuzzy model, and also inherits the benefits of type-2 fuzzy logic systems, which is able to directly handle uncertainties and can minimize the effects of uncertainties in rule-based fuzzy system. These characteristics can improve the accuracy of the system modeling and reduce the number of system rules. The proposed method using feedback control, adaptive laws, and on-line object parameters are adjusted to ensure observation error bounded. In addition, using Lyapunov synthesis approach and Lipschitz condition, the stability analysis is conducted. The simulation results show that the proposed method can handle unpredicted disturbance and data uncertainties very well in advantage of the effectiveness of observation and control.     

Ranking fuzzy quantities based on the angle of the reference functions

Ordering fuzzy quantities and their comparison play a key tool in many applied models in the world and in particular decision-making procedures. However a huge number of researches is attracted to this filed but until now there is any unique accepted method to rank the fuzzy quantities. In fact, each proposed method may has some shortcoming. So we are going to present a novel method based on the angle of the reference functions to cover a wide range of fuzzy quantities by over coming the draw backs of some existing methods. In the mentioned firstly, the angle between the left and right membership functions (the reference functions) of every fuzzy set is called Angle of Fuzzy Set (AFS), and then in order to extend ranking of two fuzzy sets the angle of fuzzy sets and α-cuts is used. The method is illustrated by some numerical examples and in particular the results of ranking by the proposed method and some common and existing methods for ranking fuzzy sets is compared to verify the advantage of the new approach. In particular, based on the results of comparison of our method with well known methods which are exist in the literature, we will see that against of most existing ranking approaches, our proposed approach can rank fuzzy numbers that have the same mode and symmetric spreads. In fact, the proposed method in this paper can effectively rank symmetric fuzzy numbers as well as the effective methods which are appeared in the literature. Moreover, unlike of most existing ranking approaches, our proposed approach can rank non-normal fuzzy sets. Finally, we emphasize that the concept of fuzzy ordering is one of key role in establishing the numerical algorithms in operations research such as fuzzy primal simplex algorithms, fuzzy dual simplex algorithms and as well as discussed in the works of Ebrahimnejad and Nasseri and coworkers , , , , ,  and .     

An adaptive Huber method for non-linear systems of weakly singular second kind Volterra integral equations

Numerical methods for systems of weakly singular Volterra integral equations are rarely considered in the literature, especially if the equations involve non-linear dependencies between unknowns and their integrals. In the present work an adaptive Huber method for such systems is proposed, by extending the method previously formulated for single weakly singular second kind Volterra equations. The method is tested on example systems of integral equations involving integrals with kernels K(t, τ) = (t − τ)^−1/2, K(t, τ) = exp[−λ(t − τ)](t − τ)^−1/2 (where λ > 0), and K(t, τ) = 1. The magnitude of the errors, and practical accuracy orders, observed for IE systems, are comparable to those for single IEs. In cases when the solution vector is not differentiable at t = 0, the estimation of errors at t = 0 is found somewhat less reliable for IE systems, than it was for single IEs. The stability of the IE systems solved appears to be sufficient, in practice, for the numerical stability of the method.     

Modelling on fuzzy control systems

A kind of modelling method for fuzzy control systems is first proposed here, which is called modelling method based on fuzzy inference (MMFI). It should be regarded as the third modelling method that is different from two well-known modelling methods, that is, the first modelling method, mechanism modelling method (MMM), and the second modelling method, system identification modelling method (SIMM). This method can, based on the interpolation mechanism on fuzzy logic system, transfer a group of fuzzy inference rules describing a practice system into a kind of nonlinear differential equation with variable coefficients, called HX equations, so that the mathematical model of the system can be obtained. This means that we solve the difficult problem of how to get a model represented as differential equations on a complicated or fuzzy control system.     

A novel analog fuzzy controller for intelligent sensors

A new analog fuzzy logic controller implemented in CMOS technology is described. The chosen membership function generator keeps the needed area for the inference engine very small while giving a big flexibility in the configuration of the membership function. The proposed solution for defuzzification gives an additional area reduction over earlier implementations. High speed, low power fuzzy controller hardware make the chip appropriate for intelligent sensor application. Simulation results as well as test measurements are presented and discussed to illustrate the properties and robustness of the proposed circuit.     

A real time algorithm for the location search of discontinuous conductivities with one measurement

We consider an inverse problem for finding the anomaly of discontinuous electrical conductivity by one current‐voltage observation. We develop a real time algorithm for determining the location of the anomaly. This new idea is based on the observation of the pattern of a simple weighted combination of the input current and the output voltage. Combined with the size estimation result, this algorithm gives a good initial guess for Newton‐type schemes. We give the rigorous proof for the location search algorithm. Both the mathematical analysis and its numerical implementation indicate our location search algorithm is very fast, stable and efficient. © 2001 John Wiley & Sons, Inc.     

On quasi‐varieties of multiple valued logic models

We extend the concept of quasi‐variety of first‐order models from classical logic to multiple valued logic (MVL) and study the relationship between quasi‐varieties and existence of initial models in MVL. We define a concept of ‘Horn sentence’ in MVL and based upon our study of quasi‐varieties of MVL models we derive the existence of initial models for MVL ‘Horn theories’. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

A simple augmented ∊-constraint method for multi-objective mathematical integer programming problems

A simple augmented ?-constraint (SAUGMECON) method is put forward to generate all non-dominated solutions of multi-objective integer programming (MOIP) problems. The SAUGMECON method is a variant of the augmented ?-constraint (AUGMECON) method proposed in 2009 and improved in 2013 by Mavrotas et al. However, with the SAUGMECON method, all non-dominated solutions can be found much more efficiently thanks to our innovations to algorithm acceleration. These innovative acceleration mechanisms include: (1) an extension to the acceleration algorithm with early exit and (2) an addition of an acceleration algorithm with bouncing steps. The same numerical example in Lokman and Köksalan (2012) is used to illustrate workings of the method. Then comparisons of computational performance among the method proposed by  and , the method developed by Lokman and Köksalan (2012) and the SAUGMECON method are made by solving randomly generated general MOIP problem instances as well as special MOIP problem instances such as the MOKP and MOSP problem instances presented in Table 4 in Lokman and Köksalan (2012). The experimental results show that the SAUGMECON method performs the best among these methods. More importantly, the advantage of the SAUGMECON method over the method proposed by Lokman and Köksalan (2012) turns out to be increasingly more prominent as the number of objectives increases.     

The systems approach and fuzzy set theory bridging the gap between mathematical and language-oriented economists

Ideas are presented to show how fuzzy mathematics can be applied in macro-economics in combination with the systems approach in order to bridge the gap between mathematical and language-oriented economists.Two reasons are given.From a mathematical point of view, fuzzy sets, fuzzy relations and fuzzy logic are not fuzzy at all. They are all well defined, but tend to be more complicated than traditional, mathematical concepts used in economics.From a language-oriented economist's point of view, fuzzy sets, etc. are used to express mathematically the type of concepts which are typical in language and most valuable in dealing with complex systems like an economy.The paper deals with economics in general terms, but examples are provided to illustrate the ideas.     

Consistency analysis of triangular fuzzy reciprocal preference relations

In order to simulate the uncertainty associated with impression or vagueness, a decision maker may give her/his judgments by means of triangular fuzzy reciprocal preference relations in the process of decision making. The study of their consistency becomes a very important aspect to avoid a misleading solution. Based on the reciprocity property, this paper proposes a new definition of consistent triangular fuzzy reciprocal preference relations. The new definition is different from that reduced by consistent fuzzy reciprocal preference relations proposed by Buckley (1985). The properties of consistent triangular fuzzy reciprocal preference relations in the light of the new definition are studied in detail. In addition, the shortcomings of the proof procedure of the proposition given by Wang and Chen (2008) are pointed out. And the proposition is reproved by using the new definition of consistent triangular fuzzy reciprocal preference relations. Finally, using the (n − 1) restricted comparison ratios, a method for obtaining consistent triangular fuzzy reciprocal preference relations is proposed, and an algorithm is shown to make a consistent decision ranking. Numerical results are further calculated to illustrate the new definition and the obtained algorithm.     

Continuous fuzzy Horn logic

The paper deals with fuzzy Horn logic (FHL) which is a fragment of predicate fuzzy logic with evaluated syntax. Formulas of FHL are of the form of simple implications between identities. We show that one can have Pavelka‐style completeness of FHL w.r.t. semantics over the unit interval [0, 1] with (residuated lattices given by) left‐continuous t‐norm and a residuated implication, provided that only certain fuzzy sets of formulas are considered. The model classes of fuzzy structures of FHL are characterized by closure properties. We also give comments on related topics proposed by N. Weaver. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)