fuzzy interval optimal control problem abstract this paper proposes the discrete time fuzzy interval optimal control problem via single level constrained fuzzy arithmetic fuzzy interval functions are established and allow us to evaluate the dynamics of the fuzzy interval difference equation moreover fuzzy interval dynamic programming is developed to obtain the optimal fuzzy interval solution helping us to make a realistic decision a numerical example illustrates the theory and provides the practical solution for an user

on stability of fuzzy systems expressed by fuzzy rules with singleton consequents addresses the issue of stability of a fuzzy system described by fuzzy rules with singleton consequents it first presents two canonical forms of a fuzzy system a parametric expression and a state space expression a fuzzy system with singleton consequents is found to be a piecewise polytopic affine system then the paper gives stability theorems for a discrete time system as well as for a continuous time system it also gives a brief survey on the stability issues of fuzzy control systems

on a 2 generated infinite 3 group the presentation problem the author and narain gupta constructed in 3 a family of residually finite 2generated infinite p groups for every odd prime p as groups of automorphisms of regular p trees this was inspired by grigorchuk s construction in z of a 3 generated infinite 2 group as a permutation group of subintervals of the unit interval in 6 merzlyakov relates grigorchuk s group to p groups constructed by aleshin in 1972 l by using automatas the regularity of our definitions has allowed us to generalize our earlier constructions see 4 and gave us ready access to some of their special properties see 51 the prototype of all our constructions has been the infinite 3 group

on the generalization of single input rule modules connected type fuzzy reasoning method yubazaki have proposed a ldquosingle input rule modules connected type fuzzy reasoning method sirms method rdquo in which its final output is obtained by summarizing the product of importance degree and inference result from single input fuzzy rule modules this paper proposes a ldquofunctional type sirms method rdquo which is an extended version of the sirms method and clarifies the relationship between the takagi sugeno t s reasoning method and the functional type sirms method the functional type sirms method can be shown to be transformed to the t s reasoning method but generally the conversion to functional type sirms method from the t s reasoning method is impossible it is shown however that the t s reasoning method can be transformed to the functional type sirms method when the t s reasoning method fills some conditions for this reason it is shown that the functional type sirms method is the subset of the t s reasoning method

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 automorphism tower of groups acting on rooted trees the group of isometries aut t n of a rooted n ary tree and many of its subgroups with branching structure have groups of automorphisms induced by conjugation in aut t n this fact has stimulated the computation of the group of automorphisms of such well known examples as the group studied by r grigorchuk and the group f studied by n gupta and the second author in this paper we pursue the larger theme of towers of automorphisms of groups of tree isometries such as and we describe this tower for all subgroups of aut t 2 which decompose as infinitely iterated wreath products furthermore we fully describe the towers of and r more precisely the tower of is infinite countable and the terms of the tower are 2 groups quotients of successive terms are infinite elementary abelian 2 groups in contrast the tower of f has length 2 and its terms are 2 3 groups we show that aut 2 aut is an elementary abelian 3 group of countably infinite rank while aut 3 aut 2

sirms connected fuzzy inference method adopting emphasis and suppression the single input rule modules connected fuzzy inference method sirms method can decrease the number of fuzzy rules drastically in comparison with the conventional fuzzy inference methods however the inference results obtained by the sirms method is generally simple compared with those of the conventional fuzzy inference methods for example the sirms method may be not equivalent to the product sum gravity method and fuzzy singleton type inference method if the fuzzy sets of the antecedent parts are limited to normal fuzzy sets in this paper we propose a fuzzy singleton type sirms method which weights the rules of the sirms method in order to solve the above problem this paper also clarifies the property of the fuzzy singleton type sirms method from the view point of equivalence and monotonicity moreover the fuzzy singleton type sirms method is shown to be superior to the conventional sirms method by applying to a medical diagnosis system

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

on subgroups of finite index in branch groups we give a structural description of the normal subgroups of subgroups of finite index in branch groups in terms of rigid stabilizers this gives further insight into the structure lattices of branch groups introduced by the second author we derive a condition concerning abstract commensurability of branch groups acting on the p ary tree for any prime p

realization of nonlinear and linear pid controls using simplified indirect fuzzy inference method abstract in this paper we propose a more practical method for realizing nonlinear and linear pid controls using fuzzy inference methods than previous ones this proposed method is based on the fact that not only nonlinear but also linear pid control can be easily realized by applying the simplified indirect fuzzy inference method for fuzzy control to few fuzzy control rules with a simple structure therefore we first show that nonlinear pid control which is based on a conventional pid controller can be realized using this proposed method secondly we show that linear pid control can also be realized simply by replacing the arctan with the linear membership function in the antecedent part of the fuzzy control rules

expected value of fuzzy variable and fuzzy expected value models this paper will present a novel concept of expected values of fuzzy variables which is essentially a type of choquet integral and coincides with that of random variables in order to calculate the expected value of general fuzzy variable a fuzzy simulation technique is also designed finally we construct a spectrum of fuzzy expected value models and integrate fuzzy simulation neural network and genetic algorithms to produce a hybrid intelligent algorithm for solving general fuzzy expected value models

on the automorphism group of the one rooted binary tree abstract let a be the automorphism group of the one rooted regular binary tree t 2 and g the subgroup of a consisting of those automorphisms admitting a finite description in their action on t 2 let n a g be the normaliser of g in a let aut g be the group of automorphisms of g and let end a g be the semigroup of endomorphisms of g induced by conjugation by elements of a then g is the infinite iterated wreath product c 2 c 2 and a is the topological limit of g we study in some detail the structure of g aut g and end a g in particular we prove n a g is isomorphic to aut g contains a copy of a itself and is a proper subgroup of end a g furthermore we discuss connections with automata and introduce the notion of functionally recursive automorphisms of t 2

on a 2 generated infinite 3 group subgroups and automorphisms this is the second paper dedicated to a detailed study of the infinite 3 group j 74 r 1 3 rr 3 1 y y ct 2 l a recursive definition to be explained later which was introduced by the author and narain gupta in 2 as a group of automorphisms of an infinite regular tree f as was shown in 4 y has the remarkable properties of containing a copy of every finite 3 group and having all its proper quotients finite the first paper s in this detailed study 99 dealt with the presentation problem here we study further aspects of its subgroup structure our prime objective though is to determine the group of automorphisms of 9 this task represents a large portion of our present paper the main results are as follows

a proposal of sirms dynamically connected fuzzy inference model for plural input fuzzy control single input rule modules sirms dynamically connected fuzzy inference model is proposed for plural input fuzzy control for each input item a sirm is constructed and a dynamic importance degree is defined the dynamic importance degree consists of a base value insuring the role of the input item through a control process and a dynamic value changing with control situations to adjust the dynamic importance degree each dynamic value can be easily tuned based on the local information of current state the model output is obtained by summarizing the products of the dynamic importance degree and the fuzzy inference result of each sirm the controller constructing method for constant value control systems is given and constant value controls of typical first and second order lag plants are tested the simulation results show that by using the proposed mode the reaching time can be reduced by more than 15 without any steady state error overshoot or vibration compared with the sirms fixed importance degree connected fuzzy inference model the proposed model is further successfully applied to stabilization control of an inverted pendulum system including the position control of the cart

on the equivalence conditions of fuzzy inference methods part 1 basic concept and definition this paper addresses equivalence of fuzzy inference methods it first presents several well known fuzzy inference methods the product sum gravity method the simplified fuzzy inference method the fuzzy singleton type inference method the single input rule modules connected type fuzzy inference method sirms method and the single input connected fuzzy inference method sic method second three fuzzy inference methods of the product sum gravity method simplified fuzzy inference method and fuzzy singleton type inference method which are all widely used as fuzzy control methods are shown to be equivalent to each other third the equivalence conditions between the sirms method and the sic method known as single input type fuzzy inference method are shown finally it also gives the equivalence conditions between the single input type fuzzy inference methods and the previous three fuzzy inference methods investigating the equivalence among various fuzzy inference methods would help to understand the relationship of those fuzzy inference methods

analysis and design of functionally weighted single input rule modules connected fuzzy inference systems the single input rule modules sirms connected fuzzy inference method can efficiently solve the fuzzy rule explosion phenomenon which usually occurs in the multivariable modeling and or control applications however the performance of the sirms connected fuzzy inference system sirm fis is limited due to its simple input output mapping in this paper to further enhance the performance of sirm fis a functionally weighted sirm fis fwsirm fis which adopts multivariable functional weights to measure the important degrees of the sirms is presented then in order to show the fundamental differences of the sirms methods properties of the traditional sirm fis the type 2 sirm fis t2sirm fis the functional sirm fis fsirm fis the sirms model with single variable functional weights sirm fw and fwsirm fis are explored these properties demonstrate that the proposed fwsirm fis has more general and complex input output mapping than the existing sirms methods such properties theoretically guarantee that better performance can be achieved by fwsirm fis furthermore based on the least squares method a novel data driven optimization method is presented for the parameter learning of fwsirm fis it can also be used to optimize the parameters of sirm fis t2sirm fis fsirm fis and sirm fw due to the properties of the least squares method the proposed parameter learning algorithm can overcome the drawbacks of the gradients based parameter learning methods and obtain both smallest training errors and smallest parameters finally to show the effectiveness and superiority of fwsirm fis and the proposed optimization method six examples and detailed comparisons are given simulation results show that fwsirm fis can obtain better performance than the other sirms methods and compared with some well known methods fwsirm fis can achieve similar or better performance but has much less parameters and faster training speed

relatively free semigroups of intermediate growth abstract the problem of calculating the growth of a finitely generated f g semigroup satisfying the given system of identities is considered examples of relatively free semigroups having intermediate growth new growth criteria and constructions are given the main ideas employed in the proofs are based on some new points of view on growth our method is also useful for constructing various examples of f g nilpotent and nil semigroups having intermediate growth and arbitrarily small gelfand kirillov superdimension

a new fuzzy controller for stabilization of parallel type double inverted pendulum system a new fuzzy controller with 6 input items and 1 output item for stabilizing a parallel type double inverted pendulum system is presented based on the single input rule modules sirms dynamically connected fuzzy inference model each input item is assigned with a sirm and a dynamic importance degree the sirms and the dynamic importance degrees are designed such that the angular control of the longer pendulum takes the highest priority over the angular control of the shorter pendulum and the position control of the cart when the angle of the longer pendulum is big by using the sirms and the dynamic importance degrees the priority orders of the three controls are automatically adjusted according to control situations the proposed fuzzy controller has a simple and intuitively understandable structure and executes the three controls entirely in parallel simulation results show that the proposed fuzzy controller can stabilize completely a parallel type double inverted pendulum system within 10 0 s for a wide range of the initial angles of the two pendulums this is the first result for a fuzzy controller to achieve successfully complete stabilization control of a parallel type double inverted pendulum system

a systematic study of fuzzy pid controllers function based evaluation approach a function based evaluation approach is proposed for a systematic study of fuzzy proportional integral derivative pid like controllers this approach is applied for deriving process independent design guidelines from addressing two issues simplicity and nonlinearity to examine the simplicity of fuzzy pid controllers we conclude that direct action controllers exhibit simpler design properties than gain scheduling controllers then we evaluate the inference structures of direct action controllers in five criteria control action composition input coupling gain dependency gain role change and rule parameter growth three types of fuzzy pid controllers using one two and three input inference structures are analyzed the results according to the criteria demonstrate some shortcomings in mamdani s two input controllers for keeping the simplicity feature like a linear pid controller a one input fuzzy pid controller with one to three mapping inference engine is recommended we discuss three evaluation approaches in a nonlinear approximation study function estimation based generalization capability based and nonlinearity variation based approximations the study focuses on the last approach a nonlinearity evaluation is then performed for several one input fuzzy pid controllers based on two measures nonlinearity variation index and linearity approximation index using these quantitative indices one can make a reasonable selection of fuzzy reasoning mechanisms and membership functions without requiring any process information from the study we observed that the zadeh mamdani s max min gravity scheme produces the highest score in terms of nonlinearity variations which is superior to other schemes such as mizumoto s product sum gravity and takagi sugeno kang schemes

functional equivalence between radial basis function networks and fuzzy inference systems it is shown that under some minor restrictions the functional behavior of radial basis function networks rbfns and that of fuzzy inference systems are actually equivalent this functional equivalence makes it possible to apply what has been discovered learning rule representational power etc for one of the models to the other and vice versa it is of interest to observe that two models stemming from different origins turn out to be functionally equivalent

optimization problems in the theory of continuous trading a unified approach based on stochastic analysis to the problems of option pricing consumption investment and equilibrium in a financial market with asset prices modelled by continuous semi martingales is presented for the first of these problems the valuation of both european and american contingent claims is discussed the former can be exercised only at a specified time t the maturity date whereas the latter can be exercised at any time in 0 t notions and results from the theory of optimal stopping are employed in the treatment of american options a general consurption investment problem is also considered for an agent whose actions cannot affect the market prices and whose intention is to maximize total expected utility of both consumption and terminal wealth under very general conditions on the utility functions of the agent it is shown how to approach the above problem by considering separately the two more elementary ones of maximizing utility from consumption only and of maxim

fuzzy optimal control of linear quadratic models optimal control is a very important field of study not only in theory but in applications based on the concept of fuzzy process a fuzzy optimal control model is investigated with a quadratic objective functional for a linear fuzzy control system

on the burnside problem for periodic groups narain gupta 1 and said sidki 2 1 university of manitoba department of mathematics winnipeg manitoba r3t 2n2 canada 2 university of brasilia department of mathematics brasilia d f brazil introduction the generalized burnside problem refers to the question are finitely generated periodic groups finite this was answered in the negative by golod 1 who proved that for each prime p there exists a finitely generated infinite p group golod s construction in not however direct and is based on his celebrated work with safarevi recently grigor uk 2 has given a direct and elegant construction of an infinite 2 group which is generated by three elements of order 2 in this paper we give for each odd prime p a direct construction of an infinite p group on two generators each of order p our group is a subgroup of the automorphism group of a regular tree of degree p and as might be expected it is residually finite and has infinite exponent preliminaries let p be an odd prime and let t 0 be the infinite regular tree of degree p with vertex 0 so that through each vertex u of t 0 there are p regular subtrees

realization of pid controls by fuzzy control methods abstract this paper shows that pid controllers can be realized by fuzzy control methods of product sum gravity method and simplified fuzzy reasoning method pid controllers however cannot be constructed by min max gravity method known as mamdani s fuzzy reasoning method furthermore extrapolative reasoning can be executed by the product sum gravity method and simplified fuzzy reasoning method by extending membership functions of antecedent parts of fuzzy rules

approximate reasoning on a basis of z number valued if then rules approximate reasoning is about reasoning with imperfect information nowadays a large diversity of approaches to approximate reasoning with fuzzy information and fuzzy type 2 information exists it should be stressed however that real world imperfect information is characterized by combination of fuzzy and probabilistic uncertainties which is referred to as bimodal information in view of this zadeh introduced the concept of a z number regarded as an ordered pair z a b of fuzzy numbers a and b where a is a linguistic value of a variable of interest and b is a linguistic value of probability measure of a playing a role of its reliability unfortunately up to day there is no research on approximate reasoning realized on the basis of if then rules with z number valued antecedents and consequents briefly z rules zadeh addressed this problem as related to an uncharted territory in this paper a new approach is developed to study approximate reasoning with z rules on a basis of linear interpolation we provide an application of the approach to job satisfaction evaluation and to students educational achievement evaluation problems related to psychological and perceptual issues naturally characterized by imperfect information the obtained results show applicability and validity of the proposed approach

comparison of fuzzy reasoning methods l a zadeh e h mamdani and m mizumoto et al have proposed methods for fuzzy reasoning in which the antecedent involves a fuzzy conditional proposition if x is a then y is b with a and b being fuzzy concepts mizumoto et al have investigated the properties of their methods in the case of generalized modus ponens this paper deals with the properties of their methods in the case of generalized modus tollens and investigates the other new fuzzy reasoning methods obtained by introducing the implication rules of many valued logic systems finally the properties of syllogism and contrapositive are investigated under each fuzzy reasoning method

fuzzy incremental control algorithm of loop heat pipe cooling system for spacecraft applications reliable and high precision thermal control technologies are essential for the safe flight of advanced spacecraft a fuzzy incremental control strategy is proposed for control of an lhp space cooling system comprising a loop heat pipe and a variable emittance radiator with mems louver the generating and performing algorithm of the fuzzy control rules is provided with an analytical form based on the understanding of dynamics and control mechanisms of the space cooling system this paper also presents a novel integrated mathematical model for the dynamic analysis of the lhp space cooling system and a numerical evaluation of the investigated control schemes numerical simulation results on the closed loop control effects suggest that the proposed control strategy takes advantage of no steady error small overshoots and short settling times thus benefiting safe highly accurate and reliable operation of the entire space cooling system the overshoots of the most important operating parameters t o b q r and p under the proposed fuzzy incremental control have been reduced to 16 3 17 6 and 18 6 of the compared pid control s while the respective settling times have been shortened to 33 9 42 3 and 30 5 of the reference values

on the monotonicity of fuzzy inference methods related to t s inference method yubazaki et al have proposed a single input rule modules connected type fuzzy inference method sirms method whose final output is obtained by combining the products of the importance degrees and the inference results from single input fuzzy rule modules moreover seki et al have proposed a functional type sirms method whose consequent parts are generalized to functions from real numbers it is expected that inference results from the functional type sirms method are monotone if the antecedent parts and the consequent parts of fuzzy rules in the functional type sirms rule modules are monotone however this paper points out that even if consequent parts in the functional type sirms rule modules are monotone the inference results are not necessarily monotone when the antecedent parts are noncomparable fuzzy sets and it clarifies the conditions for the monotonicity of inference results from the functional type sirms method moreover for the takagi sugeno t s inference method the monotonicity condition is clarified in the case of two inputs by using the equivalence relation of fuzzy inference

upswing and stabilization control of inverted pendulum system based on the sirms dynamically connected fuzzy inference model abstract a new fuzzy controller is presented based on the single input rule modules sirms dynamically connected fuzzy inference model for upswing and stabilization control of inverted pendulum system the fuzzy controller takes the angle and angular velocity of the pendulum and the position and velocity of the cart as its input items and the driving force as its output item each input item is assigned with a sirm and a dynamic importance degree when the pendulum locates at the pending domain the fuzzy controller becomes an upswing controller by using the saturation feature of the membership functions of the pendulum angle when the pendulum locates at the upright domain the fuzzy controller then becomes a stabilization controller and realizes smoothly the pendulum angular control and the cart position control in parallel by using the sirms and the dynamic importance degrees the fuzzy controller has a simple structure and is easily understandable compared with the other approaches simulation results show that the fuzzy controller can swing up the pendulum from the pending position and then stabilize the whole system in about 3 0 s