translation of the problem of complete test set generation to pseudo boolean programming an attempt is made to demonstrate that the problem of complete test set generation is amenable to the problem of pseudo boolean programming for this purpose various types of faults viz single faults multiple faults and bridging faults are considered the key issue is to obtain logical expressions for the primary output line in terms of different faulty internal nodes to find real transforms using standard rules the real transforms of a boolean function can be obtained directly without any algebraic manipulation

adaptive robot under fuzzy control an arc welding industrial robot isotron 251 is treated its adaptation is considered as an attribute of the robot to trace an arbitrary pretaught welding seam by means of a noncontact laser sensor the control strategy is proposed to use a fuzzy model describing uncertainty of working conditions the experience shows how the notion of fuzzy sets powers is used for on line estimation prediction and control of robot motions the control algorithm has been tested by a three level microprocessor controller

structure properties of min max systems and existence of global cycle time studies min max systems which are dynamic systems including three operations min max with unknown or stochastic parameters some sufficient conditions are given for the existence of global cycle times our results are based on structure properties of min max systems

solution of systems of boolean equations via the integer domain this paper presents a new method for solving systems of boolean equations the method is based on converting the equations so that we operate in the integer domain in the integer domain better and more efficient methodologies for solving equations are available the conversion leads us to a system of polynomial equations obeying certain characteristics a method is proposed for solving these equations the most computationally demanding step is the repeated multiplication of polynomials we develop a method for this problem that is significantly faster than the standard approach we also introduce another variant of the method the so called hybrid approach that leads to reduced memory requirements theoretical and experimental results indicate the superior performance of the proposed method and its variant compared to the competing methods the proposed method is also validated by applying it to the problem of hardware verification

finite solvable groups whose quillen complex is cohen macaulay abstract we will prove that the p quillen complex of a finite solvable group with cyclic derived group is cohen macaulay if p is an odd prime if p 2 we prove a similar conclusion but there is a discussion to be made

on the application of fuzzy sets theory to the optimal flood control problem arising in water resources systems abstract we first survey the application of fuzzy sets theory to various problems occurring in water resources systems the problem of optimal flood control planning by an appropriate integration of structural and non structural measures with the objective of optimizing the flood damage reduction due to recurrent floods is modeled via fuzzy sets methodologies a two level optimization model appropriate for planning decisions first on a regional or local level and then on a national level is proposed a third phase involving coordination is appended in particular a fuzzy optimization model involving an adroit combination of fuzzy dynamic programming type reasoning and a branch and bound type search procedure is offered as a more utilitarian approach than its crisp equivalent the performance of the algorithm is illustrated with an example

direct digital control auto tuning and supervision using fuzzy logic abstract we describe algorithms for the design and implementation of fuzzy logic controllers and present results of their application to temperature control of a heated air stream auto tuning methods are studied for adjustment of conventional parameters to compensate for actual values of control variables or of external variables and for improvement of performance from observation of results conditions for verifying the consistency of the linguistic protocol with its implementation are presented in an appendix

the quillen complex of groups of symplectic type the characteristic 2 case abstract let g op g s where s z pn z t is of symplectic type with t an extra special p group and op g solvable from results in 3 it is easy to show that when p is odd the quillen complex of g at p is cohen macaulay in this note we show that the result also holds when p 2

building fuzzy graphs from samples of nonlinear functions this paper considers the problem of constructing fuzzy graphs from samples of multi dimensional nonlinear functions to meet a precision requirement it starts by defining the basic notions of fuzzy granulation fuzzy graph fuzzification and defuzzification the formulation of the problem is then stated in a fuzzy granulation and function approximation framework this is followed by the development of a recursive scheme that builds a fuzzy graph by generating a set of fuzzy rules and membership functions from the samples of a nonlinear function rigorous analysis is carried out to establish the convergence of such a recursive scheme a few illustrative examples are also used to assess both the efficacy and the efficiency of the proposed scheme

obdd minimization based on two level representation of boolean functions in this paper we analyze the basic properties of some boolean function classes and propose a low complexity obdd variable ordering algorithm which is exact optimum to some classes of functions and very effective to general two level form functions we show that the class of series parallel functions which can be expressed by a factored form where each variable appears exactly once can yield exact obdd variable orderings in polynomial time we also study the thin boolean functions whose corresponding obdds can be represented by the form of thin obdds in which the number of nonterminal nodes is equal to the number of input variables we show that a thin boolean function always has an essential prime cube cover and the class of series parallel functions is a proper subset of thin boolean functions we propose a heuristic viewing obdds as evaluation machines with function cube covers as their inputs and apply a queuing principle in the algorithm design our heuristic the augmented dynamic shortest cube first algorithm is proven to be optimum for the series parallel functions and also be very effective for general two level form functions experimental results on a large number of two level form benchmark circuits show that the algorithm yields an obdd total size reduction of over 51 percent with only 7 percent cpu time compared to the well known network based fan in heuristic implemented in the sis package comparing to the known exact results ours is only 49 percent larger in size while only uses 0 001 percent cpu time

a pid type fuzzy controller with self tuning scaling factors by relating to the conventional pid control theory we propose a new fuzzy controller structure namely pid type fuzzy controller in order to improve further the performance of the transient state and the steady state of the pid type controller we develop a method to tune the scaling factors of the pid type fuzzy controller on line simulation of the pid type fuzzy controller with the self tuning scaling factors shows a better performance in the transient and steady state response

experiments with the use of a rule based self organising controller for robotics applications abstract the rule based self organising controller soc has as one of its main advantages the fact that there is no need to have a mathematical description of the system to be controlled in this controller the rules are linguistic statements expressed mathematically through the concepts of fuzzy sets and correspond to the actions a human operator would take when controlling a given process this paper describes several experiments which were performed with soc the control was considered of both simulated linear and non linear processes the performance of the controller was investigated for step inputs as well as for waveforms which the process output had to track the effect of process noise was also considered it was shown that soc had a performance slightly superior to that of a pid controller when noise was present and the process had time varying coefficients as well as pronounced non linear characteristics this paper also reviews some of the successful initial work carried out in connection with the application of soc to a revolute joint robot arm this presented a system with highly non linear dynamics to each of several socs working in paralle the sampling times of only a few milliseconds were short compared with several minutes or even hours associated with previous applications of fuzzy controllers to cement kilns

fuzzy system technologies at siemens r d abstract applications of fuzzy logic are usually identified with fuzzy control but besides fuzzy control there are many other fuzzy theories that are used in applications among them fuzzy classification and diagnosis fuzzy control has to do with closed loops but besides the large amount of fuzzy control applications there are many other fuzzy theories being used in applications among them fuzzy classification and diagnosis we consider several recent results in fuzzy control and show their use in applications furthermore we give some examples of applications in fuzzy classification and fuzzy diagnosis

solution of optimal control problems with lumped parameters having single or multiple goal objectives in fuzzy environment abstract in this paper optimal control problems ocp of both linear and nonlinear type with lumped parameters are considered continuous ocp with single or multiple objectives are transformed to finite dimensional optimization problems through discretization the formulation of goal optimal control problem gocp using goal programming methodology first given by levary 1986 for equal time subintervals is extended for unequal subintervals by a generalized formulation the concept of local and global goals proposed here is very useful for multicriteria dynamic optimization problems in several physical situations ocp involve fuzziness in their goals priorities parameters or relative weights and associated linguistic variables etc a new formulation of ocp in fuzzy environment is given as a fuzzy goal optimal control problem fgocp and the solution procedure is illustrated by linear and nonlinear examples

fuzzy controller for a sensor guided robot manipulator sensor guided robots require according to nonlinear characteristics of certain interaction processes between robot effector and object appropriate robust control algorithms for the external sensory control loop this paper deals with a fuzzy controller which bases on linguistic production rules following the pattern of the suboptimal control method its structure is available in a large field of applications simulations and real time experiments concerning the contour tracking problem show compared with a conventional pd controller the high tracking quality of the controller

multiplicity of the trivial representation in rank selected homology of the partition lattice abstract we study the multiplicity bs n of the trivial representation in the symmetric group representations s on the top homology of the rank selected partition lattice ns we break the possible rank sets s into three cases 1 1 s 2 s 1 i for i 1 and 3 s 1 i j1 jl for i l 1 j1 i 1 it was previously shown by hanlon that bs n 0 for s 1 i we use a partitioning for n sn due to hersh to confirm a conjecture of sundaram s sundaram the homology representations of the symmetric group on cohen macaulay subposets of the partition lattice adv math 104 1994 225 296 that bs n 0 for 1 s on the other hand we use the spectral sequence of a filtered complex to show bs n 0 for s 1 i j1 jl unless a certain type of chain of support s exists the partitioning for n sn allows us then to show that a large class of rank sets s 1 i j1 jl for which such a chain exists do satisfy bs n 0 we also generalize the partitioning for n sn to n s when n 1 1 this partitioning leads to a proof of a conjecture of sundaram about s1 sn 1 representations on the homology of the partition lattice

a heuristic self tuning fuzzy controller abstract in this paper a self tuning fuzzy controller based on the tuning of scaling factors is presented the tuning schemes are tuning the scaling factors is individual tuning rules the tuning rules are transformed into numeric tuning tables by applying suitable membership functions so that the adjustings of the scaling factors are merely matrix mappings since the tuning rules are constructed with the control signal and the output error and change in output error of the plant as their antecedent parts the tuning processes have the advantage of real time property simulation results with a perturbed servo and the inverted pendulum system as the controlled plants show the performance and adaptivity of the proposed controller

simple homotopy types and finite spaces whitehead s theory of simple homotopy types is inspired by tietze s theorem in combinatorial group theory which states that any finite presentation of a group could be deformed into any other by a finite sequence of elementary moves which are now called tietze transformations whitehead translated these algebraic moves into the well known geometric moves of elementary collapses and expansions of finite simplicial complexes

a fuzzy dynamic learning controller for chemical process control a fuzzy dynamic learning controller is proposed and applied to control of time delayed non linear and unstable chemical processes the proposed fuzzy dynamic learning controller can self adjust its fuzzy control rules using the external dynamic information from the process during on line control and it can create the new fuzzy control rules autonomously using its learning capability from past control trends the proposed controller shows better performance than the conventional fuzzy logic controller and the fuzzy self organizing controller

model reference adaptive fuzzy control a linguistic space approach in this paper a model reference adaptive fuzzy controller with the adaptivity achieved by tuning both the scaling factors and the control rules is presented the proposed tuning strategy includes two parts 1 by referring a reference trajectory created in the linguistic space to tune the scaling factors and 2 by applying an auxiliary correction matrix generated by specific tuning rules to compensate the control rules since only the control signal the output error and change in output error of the plant are needed in the construction of the reference trajectory and the tuning rules the tuning strategy has the advantage of real time property simulation results with a damping process and an oscillating process as the controlled plants show the performance and adaptivity of the proposed controller

fuzzy modelling and identification with genetic algorithm based learning abstract a ga based learning algorithm is proposed in this paper for the identification of tsk models the algorithm consists of four blocks partition block ga block tuning block and termination block the partition block is to determine an estimated partition of input variables the ga block is to optimise the structure of a tsk model the tuning block is to fine tune the parameters of the tsk model using the gradient descent based approach and the termination block checks that the resultant tsk model is satisfactory the proposed gabl algorithm has the advantage of simplicity flexibility high accuracy and automation the presented numerical examples indicate that the gabl algorithm is effective in constructing a good tsk model for complex nonlinear systems

expert fuzzy controller abstract we describe a fuzzy controller based on our general purpose fuzzy expert system shell flops we take a decision theoretic view in designing an optimal fuzzy controller the variables in the decision problem are 1 the defuzzification rules 2 the fuzzification rules and 3 the fuzzy control rules the objective function is composed of fuzzy goals specified for each system output we differentiate between decision making under certainty risk or uncertainty depending whether or not random elements are present in the system an example is presented illustrating varying the defuzzification rules to improve system performance

an algorithm to derive the complement of a binary function with multiple valued inputs a recursive algorithm to obtain a complement of a sum of products expression for a binary function with p valued inputs is presented it produces at most pn 2 products for n variable functions whereas a conventional elementary algorithm produces o tn n 1 t 2 products where t 2p 1 it is 10 20 times faster than the elementary one when p 2 and n 8 for large practical problems it produces many fewer products than the disjoint sharp algorithm used by mini appplications of the algorithm to pla minimization are also presented

after the fuzzy wave reached europe abstract we briefly describe the situation of the fuzzy community in europe before the fuzzy wave we show that there was a lot of expertise in almost all subareas of fuzzy logic then we describe some aspects of the fuzzy wave itself in particular fuzzy control and first generation fuzzy systems that played a role during the time the fuzzy wave reached europe we also make some remarks about european companies and their activities during this time then we discuss the situation after the fuzzy wave some aspects of second generation fuzzy systems the combination of fuzzy logic with other theories and techniques and some new application areas finally we will discuss the chances of fuzzy systems in europe in the future

derivation and application of an expert fuzzy optimal control system abstract this paper presents derivation of a fuzzy optimal controller which may be used to develop a knowledge based expert control system for supervising and tuning of conventional feedback control loops a general theory based on the conceptual framework for optimization in a fuzzy environment is presented for the development of linear and nonlinear fuzzy optimal control systems this technique is based on integration of the optimal control theorem and fuzzy variables the resulting expert controller is expressed in the form of linguistic fuzzy rules representing the knowledge base for tuning of the feedback control loops tuning inferences are made from the response of local feedback control loops by applying the compositional rule of inference to the knowledge base

a model reference control structure using a fuzzy neural network in this paper we present a design method for a model reference control structure using a fuzzy neural network we study a simple fuzzy logic based neural network system knowledge of rules is explicitly encoded in the weights of the proposed network and inferences are executed efficiently at high rate two fuzzy neural networks are utilized in the control structure one is a controller called the fuzzy neural network controller fnnc the other is an identifier called the fuzzy neural network identifier fnni adaptive learning rates for both the fnnc and fnni are guaranteed to converge by a lyapunov function the on line control ability robustness learning ability and interpolation ability of the proposed model reference control structure are confirmed by simulation results

solving boolean equations using rosop forms boolean equations are important tools in digital logic previous algorithms for solving boolean equations are based on the boolean algebra of disjoint sop forms in this paper we develop a new boolean algebra with more efficient boolean operation algorithms called the reduced ordered sop rosop forms which are canonical representations rosops are closely related to the well known obdd data structure the results here also show the algebraic structure of obdds

fuzzy self organizing controller and its application for dynamic processes abstract this paper deals with a self organizing controller used in real time and its application for dynamic processes the control policy of the controller is able to develop and improve automatically a new self organizing control algorithm which modifies the fuzzy control decision table is presented in this paper the control algorithm needs much less computation time and memory of the computer this paper provides two examples of the fuzzy self organizing control a set of experiment results is described it shows that the controller can be applied to some processes such as processes with time lag and non linearity or one whose parameter or running conditions are varied which were usually not controlled very well with a conventional controller

shellable nonpure complexes and posets ii this is a direct continuation of shellable nonpure complexes and posets i which appeared in transactions of the american mathematical society 348 1996 1299 1327 8 interval generated lattices and dominance order in this section and the following one we will continue exemplifying the applicability of lexicographic shellability to nonpure posets let f i1 i2 in be a family of intervals of integers by which is meant sets of the form a b a a 1 b a b we assume that there are no containments among these intervals and that they are ordered so that their left and right endpoints are increasing let l f be the lattice of all sets that are unions of subfamilies of f ordered by inclusion such interval generated lattices l f were introduced and studied by greene g define an edge labeling of l f as follows if a b is a covering and a max b a then a b a if a 1 a and a is the left endpoint of some i f

some additions to solution of switching equations based on a tabular algebra a method was presented by a l ruiz p p trabado and j o lopera see ibid vol 42 no 5 p 591 6 1993 for efficiently generating the solutions of boolean equations by using tables i e rectangular arrays or matrices of 0 s 1 s and dashes to represent boolean expressions some enhancements of their method are presented first it is shown how the uniting theorem can be applied directly to simplify tables then it is shown how to complement a table which would make their method henceforth referred to as rtl directly applicable to expressions containing complemented subexpressions the latter result allows the method to be extended from the solution of equations of the form f x 1 to equations of the form f x 0 and more generally to equations of the form f x g x or to simultaneous equations of the same types

credibility based chance constrained integer programming models for capital budgeting with fuzzy parameters in this paper we discuss a problem of capital budgeting in a fuzzy environment two types of models are proposed using credibility to measure confidence level since the proposed optimization problems are difficult to solve by traditional methods a fuzzy simulation based genetic algorithm is applied two numerical experiments demonstrate the effectiveness of the proposed algorithm

on pid controller tuning using orthonormal series identification abstract the step response of a closed loop system is identified by means of a laguerre expansion this offers certain advantages over arma models namely lack of bias in the estimates structural flexibility and the ability to precompute the regressors the laguerre coefficients of the retuned system are calculated in terms of the tuning constants and a quadratic performance index is optimized results from simulations and from industrial trials are given

studies on the output of fuzzy controller with multiple inputs abstract in this paper we discuss the output of a fuzzy controller in which an arbitrary number of fuzzy control inputs and an arbitrary number of fuzzy sets employed to fuzzify every linguistic variable are considered in the fuzzy control rules a rule base with a rule mapping concept is considered a defuzzifier with the general t norm and t conorm operators is formulated a triangular family is adopted so that the defuzzifier of the complete rule mapping is represented by a formula consisting of only some rules using a specific logic pair to evaluate values we derive that the output of the fuzzy controller can be simply represented by a linear parametric function of the inputs to the fuzzy controller

optimization of rational powered membership functions using extended kalman filter this paper presents an extension to the application of the extended kalman filter ekf in membership function mf optimization since the ekf is a derivative based method and derivative calculations of various mf shapes are too complicated so far only triangular type has been optimized via this approach in this article the ekf is applied in optimizing the rational powered mfs which are extended form of triangular trapezoidal functions and hence can offer better performance in almost all applications in addition because of the efficiency of the singleton mfs which makes them a common and desirable choice in hardware software realization of fuzzy systems these mfs are also optimized using the ekf the corresponding analytical equations and derivative formulas are given and finally the efficiency of the ekf in mf optimization is discussed

a method for closed loop automatic tuning of pid controllers abstract a simple method for the automatic tuning of pid controllers in closed loop is proposed a limit cycle is generated through a nonlinear feedback path from the process output to the controller reference signal the frequency of this oscillation is above the crossover frequency and below the critical frequency of the loop transfer function the amplitude and frequency of the oscillation are estimated and the control parameters are adjusted iteratively such that the closed loop transfer function from the controller reference to the process output attains a specified amplitude at the oscillation frequency

genetic algorithm based optimal fuzzy controller design in the linguistic space in this paper a genetic algorithm ga based optimal fuzzy controller design is proposed the design procedure is accomplished by establishing an index function as the consequent part of the fuzzy control rule the inputs of the controller after scaling are utilized by the index function for computing the output linguistic value this linguistic value can then be used to map the suitable fuzzy control actions this proposed novel fuzzy control rule has crisp input and fuzzified output characteristics the index function plays a role in mapping the desired fuzzy sets for defuzzification resulting in a controlled hypersurface in the linguistic space formed by the input fuzzy variables two types of index functions both linear and nonlinear are introduced for controlling systems with different degrees of nonlinearity the parameters of the index function are obtained by applying a simple ga with a suitable fitness function various controlled systems result in various parameter sets depending on their dynamics under the acquired optimal parameter set the optimal index function can be used to generate the desired control actions several simulation examples are given to verify the performance of the proposed ga based fuzzy controller

counterexamples to a fiber theorem we exhibit a counterexample to a fiber theorem stated by f fumagalli j algebra 283 2 2005 639 654 and show how it affects the rest of fumagalli s paper as a consequence whether the poset a p g is homotopy equivalent to a wedge of spheres for any finite solvable group g seems to remain an open question

group actions on arrangements of linear subspaces and applications to configuration spaces for an arrangement of linear subspaces in ri that is invariant under a finite subgroup of the general linear group gin ir we develop a formula for the g module structure of the cohomology of the complement m a our formula specializes to the well known goresky macpherson theorem in case g 1 but for g 1 the formula shows that the g module structure of the complement is not a combinatorial invariant as an application we are able to describe the free part of the cohomology of the quotient space ma4ig our motivating examples are arrangements in cn that are invariant under the action of sn by permuting coordinates a particular case is the k equal arrangement first studied by bj6rner lovasz and yao motivated by questions in complexity theory in these cases ma4 and ma sn are spaces of ordered and unordered point configurations in cn many of whose properties are reduced by our formulas to combinatorial questions in partition lattices more generally we treat point configurations in rd and provide explicit results for the k equal and the k divisible cases

multicriteria decision analysis with fuzzy pairwise comparisons abstract we present a modification of the fuzzy multi criteria method proposed by van laarhoven and pedrycz 1983 first the weights of the decision criteria are calculated by the minimization of a logarithmic regression function next the weights of the decision alternatives are calculated for each criterion separately lastly the fuzzy final scores of the alternatives are determined by an appropriate aggregationm of the calculated weights we will show that our modified method in contrast with the original one yields weights which are optimal with respect to the logarithmic regression function we also present a version of our method with geometric ratio scales rather than saaty s equi distant scale to quantify the gradations of human comparative judgement this approach also enables us to develop an efficient procedure for investigating the scale sensitivity of the calculated weights and the final scores of the alternatives

a rule self regulating fuzzy controller abstract the most effective way to improve the performance of a fuzzy controller may be to optimize the fuzzy control rules usually fuzzy control rules are generated by 1 translating the operators experience into fuzzy linguistic form directly 2 monitoring and summarizing the control behaviour of the operators 3 modelling the process to be controlled using fuzzy set theory 4 self organizing in running of the control systems different from the above means the authors in 10 have proposed a method to regulate fuzzy control rules where the control rules are represented by an analytic expression with a regulating factor the authors in this paper employ such a method and use a simplified fuzzy control algorithm which allows fuzzy control rules to be regulated on line thus constructing a rule self regulating fuzzy controller rsfc simulation results demonstrate that the performance of rsfc is better than that of a non rule regulating fuzzy controller

building a model based fuzzy controller a new form of fuzzy model based controller is introduced the new controller is based on a conventional predictive controller design but utilises a fuzzy relational model the controller is described and compared with existing fuzzy controllers practical advice is given on generating suitable relational models for control purposes and an appropriate identification algorithm is recommended the controller is tested on a liquid level process and its performance compared to another fuzzy model based controller which has been previously reported

the size of reduced obdd s and optimal read once branching programs for almost all boolean functions boolean functions are often represented by ordered binary decision diagrams obdds introduced by bryant 1986 liaw and lin 1992 have proved upper and lower bounds on the minimal obdd size of almost all boolean functions now tight bounds are proved for the minimal obdd size for arbitrary or optimal variable orderings and for the minimal read once branching program size of almost all functions almost all boolean functions have a sensitivity of almost 1 i e the minimal obdd size for an optimal variable ordering differs from the minimal obdd size for a worst variable ordering by a factor of at most 1 spl epsi n where spl epsi n converges exponentially fast to 0

fuzzy controllers synthesis and equivalences it has been proved that fuzzy controllers are capable of approximating any real continuous control function on a compact set to arbitrary accuracy in particular any given linear control can be achieved with a fuzzy controller for a given accuracy the aim of this paper is to show how to automatically build this fuzzy controller the proposed design methodology is detailed for the synthesis of a sugeno or mamdani type fuzzy controller precisely equivalent to a given pi controller the main idea is to equate the output of the fuzzy controller with the output of the pi controller at some particular input values called modal values the rule base and the distribution of the membership functions can thus be deduced the analytic expression of the output of the generated fuzzy controller is then established for sugeno type fuzzy controllers precise equivalence is directly obtained for mamdani type fuzzy controllers the defuzzification strategy and the inference operators have to be correctly chosen to provide linear interpolation between modal values the usual inference operators satisfying the linearity requirement when using the center of gravity defuzzification method are proposed

control of dynamical processes using an on line rule adaptive fuzzy control system abstract in this paper we present a detailed discussion on the design of a rule adaptive fuzzy control system along with simulation analysis demonstrating its usefulness in controlling plants of various dynamical natures conceived first by wang and further clarified in 8 the rule adaptive fuzzy controller considered here generates the fuzzy control signal as a convex combination of the standard fuzzy inputs to the controller the error and the error rate such a combination is automatically adjusted on line in response to the varying control situations with certain updating scheme this paper considers two different updating schemes the first one is based on a fuzzy relationship and is a revision of the rule presented in 11 the present paper also proposes the second updating rule that is essentially a nonlinear differential equation both of the rules are applied to the simulations of several selected dynamical plants the simulation results show that the controller is effective in controlling a wide range of dynamical plants especially it shows better performance in controlling the plants found difficult to be controlled by the conventional means the simulation also shows that the controller can be used to curb the effect of load disturbance in the control process

a lefschetz fixed point theorem for multivalued maps of finite spaces we prove a version of the lefschetz fixed point theorem for multivalued maps f x multimap x in which x is a finite t 0 space

elementary abelian subgroups in p groups with a cyclic derived subgroup let p be an arbitrary prime and let p be a finite p group the general objective of this paper is to obtain refined information on the homotopy type of the poset of all non trivial elementary abelian subgroups of p ordered by inclusion and the poset of all elementary abelian subgroups of p of rank at least 2

homotopy types of subspace arrangements via diagrams of spaces we prove combinatorial formulas for the homotopy type of the union of the subspaces in an affine compactified affine spherical or projective subspace arrangement from these formulas we derive results of goresky macpherson on the homology of the arrangement and the cohomology of its complement the union of an arrangement can be interpreted as the direct limit of a diagram of spaces over the intersection poset a closely related space is obtained by taking the homotopy direct limit of this diagram our method consists in constructing a combinatorial model diagram over the same poset whose homotopy limit can be compared to the original one by usual homotopy comparison results for diagrams of spaces

generating rules for fuzzy logic controllers by functions abstract in this paper we introduce a method of generating control rules for fuzzy logic controllers called parametric functions method by this method we can obtain control rules by adjusting several parameters

on the homotopy type of the quillen complex of finite soluble groups abstract we prove that the homotopy type of the quillen complex of a finite soluble group at the prime p 2 is that of a wedge of spheres of possible different dimensions

finding the optimal variable ordering for binary decision diagrams the ordered binary decision diagram is a canonical representation for boolean functions presented by r e bryant 1985 as a compact representation for a broad class of interesting functions derived from circuits however the size of the diagram is very sensitive to the choice of ordering on the variables hence for some applications such as differential cascode voltage switch dcvs trees it becomes extremely important to find the ordering leading to the most compact representation an algorithm for this problem with time complexity o n sup 2 3 sup n is presented this represents an improvement over the previous best algorithm

a self tuning fuzzy controller abstract the aim of a fuzzy controller is to compensate the dynamic characteristics of the controlled system it is the same purpose as for the fuzzy logic controller flc now the best design of the flc is required for achievement of this purpose but such a controller has not yet been completely designed because the fuzzy controller is constructed of control rules which are ambiguously described by conventional controller strategies and expert knowledge and because its structure theory is not well established yet that is in order to construct the best rules a highly skilled technique and a tuning technique using trial and error are required as a way to easily design a flc a method which improves a given standard flc is considered in this paper we propose a self tuning algorithm of the flc it has two functions in adjusting the scaling factors which are the parameters of the flc and in improving the control rules of flc by evaluating the control response at real time and the control results after operations we add these functions to the flc and design the self tuning fuzzy controller stfc this makes the flc a good controller

fuzzy optimal control the problem of fuzzy optimal control of nonlinear systems is formulated and solved on the basis of fuzzy mathematical programming the fuzzy optimal control problem is extended to the case of multicriteria optimal control a particular case of fuzzy optimal control with fuzzy objective function and crisp transversality conditions is also considered

scaling of fuzzy controllers using the cross correlation the paper deals with the optimal adjustment of input scaling factors for fuzzy controllers fcs the method is based on the assumption that in the stationary case an optimally adjusted input scaling factor meets a specific statistical input output dependence a measure for the strength of statistical dependence is the correlation function and the correlation coefficient respectively without loss of generality the adjustment of input scaling factors using correlation functions is pointed out by means of a single input single output siso system first the paper deals with the so called equivalent gain which is closely connected to the cross correlation of the controller input and the defuzzified controller output next it considers the computation of correlation functions and their representation inside the fc the paper concludes with an example of a system of fuzzy rules controlling a redundant robot manipulator

on line off line optimization of complex processes using a linguistic self organized optimizing control scheme abstract chemical processes usually have a complicated structure and are subjected to unknown long term and short term disturbances many process optimization schemes were developed under the assumption of the existence of a model that can predict the process steady state and or dynamics however such a model may not be precise nor even exist a rule based methodology without the need of such a model is hence developed in this work the optimizing control scheme developed here is actually a combination of a modified version of the linguistic control scheme developed by procyk and mamdani and the concept of reduced gradient optimization it is assumed that the objective function and constraints of the optimization problem are functions of manipulated variables and measurements only the optimizing control algorithm is also formulated into a look up table the rule based optimizing control scheme possesses three important properties adapting learning and decision making some numerical examples of multivariable nature and constrained situations are solved by this approach and compared with well known approaches it is shown that the method is superior to the previous methods a process system consisting of a series of cstr has been simulated as an illustrative example the simulation results show that the optimizing control scheme is promising and should be of interest to process industry

negation trees a unified approach to boolean function complementation boolean function complementation is a basic operation of boolean algebra for functions given in sop form the complementation methods include the demorgan s law sharp disjoint sharp unate complementation recursive and sasao s method this paper accomplishes three purposes 1 it exposes an underlying unification of the existing complementation algorithms it is proven that a unate complementation and sharp are the same as the demorgan law algorithm b sasao s algorithm is the same as disjoint sharp c disjoint sharp is a special case of the recursive method 2 it proposes negation trees for the representation of functions and their complements 3 it gives faster algorithms for finding complements of functions in sop form based on negation trees

top homology of hypergraph matching complexes p cycle complexes and quillen complexes of symmetric groups abstract we investigate the representation of a symmetric group s n on the homology of its quillen complex at a prime p for homology groups in small codimension we derive an explicit formula for this representation in terms of the representations of symmetric groups on homology groups of p uniform hypergraph matching complexes we conjecture an explicit formula for the representation of s n on the top homology group of the corresponding hypergraph matching complex when n 1 mod p our conjecture follows from work of bouc when p 2 and we prove the conjecture when p 3

fuzzy adaptive control of a first order process abstract fuzzy adaptive control of a first order process with a varying gain and time constant is demonstrated the fuzzy adaptive controller is based on a fuzzy model based controller that uses an explicit fuzzy model of the process adaptation is achieved by the addition of on line identification of the fuzzy process model starting with a crude initial model the adaptive controller matches the model to the process to self tune the controller the model is further modified when the operating point is changed to adapt the controller to the new process conditions two different fuzzy identification algorithms are both shown to provide a successful fuzzy adaptive controller the robustness of the algorithms in the presence of process noise is investigated and improved by the addition of weighting factors

on the obdd representation of general boolean functions the behavior of ordered binary decision diagrams obdd for general boolean functions is studied a tight upper bound of 2 sup n n 2 epsilon for the worst case obdd size is derived although the size of an obdd is dependent on the ordering of decision variables it is shown that almost all functions are not sensitive to variable ordering

risk curve and fuzzy portfolio selection in stochastic environment variance semivariance and probability of a bad outcome are three popular definitions of risk for portfolio selection in fuzzy environment variance is carried on as the definition of risk however in real life risk is understood in many different ways in this paper we propose a new definition of risk for portfolio selection in fuzzy environment based on this new definition a new type of model is provided to give a general solution to the new model problem a hybrid intelligent algorithm is designed one numerical example is also presented to illustrate the optimization idea and the effectiveness of the designed algorithm

self learning fuzzy controllers based on temporal backpropagation a generalized control strategy that enhances fuzzy controllers with self learning capability for achieving prescribed control objectives in a near optimal manner is presented this methodology termed temporal backpropagation is model sensitive in the sense that it can deal with plants that can be represented in a piecewise differentiable format such as difference equations neural networks gmdh structures and fuzzy models regardless of the numbers of inputs and outputs of the plants under consideration the proposed approach can either refine the fuzzy if then rules of human experts or automatically derive the fuzzy if then rules if human experts are not available the inverted pendulum system is employed as a testbed to demonstrate the effectiveness of the proposed control scheme and the robustness of the acquired fuzzy controller

on commuting and non commuting complexes in this paper we study various simplicial complexes associated to the commutative structure of a finite group g we define nc g resp c g as the complex associated to the poset of pairwise non commuting resp commuting sets of nontrivial elements in g we observe that nc g has only one positive dimensional connected component which we call bnc g and we prove that bnc g is simply connected our main result is a simplicial decomposition formula for bnc g

poset fiber theorems suppose that f p q is a poset map whose fibers f 1 qless than or equal to q are sufficiently well connected our main result is a formula expressing the homotopy type of p in terms of q and the fibers several fiber theorems from the literature due to babson baclawski and quillen are obtained as consequences or special cases homology cohen macaulay and equivariant versions are given and some applications are discussed

a stability approach to fuzzy control design for nonlinear systems abstract by the application of fuzzy set theory a method for feedback control of nonlinear systems based on the principle of sliding mode control is developed called fuzzy sliding mode control the control method provides a simple way to achieve asymptotic stability of the systems other attractive features of the method include a minimal realization of the fuzzy controller and robustness against model uncertainties and external disturbances in addition the method is capable of handling the chattering problem inherent to sliding mode control simply and effectively a simulation study of an inverted pendulum system is presented to demonstrate these features of the method also it is indicated that the method is easy to use for practicing control engineers

on the edge of the stable range we prove a general homological stability theorem for certain families of groups equipped with product maps followed by two theorems of a new kind that give information about the last two homology groups outside the stable range these last two unstable groups are the edge in our title applying our results to automorphism groups of free groups yields a new proof of homological stability with an improved stable range a description of the last unstable group up to a single ambiguity and a lower bound on the rank of the penultimate unstable group we give similar applications to the general linear groups of the integers and of the field of order 2 this time recovering the known stability range the results can also be applied to general linear groups of arbitrary principal ideal domains symmetric groups and braid groups our methods require us to use field coefficients throughout

boolean sets and most general solutions of boolean equations the aim of this paper is twofold first we determine the most general form of the subsumptive general solution of a boolean equation theorems 1 and 2 then we discuss several characterizations of boolean sets meaning sets of zeros of boolean functions and prove that every boolean transformation email protected t is the parametric general solution of a certain boolean equation