entropy based operations on fuzzy sets by using a fuzzy entropy approach three sets of new generalized operators are presented after a general discussion on fuzzy entropy the concept of an elementary entropy function of a fuzzy set is introduced using this mapping the generalized intersections and unions are defined as mappings that assign the least and the most fuzzy membership grade to each of the elements of the domain of the operators respectively it is shown that these operators can be constructed from the conventional min and max operations next two modified sets of operations are introduced the second part of the paper investigates the applicability of the new operators in fuzzy logic controllers simulations have been carried out so as to determine the effects of the operators on the performance of the fuzzy controllers it is concluded that the first set of operators does not provide stable control but the performance of the fuzzy controller can be improved by using the modified operations for a class of plants

fuzzy modeling based on generalized conjunction operations an approach to fuzzy modeling based on the tuning of parametric conjunction operations is proposed first some methods for the construction of parametric generalized conjunction operations simpler than the known parametric classes of conjunctions are considered and discussed second several examples of function approximation by fuzzy models based on the tuning of the parameters of the new conjunction operations are given and their approximation performances are compared with the approaches based on a tuning of membership functions and other approaches proposed in the literature it is seen that the tuning of the conjunction operations can be used for obtaining fuzzy models with a sufficiently good performance when the tuning of membership functions is not possible or not desirable

generalized lagrange functions and weighting coefficient formulae for the harmonic differential quadrature method in the harmonic differential quadrature method truncated fourier series comprising the trigonometric functions are used to approximate the solutions the generalized lagrange functions composed of trigonometric functions are constructed as interpolation functions so that the unknowns are the function values rather than the fourier coefficients in the spirit of the differential quadrature method the derivatives at a sampling grid point are expressed as weighted linear sums of function values at all the sampling grid points it is shown that the corresponding weighting coefficients of higher order derivatives can be evaluated recursively and the general explicit formulae are given in this paper the differential quadrature analog of the governing equations can then be established easily at the sampling grid points for the periodic boundary value problems the periodic boundary conditions are satisfied automatically and no other boundary conditions are required in general it is also shown that the harmonic differential quadrature method is related to the trigonometric collocation method and the harmonic balance method numerical examples are given to illustrate the validity and efficiency of the present method copyright 2003 john wiley sons ltd

reference motion in deformable bodies under rigid body motion and vibration part ii evaluation of the coefficient of restitution for impacts abstract the dynamic analysis of rigid body impacts is usually performed by using the coefficient of restitution as a measure of the mechanical energy lost in the process the coefficient of restitution provides an algebraic equation that allows impulse momentum balance equations to be solved this paper reports a method for calculating the kinematic coefficient of restitution for the impact of deformable bodies by using a numerical simulation procedure calculations were done within the framework of the floating reference frame approach as shown here for the first time discriminating between reference velocities and rigid body equivalent velocities is essential with a view to accurately calculating the kinematic coefficient of restitution thus the velocities at which the contact points approach and depart must be calculated as rigid body equivalent velocities if references velocities are used instead the resulting coefficient of restitution lacks physical significance the proposed method is illustrated with two applications namely an axial impact of a rigid body on a deformable rod and a transverse impact of a beam on a fixed stop

fuzzy controls under various fuzzy reasoning methods abstract a fuzzy logic controller consists of linguistic control rules tied together by means of two concepts fuzzy implications and a compositional rule of inference most of the existing fuzzy logic controllers are based on the approximate reasoning method due to mamdani this paper introduces other fuzzy implications such as the arithmetic rule and maximin rule for linguistic control rules and compares control results for a plant model with first order delay under various approximate reasoning methods moreover control results are compared when the widths of fuzzy sets of linguistic control rules are changed

the simplest fuzzy controllers using different inference methods are different nonlinear proportional integral controllers with variable gains abstract the author analytically proves that the simplest fuzzy controllers using different inference methods are different nonlinear proportional integral pi controllers with proportional gains and integral gains changing with inputs of the controllers the inference methods involved are mamdani s minimum inference method larsen s product inference method the drastic product inference method and the bounded product inference method configuration of the fuzzy controllers is minimal which includes two input fuzzy sets three output fuzzy sets four control rules zadeh fuzzy logic and lukasiewicz fuzzy logic or and a center of gravity defuzzification algorithm after analytically investigating properties of the nonlinear pi controllers the author reveals that the bounded product inference method is inappropriate for the control purpose while the other three inference methods are appropriate dynamic and static control behaviors of the fuzzy controllers with the appropriate inference methods are analytically compared with each other and are also compared with those of the linear pi controller finally it is analytically proven that the fuzzy control systems have the same local stability at the equilibrium point as the corresponding linear pi control system does

construction of fuzzy σ algebras using triangular norms abstract generalizing the definitions given by the author fuzzy sets and systems4 1980 83 93 we introduce and study t fuzzy algebras t being any triangular norm the main result is that for a large class of triangular norms each t fuzzy algebra is generated i e consists of all functions x 0 1 being measurable with respect to some algebra on x

a note on coefficient of restitution models including the effects of impact induced vibration in this work multi modal systems subject to impact are considered using energy balance techniques for an arbitrary contact interval the effects of modal vibration can be included the energy balance is used to obtain a relationship between the coefficient of restitution and the modal energy during the contact period this allows the effects of impact induced vibration to be considered the subsequent analytical relationships demonstrate that increasing contact duration and excitation of higher modes can reduce the effective value of the coefficient of restitution it is also shown how this approach can be related to work on energetically consistent impacts

the linear rational collocation method we introduce the collocation method based on linear rational interpolation for solving general hyperbolic problems prove its stability and its convergence in weighted norms and give numerical examples for its use

dynamic response of a constrained axially loaded beam a dynamic beam system loaded harmonically in the axial direction and constrained in the transverse direction is modelled using different theoretical descriptions results from an experimental set up are compared to calculations using bernoulli as well as timoshenko beam theories some results from investigations of this beam system unveiling its chaotic nature have earlier been presented but here the refining of timoshenko theory is done in order to get a better understanding of the influence of the impacts on the beam motion the free motion of the beam is described as a finite sum of modes while at impact an infinite number of modes is considered albeit approximately these ideas were also used for the bernoulli beam but modifications will be made here to account for the modal equations of fourth order in time for the timoshenko beam the investigation is complemented with new experiments

the distributivity property of increasing binary operations abstract this paper is mainly devoted to solving the functional equations of distributivity and conditional distributivity of increasing binary operations with the unit our investigations are motivated by distributive logical connectives and their generalizations used in fuzzy set theory in particular some assumptions namely associativity and commutativity and results about conditional distributivity of uninorms and triangular norms and triangular conorms were simplified moreover some other properties e g componentwise convexity concavity for special operations from the class of quasi copulas is considered

parametric classes of generalized conjunction and disjunction operations for fuzzy modeling it is argued that inference procedures of fuzzy models do not always require commutativity and associativity of the operations used this raises the possibility of considering nonassociative and noncommutative conjunction and disjunction operations such operations are investigated in this paper and different methods for their generation are proposed a number of new types of conjunction operations that are simpler than the known parametric classes of t norms are given and as an application example the approximation of a function by a fuzzy inference system is considered

a note on using the collocation method for modelling the dynamics of a flexible continuous beam subject to impacts the use of non smooth modelling techniques to model the dynamics of a flexible impacting beam has recently been reported in ref 1 the method used was based on taking a galerkin approximation 2 of the partial differential equation pde governing the dynamics of the beam away from impact and coupling this to a non smooth coefficient of restitution rule to model the impact 3 in this letter the advantages and limitations of using a collocation method instead of the galerkin method combined with a non smooth impact law are discussed

fibred triangular norms abstract in this paper we deal with the formula g t f x f y where f g are functions mapping from the unit interval to itself and t is a triangular norm we are interested in the conditions under which this formula yields a triangular norm the case when f is continuous is investigated in detail as a result a new method which generates new triangular norms from an arbitrary triangular norm is developed these new triangular norms are the so called fibred triangular norms which are closely related to the homomorphism of semigroups it is well known that continuous archimedean triangular norms can be generated with additive generator functions we investigate a possible generalization of the additive generator function and characterize the class of t norms which can be generated with them this class turns out to be the class of fibred continuous archimedean t norms finally some examples are given for the case when f is not continuous

a survey of weak connectives and the preservation of their properties by aggregations the aim of this paper is to choose diverse definitions of generalized logical connectives and to present them in a coherent order from the weakest to the richest such a rich list of notions allows us to consider the problem of admissible aggregations in the presented classes of unary and binary operations this gives a contribution to the discussion of tolerance analysis in soft computing decision making approximate reasoning and fuzzy control first we present a short survey of the development of mv logic s connectives next we discuss postulates used for generalized logical connectives finally we describe families of weak connectives and indicate the preservation of their properties by some aggregation functions

strict preference relations based on weak t norms abstract in this paper we introduce and investigate weak t norms and related concepts in order to give a general representation of valued strict preference relations associated with a given valued preference relation all the well known forms of valued strict preference relations are particular cases of our results moreover when some types of rationality assumptions are made our unified approach seems to be the only possible one

comparison of time and spatial collocation methods for the heat equation we combine a high order compact finite difference scheme to approximate the spatial derivatives and collocation techniques for the time component to numerically solve the two dimensional heat equation we use two approaches to implement the time collocation methods the first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadratures we also implement a spatial collocation method where differential quadratures are utilized for spatial derivatives and an implicit scheme for marching in time we compare all the three techniques by studying their merits and analyzing their numerical performance our experiments show that all of them achieve high accurate approximate solution but the time collocation method with differential quadrature offers with respect to the one with explicit polynomials less computational complexity and a better efficiency all our computations based on parallel algorithms are carried out on the cray sv1

the compensation method applied to a one product production inventory problem this paper considers a one product one machine production inventory problem demand requests for the product are governed by a poisson process with demand size being an exponential random variable the production facility may be in production or idle while in production the facility produces continuously at a constant rate the objective is to minimize system costs consisting of setup costs inventory holding costs and backorder costs given a two critical number policy the problem is analyzed as a constrained markov process using the compensation method a closed form expression is found for system cost as a function of the policy parameters this cost function may then be searched to find an optimal policy the production inventory problem is related to a server backlog process for an m m 1 system in which the server departs when the system empties and returns when the backlog exceeds a specified threshold the application of the compensation method to this server backlog process is discussed

exact solutions for interacting rules in generalized modus ponens with parameterized implication functions many authors have presented exact analyses of the behavior of an isolated fuzzy inference rule and many have presented empirical studies of the behavior of multiple rule systems this paper presents an exact analysis of the behavior of a class of two rule systems in which the antecedent and consequent membership functions are trapezoidal and the implication operator is a strong implication s implication or a residuated implication r implication formed by the schweizer sklar family of parameterized t norms the two rule system exhibits many emergent properties not found when a single rule is studied and much of the behavior of many rule systems is dominated by two rule interactions

optimal control of production rate in a failure prone manufacturing system we address the problem of controlling the production rate of a failure prone manufacturing system so as to minimize the discounted inventory cost where certain cost rates are specified for both positive and negative inventories and there is a constant demand rate for the commodity produced the underlying theoretical problem is the optimal control of a continuous time system with jump markov disturbances with an infinite horizon discounted cost criterion we use two complementary approaches first proceeding informally and using a combination of stochastic coupling linear system arguments stable and unstable eigenspaces renewal theory parametric optimization etc we arrive at a conjecture for the optimal policy then we address the previously ignored mathematical difficulties associated with differential equations with discontinuous right hand sides singularity of the optimal control problem smoothness and validity of the dynamic programming equation etc to give a rigorous proof of optimality of the conjectured policy it is hoped that both approaches will find uses in other such problems also we obtain the complete solution and show that the optimal solution is simply characterized by a certain critical number which we call the optimal inventory level if the current inventory level exceeds the optimal one should not produce at all if less one should produce at the maximum rate while if exactly equal one should produce exactly enough to meet demand we also give a simple explicit formula for the optimal inventory level

improved approximations for a beam impacting a stop abstract illustrative comparisons are given of several numerical procedures for finding the contact forces and their peak values when an elastic beam collides repeatedly with a resilient stop computational efficiency is shown to depend upon the variable of interest

preservation of fuzzy relation properties based on fuzzy conjunctions and disjunctions during aggregation process in this contribution necessary and sufficient conditions for n argument functions to preserve properties of fuzzy relations during aggregation process are presented the proposed properties depend on binary operations including t norms and t conorms and more generally fuzzy conjunctions and disjunctions generalizations of the following properties are studied antisymmetry asymmetry connectedness transitivity negative transitivity semitransitivity and ferrers property

differential cubature method a solution technique for kirchhoff plates of arbitrary shape a treatment for bending analysis of kirchhoff plates using the differential cubature dc method is presented to the authors knowledge this represents the first known successful application of the dc method to this problem the plates treated are subjected to various combinations of boundary conditions and of arbitrary plate geometry a discussion on the implementation issues is presented and several numerical test examples are included to demonstrate the applicability efficiency and simplicity of the approximate procedures the accuracy of the procedures is verified by direct comparing the present numerical results of different plate shapes with the existing exact analytical solutions 1 and other sources of numerical values

production control of a manufacturing system with multiple machine states the production control of a single product manufacturing system with arbitrary number of machine states failure modes is discussed the objective is to find a production policy that would meet the demand for the product with minimum average inventory or backlog cost the optimal production policy has a special structure and is called a hedging point policy if the hedging points are known the optimal production rate is readily specified assuming a set of tentative hedging points the simple structure of the optimal policy is utilized to find the steady state probability distribution of the surplus inventory or backlog once this function is determined the average surplus cost is easily calculated in terms of the values of the hedging points the average cost is then minimized to find the optimum hedging points

sporadic and continuous clearing policies for a production inventory system under an m g demand process a production inventory system is filled continuously at rate 1 and satisfies demands of i i d random sizes that arrive at poisson times for this system we consider two clearing policies under sporadic review clearing takes place after a random time independent of the content process under continuous review the system is cleared as soon as the inventory level reaches some pre specified threshold we derive explicit results for the associated expected discounted cost functionals under both types of clearing

unreliable production inventory model with a two phase erlang demand arrival process a production inventory system is studied in which an unreliable machine is susceptible to failure following which it must be repaired to make it operative again the demand for the product is governed by a two phase erlang process and demand sizes are independent and identically distributed random variables a two critical number policy m m is used to control a machine s setups and shutdowns namely the machine is shut down whenever the inventory level reaches m and is resumed to operate only when the inventory level falls below the critical number m m m we obtain the steady state distribution of the inventory process and some performance measures of the process

stability analysis of parametrically excited systems using spectral collocation abstract the spectral collocation method is used to determine the stability of parametrically excited systems and compared with the traditional transition matrix approach results from a series of test problems demonstrate that spectral collocation converges rapidly in addition the spectral collocation method preserves the sparsity of the underlying system matrices a property not shared by the transition matrix approach as a result spectral collocation can be used for very large systems and can utilize sparse eigensolvers to reduce computational memory and time for the large scale system studied up to 40 degrees of freedom the spectral collocation method was on average an order of magnitude faster than the transition matrix approach using matlab this computational advantage is implementation specific in a c implementation of the algorithm the transition matrix method is faster than the spectral collocation overall the method proves to be simple efficient reliable and generally competitive with the transition matrix method

design of fuzzy logic controllers based on generalized t operators abstract since zadeh first proposed the basic principle of fuzzy logic controllers in 1968 the min and max operators have been popular in the design of fuzzy logic controllers in this paper the general concept of t operators is introduced into the conventional design methods for fuzzy logic controllers so that a general and flexible methodology for the design of these fuzzy logic controllers is available then by computer simulations studies are made so as to determine the relations between the various t operators and the performance of a fuzzy logic controller it is concluded that the performance of the fuzzy logic controller for a given class of plants very much depends upon the choice of the t operators

application of non smooth modelling techniques to the dynamics of a flexible impacting beam non smooth modelling techniques have been successfully applied to lumped mass type structures for modelling phenomena such as vibro impact and friction oscillators in this paper the application of these techniques to continuous elements using the example of a cantilever beam is considered employing a galerkin reduction to form an n degree of freedom modal model a technique for modelling impact phenomena using a non smooth dynamics approach is demonstrated numerical simulations computed using the non smooth model are compared with experimentally recorded data for a flexible beam constrained to impact on one side a method for dealing with sticking motions when numerically simulating the beam motion is presented in addition choosing the dimension of the model based on power spectra of experimentally recorded time series is discussed

differential quadrature method for thick symmetric cross ply laminates with first order shear flexibility a global numerical technique the differential quadrature dq method is examined here for its suitability to solve the boundary value problem of symmetric cross ply laminates using the first order shear deformation plate theory by whitney and pagano j appl mech 37 1031 1036 1970 the bending behaviours of symmetric cross ply laminates subject to different boundary constraints are investigated in this study the method is used to transform the sets of governing differential equations and boundary conditions of the laminated plates into sets of linear algebraic equations boundary conditions along the edges are implemented through the discrete grid points by constraining the displacements bending moments and rotations the theoretical formulations and solution procedures of the method are illustrated through solving several numerical examples the accuracy and validity of the present formulation if available are examined by direct comparison with the known values