fuzzy group theory a comparison of different notions of product of fuzzy sets the notion of penultimate subgroup of a fuzzy group is introduced this leads to the concept of penultimate product of fuzzy subgroups a detailed study of different notions of product of fuzzy sets in a groupoid is carried out the ultimate superiority of liu s set product is established level subsets and strong level subsets of these products are also analysed consequently simplified proofs of some of the results on free product are obtained

non linear observer design by transformation into a generalized observer canonical form an observer design method for a certain class of non linear single output systems is introduced the characteristic feature of this method consists of the fact that it does not require any linearization in the way that the given non linear system is approximated by a linear one the present paper deals with the derivation of a transformation of the considered non linear system into a generalized observer canonical form gocf which enables a systematic observer design similar to the linear one based on the well known linear observer canonical form to assign conditions for its existence the transformation into the gocf is carried out in two steps via a generalized observability canonical form gobcf in contrast to previous forms used for linear systems the two non linear canonical forms presented here also depend on the time derivatives of the input variables this means that the resulting observer has to be supplied not only with the input and output variables of the given system but also with deri

restricted dynamic observer error linearizability following the general dynamic observer error linearization problem state equivalence to a triangular nonlinear observer canonical form with index d and the restricted dynamic observer error linearization problem are defined in this paper the necessary and sufficient conditions for the above two problems are given since our proofs are constructive a desired state transformation can also be found in the theorem

some properties of fuzzy groups on definit des sous groupes flous normaux des sous groupes flous normaux de niveau et leurs homomorphismes et on donne certaines de leurs proprietes

a fuzzy subgroupoid which is not a fuzzy group abstract we give an example to show that the proposition a fuzzy subgroupoid of a group must be a fuzzy group which appeared in fuzzy sets and systems 51 1992 105 109 structure and constructing of fuzzy subgroups of a group by l filep is wrong we also point out that the proof of theorem 6 in the same article is not true we give a valid proof of it

fuzzy subgroups having the property ii abstract in 3 the notion of the property of a fuzzy subgroup of a group which is a more fuzzified notion of the notion of a generalized characteristic fuzzy subgroup of a finite group is introduced in this paper we show that a generalized characteristic fuzzy subgroup of any group has always the property

time scaling for observer design with linearizable error dynamics in this paper we consider the problem of observer design for dynamical systems with scalar output by linearization of the error dynamics via coordinate change output injection and time scaling we present necessary and sufficient conditions which guarantee the existence of a coordinate change and output dependent time scaling such that in the new coordinates and with respect to the new time the system has linear error dynamics

some characterizations of fuzzy subgroups abstract we show that if a fuzzy subgroup can be written as the intersection of all its minimal fuzzy p subgroups or the intersection of all its minimal fuzzy p subgroups then some properties of the fuzzy subgroup characterize the properties of all its minimal fuzzy p subgroups or all its minimal fuzzy p subgroups and investigate interrelationships among some properties of fuzzy subgroups

fuzzy normal subgroups and fuzzy cosets abstract we introduce here the notion of 1 i a fuzzy normal subgroup and 2 ii a fuzzy coset we prove that for a group g a fuzzy subgroup is fuzzy normal if and only if it is constant on the conjugate classes of g further we show that the level subgroups of a fuzzy normal subgroup are all normal we obtain several results which are analogs of some basic theorems of group theory in particular a fuzzy version of lagrange s theorem is established

finite time observers application to secure communication in this paper control theory is used to formalize finite time chaos synchronization as a nonlinear finite time observer design issue this paper introduces a finite time observer for nonlinear systems that can be put into a linear canonical form up to an output injection the finite time convergence relies on the homogeneity properties of nonlinear systems the observer is then applied to the problem of secure data transmission based on the finite time chaos synchronization and the two channel transmission method

fuzzy groups some group theoretic analogs abstract we introduce the concepts of 1 order of a fuzzy subgroup of a finite group 2 a fuzzy abelian group and 3 a fuzzy solvable group we obtain some results involving these notions which are analogs of results from group theory also we prove analogs of two basic theorems of group theory namely cayley s theorem and lagrange s theorem

a contribution to the theory of fuzzy subgroups abstract in this paper we continue our study in order to give a partial answer to the question suggested by asaad in 1991 what can be said about the structure of a group g when the information are known about the structure of a fuzzy subgroup a of g and viceversa

fuzzy sylow subgroups abstract an attempt is made to define a fuzzy sylow p subgroup of a finite group some basic results regarding sylow p subgroups are extended to the fuzzy setting in particular fuzzy versions of sylow s theorems are obtained

tropical implementation of the analytical hierarchy process decision method abstract we apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the analytic hierarchy process in multi criteria problems of rating alternatives from pairwise comparison data in this framework we first consider the minimax chebyshev approximation of pairwise comparison matrices by consistent matrices in the logarithmic scale recasting this approximation problem as a problem of tropical pseudo quadratic programming we then write out a closed form solution to it this solution might be either a unique score vector up to a positive factor or a set of different score vectors to handle the problem when the solution is not unique we develop tropical optimization techniques of maximizing and minimizing the hilbert seminorm to find those vectors from the solution set that are the most and least differentiating between the alternatives with the highest and lowest scores and thus are well representative of the entire solution set

extended valued topical and anti topical functions on semimodules in the papers 16 and 17 we have studied functions defined on a b complete idempotent semimodule x over a b complete idempotent semifield k k with values in k where k may or may not contain a greatest element supk and the residuation x y is not defined for x x and y infx in the present paper we assume that k has no greatest element then adjoin to k an outside greatest element supk and extend the operations and from k to k k so as to obtain a meaning also for x infx for any x x and study functions with values in k in fact we consider two different extensions of the product from k to k denoted by and respectively and use them to give characterizations of topical i e increasing homogeneous defined with the aid of and anti topical i e decreasing anti homogeneous defined with the aid of functions in terms of some inequalities next we introduce and study for functions f x k their conjugates and biconjugates of fenchel moreau type with respect to the coupling functions x y x y x y x and x y d inf x y d x y x d k and use them to obtain characterizations of topical and anti topical functions in the subsequent sections we consider for the coupling functions and some concepts that have been studied in rubinov and singer 2001 11 and singer 2004 15 for the so called additive min type coupling functions rmaxn rmaxn rmax and an an a respectively where a is a conditionally complete lattice ordered group and x y inf1 i n xi yi x y rmaxn or an thus we study the polars of a set g x for the coupling functions and and we consider for a function f x k the notion of support set of f with respect to the set t of all elementary topical functions t y x x y x x y x infx and two concepts of support set of f at a point x0 x the main differences between the properties of the conjugations with respect to the coupling functions and and between the properties of the polars of a set g with respect to the coupling functions and are caused by the fact that while is symmetric with values only in rmax resp a and are not symmetric and take values also outside rmax resp a

tropical polar cones hypergraph transversals and mean payoff games we discuss the tropical analogues of several basic questions of convex duality in particular the polar of a tropical polyhedral cone represents the set of linear inequalities that its elements satisfy we characterize the extreme rays of the polar in terms of certain minimal set covers which may be thought of as weighted generalizations of minimal transversals in hypergraphs we also give a tropical analogue of farkas lemma which allows one to check whether a linear inequality is implied by a finite family of linear inequalities here the certificate is a strategy of a mean payoff game we discuss examples showing that the number of extreme rays of the polar of the tropical cyclic polyhedral cone is polynomially bounded and that there is no unique minimal system of inequalities defining a given tropical polyhedral cone

join reducibility of fuzzy subgroups abstract we show that the lattice of all normal fuzzy subgroups of a group g is a sublattice of the lattice of all fuzzy subgroups of g and discuss join ir reductibility of fuzzy subgroups and representations of fuzzy subgroups as joins of join irreducible fuzzy subgroups

characterization of fuzzy subgroups abstract this paper is a continuation of our earlier work abou zaid 1991 1992 asaad 1991 asaad and abou zaid 1993 1995 in order to investigate further the problem given by asaad 1991 what can be said about the structure of a fuzzy subgroup a of a group g when information is available about the structure of g and vice versa

fuzzy l structure abstract in the present paper the authors introduce the concepts of fuzzy l stracture fuzzy sub l structure pseudo fuzzy l stracture and anti fuzzy l structure some characterisations of the above structures are made and some examples are presented

immersion of non linear systems into linear systems up to output injection characteristic equation approach there exists a class of non linear systems which cannot be transformed into non linear observer form via diffeomorphism but can be immersed into higher dimensional non linear observer form this paper investigates when n dimensional non linear systems can be immersed into n m dimensional non linear systems in non linear observer form and provides a necessary and sufficient condition we also present an algorithm to check the immersibility in general at the first step of the algorithm one should solve a differential equation with m 1 unknowns rather than solving one with n m unknowns simultaneously when a solution to the differential equation can be obtained the immersibility can be checked by a recursive algorithm moreover when 2m n a straightforward algorithm is provided to check the immersibility

a finiteness criterion for nonlinear input output differential systems we solve the following problem which has been dealt with in several publications when does a system have the same input output behaviour as a system depending linearly on the state variables precise definitions of this question are supplied in the text a particular case of the problem is the equivalence of a system with a bilinear one at the end we illustrate our methods and the scope of our results by a brief study of several examples

scheduling with and or precedence constraints in many scheduling applications it is required that the processing of some job be postponed until some other job which can be chosen from a pregiven set of alternatives has been completed the traditional concept of precedence constraints fails to model such restrictions therefore the concept has been generalized to so called and or precedence constraints which can cope with this kind of requirement in the context of traditional precedence constraints feasibility transitivity and the computation of earliest start times for jobs are fundamental well studied problems the purpose of this paper is to provide efficient algorithms for these tasks for the more general model of and or precedence constraints we show that feasibility as well as many questions related to transitivity can be solved by applying essentially the same linear time algorithm in order to compute earliest start times we propose two polynomial time algorithms to cope with different classes of time distances between jobs

dynamic observer error linearization in this paper a new framework of observer error linearization problem is proposed the main idea of our approach is twofold the one is to introduce an auxiliary dynamics whose input is the system output and the other is to transform the augmented system into an observable linear system with an injection term which contains the system output as well as the state of the auxiliary dynamics it is a natural extension of the recently developed dynamic observer error linearization where the injection term contains only newly defined output it is also shown that whenever an n dimensional system is immersible into an n d dimensional linear system up to an output injection then it can be also dynamically observer error linearizable in our sense with a d dimensional auxiliary dynamics moreover we show that the converse is not true by providing a counterexample which implies that our approach is applicable to a strictly wider class of systems than that of the system immersion method

fuzzy submodules some analogues and deviations abstract product of a fuzzy ideal and a fuzzy submodule is defined the sum of two fuzzy submodules is also defined and discussed fuzzy version of nakayama s lemma is formulated and studied certain deviations from some known results on modules are highlighted

on generalized characteristic fuzzy subgroups of a finite group abstract in 1991 asaad 2 suggested the following two questions i what can be said about the structure of a fuzzy subgroup a of a finite group g when information is known about the structure of g ii what can be said about the structure of group g when information is known about the structure of a fuzzy subgroup a of g the purpose of this paper is to continue the investigation of the above questions

reduced order dynamic observer error linearisation a natural extension of observer error linearisation this paper introduces the concept of reduced order dynamic observer error linearisation rdoel for multi output systems which is the problem of transforming a nonlinear system into a nonlinear observer canonical form with the aid of auxiliary dynamics the proposed rdoel framework is not only a modified version of dynamic observer error linearisation doel but also a natural extension of observer error linearisation oel we provide three necessary conditions for the rdoel problem and then derive a necessary and sufficient condition described in terms of lie algebras of vector fields furthermore from the result we also give a geometric necessary and sufficient condition for the oel problem which has not yet been completely established in the case where a diffeomorphism on the output of general form is considered

on fuzzy subnormal and pronormal subgroups of a finite group abstract throughout this paper all groups are finite in 1989 asaad 2 suggested the following question knowing some information about a fuzzy subgroup a of a group g what is the structure of g and if some information is known about g what is the structure of a for example he proved that if g is a group of prime power order then g is cyclic iff there exists a fuzzy subgroup a of g such that for x y in g i if a x a y then x y and ii if a x a y then x y the aim of this paper is to continue the investigation of this question

on fuzzy ideals of a ring 1 abstract the aim of this paper is to study fuzzy ideals of a ring to characterise regular rings and noetherian rings by fuzzy ideals and to determine all fuzzy prime ideals of the ring z of integers

the observer error linearization problem via dynamic compensation linearization by output injection has played a key role in the observer design for nonlinear control systems for almost three decades in this paper following some recent works ge ometric necessary and sufficient conditions are derived for the existence of a dynamic compensator solving the problem under regular output transformation an algorithm which computes a compensator of minimal order is given

a note on an equivalence relation of fuzzy subgroups the purpose of this paper is to discuss the following three problems 1 the number of equivalent classes of fuzzy subgroups of a group g 2 the relationship between the number of equivalent classes of fuzzy subgroups and the order of a cyclic group g 3 the relationship between the order of fuzzy subgroups and the order of a cyclic group g 4 a classification of a group using membership values of fuzzy subgroups is given

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

fuzzy subgroups having the property abstract we introduce the notion of the property for a fuzzy group and characterize all finite cyclic groups in terms of this notion this property concerns the transition of the order of an element of a group from the classical to the fuzzy setting

observer linearization by output dependent time scale transformations we study the problem of observer linearization for single output dynamical systems in the presence of output dependent time scaling changes an alternative algorithm for the solution of the observer linearization problem is introduced the algorithm employs an exterior calculus approach that provides a simple procedure for the solution of the observer linearization problem by means of an output dependent time scale transformation

fuzzy ideals and fuzzy prime ideals of a ring abstract besides obtaining certain ring theoretic analogues some peculiarities of the fuzzy setting are also discussed in particular a study of i the conditions under which a given fuzzy ideal can or cannot be expressed as a union of two proper fuzzy ideals ii the algebraic nature of images and preimages of fuzzy prime ideals under homomorphisms and iii the ring of all the fuzzy cosets of a fuzzy prime fuzzy maximal ideal is carried out

fuzzy characteristic subgroups of a group abstract a fuzzy characteristic subgroup of a group is characterized in terms of its level subgroups without any restriction on the order of the underlying group

nonlinear observer design by dynamic observer error linearization in this note we address the problem of transforming a nonlinear system into nonlinear observer canonical form in the extended state space with the aid of dynamic system extension and introduction of virtual outputs as an intermediate step for the general problem we consider a restricted structure of dynamic extension which is obtained roughly speaking by adding the chains of integrators to the outputs of original system we propose sufficient conditions which can be verified using the system dynamics expressed in their original coordinates an illustrative example is included that demonstrates the advantage of the proposed method over the conventional method

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

on dynamic feedback linearization abstract we address the problem of transforming a nonlinear multi input system into a linear controllable one via nonsingular dynamic feedback and extended state space diffeomorphism we show that in the single input case if a system is dynamic feedback linearizable it is also static feedback linearizable we then give sufficient conditions for a class of multi input systems to be dynamic feedback linearizable all three dimensional systems with two controls and a controllable linear approximation about the origin are shown to belong to such a class

on constructing nonlinear observers two algorithmic approaches to constructing nonlinear observers currently exist here one of these is improved by finding an explicit solution to the partial differential equations describing the change of state coordinates thereby avoiding expensive bracket computations this simplifies the algorithm and has implications for system identification

the lattices of fuzzy subgroups and fuzzy normal subgroups abstract here we discuss various types of sublattices of the lattice of fuzzy subgroups of a given group we prove that a special class of fuzzy normal subgroups constitutes a modular sublattice of the lattice of fuzzy subgroups

sufficient conditions for dynamic state feedback linearization sufficient conditions are given for the existence of a dynamic state feedback compensator for a multi input nonlinear system such that the closed loop system is transformable into a linear controllable one by an extended state space change of coordinates an example shows that the conditions are not necessary necessary conditions are also given which are shown to be sufficient when the number of states minus the number of controls is equal to one several examples illustrate how the sufficient conditions obtained lead to the design of the dynamic compensator

on fuzzy ideals and fuzzy bi ideals in semigroups abstract in this paper we give some properties of fuzzy ideals and fuzzy bi ideals of semigroups and characterize semigroups that are left duo left simple and semilattices of subsemigroups in terms of fuzzy ideals and fuzzy bi ideals

groups and fuzzy subgroups ii abstract in 1991 asaad has suggested the following question what can be said about the structure of a group g when information is known about the structure of a fuzzy subgroup a of g and vice versa the purpose of this paper is to continue the investigation of the above mentioned question

a complete study of the lattices of fuzzy congruences and fuzzy normal subgroups in this paper we introduce the concepts of t fuzzy congruences and t fuzzy equivalences using these ideas we investigate completely on one hand the lattice structures of the set of fuzzy equivalence relations on a group and the set of fuzzy congruences and on the other hand the lattice structures of the set of fuzzy subgroups and fuzzy normal subgroups our study reveals some finer and interesting facts about these lattices it is proved among other results that the set ct of all t fuzzy congruences of a group g forms lattice and also the set lnt of all those fuzzy normal subgroups which assume the same value t at e the identity of g forms a lattice as an important result we prove that the lattices ct and lnt are isomorphic it is also shown that the lattices ct and lnt are modular moreover we construct various important sublattices of the lattice ct and exhibit their relationship by lattice diagrams in the process we improve and unify many results of earlier authors on fuzzy congruences

fuzzy irreducible ideals in rings abstract in this paper the concept of a fuzzy set is extended by introducing the concept of a fuzzy irreducible ideal in a ring the characteristic function of an irreducible ideal and the level ideals of a fuzzy irreducible ideal are studied the algebraic nature of homomorphic images and preimages of fuzzy irreducible ideals is also examined some other fundamental results pertaining to this concept are discussed

fuzzy semiprimary ideals of rings abstract the concept of fuzzy ideals is extended by introducing fuzzy semiprimary ideals in rings this class of fuzzy ideals generalizes the class of fuzzy semiprimary ideals it is shown that there do exist fuzzy ideals which are fuzzy semiprimary but not fuzzy primary a study of i the level ideals of a fuzzy semiprimary ideal ii the characteristic function of a semiprimary ideal iii the zero divisors in the ring of all fuzzy cosets of a fuzzy semiprimary ideal and iv the algebraic nature of direct and inverse images of fuzzy semiprimary ideals under homomorphisms is carried out

level subgroups and union of fuzzy subgroups abstract in this paper we investigate the conditions under which a given fuzzy subgroup of a given group can or can not be realized as a union of two proper fuzzy subgroups moreover we formulate the notion of fuzzy subgroup generated by a given fuzzy subset by level subgroups we also give characterizations of fuzzy conjugate subgroups and fuzzy characteristic subgroups by their level subgroups also we discuss the relationship between level subgroups of a given fuzzy subgroup and the level subgroups of its homomorphic image

the equation a x b y over max for the two sided homogeneous linear equation system a x b y over max with no infinite rows or columns in a or b an algorithm is presented which converges to a finite solution from any finite starting point whenever a finite solution exists if the finite elements of a b are all integers convergence is in a finite number of steps for which a precise bound can be calculated if moreover one of a b has only finite elements the algorithm is thus pseudopolynomial in complexity

linearization by generalized input output injection abstract the problem under interest is the linearization of nonlinear mimo systems by generalized input output injection in order to design observers with linear error dynamics the method is based on the study of the structure of the input output differential equations thus the problem is solved as a realization problem in this note one considers the linearization under two kinds of inout output injection in the first case the transformation depends on the output and time derivatives of the input whereas in the second case derivatives of both the input and the output are considered necessary and sufficient conditions are obtained which generalize the ones on standard input output injection linearization

nonlinear observer design by observer error linearization this paper studies the observer design problem by the observer error linearization approach for nonlinear systems with and without inputs necessary and sufficient conditions for the existence of the linearization transformation are derived for nonlinear systems without inputs the conditions are shown to be corrections to an existing result a computation procedure and a different set of necessary and sufficient conditions based on the computation procedure are presented

a characterization of fuzzy subgroups abstract an ordinary subgroup of a group g is 1 a subset of g 2 closed under the group operation in a fuzzy subgroup it is precisely these two notions that lose their deterministic character a fuzzy subgroup of a group g associates with each group element a number the larger the number the more certainly that element belongs to the fuzzy subgroup the closure property is captured by the inequality x y t x y in a rosenfeld s original definition t was the function minimum however any t norm t provides a meaningful generalization of the closure property two classes of fuzzy subgroups are investigated the fuzzy subgroups in one class are subgroup generated those in the other are function generated each fuzzy subgroup in these classes satisfies the above inequality with t given by t a b max a b 1 0 while the two classes look different each fuzzy subgroup in either is isomorphic to one in the other it is shown that a fuzzy subgroup satisfies the above inequality with t minimum if and only if it is subgroup generated of a very special type finally these notions are applied to some abstract pattern recognition problems

extended output depending normal form this paper concerns the design of a nonlinear observer through a transformation of a nonlinear system into an observer form that supports a high gain observer sufficient geometrical condition is deduced to guarantee the existence of change of coordinates allowing the transformation of a nonlinear system into the proposed normal form the result is highlighted by studying the susceptible exposed infected and recovered seir model

fuzzy cosets and some fuzzy radicals abstract an attempt is made to formulate fuzzy versions of jacobson and prime radicals of a ring certain basic results pertaining to the notions of jacobson and prime radicals of a ring are extended to the fuzzy setting in particular the following is obtained the jacobson radical prime radical of the ring of fuzzy cosets of in r is zero where r is a commutative ring with identity and is the fuzzy jacobson radical fuzzy prime radical of r

partial observer normal form for nonlinear system in this paper we investigate the estimation problem for a class of partially observable nonlinear systems for the proposed partial observer normal form ponf necessary and sufficient conditions are deduced to guarantee the existence of a change of coordinates which can transform the studied system into the proposed ponf examples are provided to illustrate the effectiveness of the proposed results

duality and separation theorems in idempotent semimodules abstract we consider subsemimodules and convex subsets of semimodules over semirings with an idempotent addition we introduce a nonlinear projection on subsemimodules the projection of a point is the maximal approximation from below of the point in the subsemimodule we use this projection to separate a point from a convex set we also show that the projection minimizes the analogue of hilbert s projective metric we develop more generally a theory of dual pairs for idempotent semimodules we obtain as a corollary duality results between the row and column spaces of matrices with entries in idempotent semirings we illustrate the results by showing polyhedra and half spaces over the max plus semiring

tl subgroups having the property abstract we introduce the notion of a tl subgroup having the property that is a generalization of the notion of a generalized characteristic tl subgroup as abou zaid s notion was generalized in kim 1994 5 and investigate interrelationship between the notion of a tl subgroup having the property and the notion of a generalized characteristic tl subgroup

best approximation in max plus semimodules abstract we establish new results concerning projectors on max plus spaces as well as separating half spaces and derive an explicit formula for the distance in hilbert s projective metric between a point and a half space over the max plus semiring as well as explicit descriptions of the set of minimizers as a consequence we obtain a cyclic projection type algorithm to solve systems of max plus linear inequalities

verifiable conditions for multioutput observer error linearizability the verifiable necessary and sufficient conditions for the multioutput observer error linearization problem have not been found over the last three decades in this technical note we give the unverifiable necessary and sufficient conditions which are more specific than the ones in the literature using these conditions a verifiable sufficient condition also necessary with additional restriction on the problem is derived since our proofs are constructive a desired state transformation can also be found in the theorem also our algorithmic conditions can be easily implemented by a matlab programming

the lattice of fuzzy normal subgroups is modular abstract we have introduced and discussed in a recent paper 2 various sublattices such as lf lt and lfnt of the lattice l of fuzzy subgroups of a given group in particular we proved that the sublattice lfn of fuzzy normal subgroups with finite range and tip t is a modular sublattice of l here we remove all the restrictions on the choice of fuzzy normal subgroups and prove that the class of all fuzzy normal subgroups ln forms the modular sublattice of l as a tool we prove an important result that the fuzzy subgroups generated by a pair of fuzzy normal subgroups of a group is fuzzy normal

fuzzy orders relative to fuzzy subgroups abstract in this paper we introduce the notion of fuzzy orders of the elements of a group and show that most of the basic properties of orders of elements in the group theory are valid in the theory of fuzzy groups where ordinary orders of elements are replaced by fuzzy orders of elements reports of further development of the subject will follow in subsequent essays

fuzzy semiprime ideals in semigroups abstract in this paper we shall introduce the notion of fuzzy semiprimality in a semigroup which is an extension of semiprimality in it and characterize a semigroup that is a semilattice of simple semigroups in terms of fuzzy semiprimality

characterization of tropical hemispaces by p r decompositions abstract we consider tropical hemispaces defined as tropically convex sets whose complements are also tropically convex and tropical semispaces defined as maximal tropically convex sets not containing a given point we introduce the concept of p r decomposition this yields to our knowledge a new kind of representation of tropically convex sets extending the classical idea of representing convex sets by means of extreme points and rays we characterize tropical hemispaces as tropically convex sets that admit a p r decomposition of certain kind in this characterization with each tropical hemispace we associate a matrix with coefficients in the completed tropical semifield satisfying an extended rank one condition our proof techniques are based on homogenization lifting a convex set to a cone and the relation between tropical hemispaces and semispaces

nonlinear system immersion observers and finite dimensional filters abstract nonlinear deterministic and stochastic systems which can be immersed into linear observable ones are identified by necessary and sufficient conditions those systems are shown to admit observers in the deterministic case and exact finite dimensional filters in the stochastic case the sufficient conditions obtained generalize earlier results in both cases

immersion of nonlinear systems into linear systems modulo output injection the problem of the immersion of a siso system into a linear up to an output injection one is studied in order to design luenberger like observers necessary and sufficient conditions are stated within a very general framework effective computations and examples are then provided

interval state estimation for a class of nonlinear systems the goal of this technical note is to design interval observers for a class of nonlinear continuous time systems the first part of this work shows that it is usually possible to design an interval observer for linear systems by means of linear time invariant changes of coordinates even if the system is not cooperative this result is extended to a class of nonlinear systems using partial exact linearisations the proposed observers guarantee to enclose the set of system states that is consistent with the model the disturbances and the measurement noise moreover it is only assumed that the measurement noise and the disturbances are bounded without any additional information such as stationarity uncorrelation or type of distribution the proposed observer is illustrated through numerical simulations

fuzzy subgroups of nilpotent groups in 1991 asaad has suggested the following question what can be said about the structure of a group g when information is known about the structure of a fuzzy subgroup a of g and vice versa this question has been partially investigated in fuzzy sets and systems39 1991 323 328 the purpose of this paper is to continue more investigations for the above mentioned question

fixed time observer with simple gains for uncertain systems abstract in this article we consider the problem of fixed time observer for nonlinear systems that is a finite time observer whose settling time can be bounded independently of the initial condition we consider a large class of nonlinear systems which includes two main classes linearizable systems up to input output injection and uniformly observable systems furthermore the effect of noise and uncertainty is analyzed

fuzzy subgroups some characterizations the notion of a fuzzy set was first introduced in 1965 by zadeh 12 since then the theory of fuzzy sets has gone through remarkably rapid strides with well over 4000 papers by now see for example the bibliography 3 several textbooks for example 2 and 6 and an international journal solely devoted to it s the theory has found wideranging applications in such diverse fields as automata control theory decision theory and social behavior pattern studies to name just a few for an interesting expository account see rosenfeld lo and also the book review 7 in 9 rosenfeld introduced the notion of a fuzzy group and showed that many concepts of group theory can be extended in an elementary manner to develop the theory of fuzzy groups in particular he characterized all the fuzzy subgroups of cyclic groups of prime order 9 proposition 5 101 fuzzy groups were further investigated by das in 1 where he characterized all the fuzzy subgroups of finite cyclic groups l theorem 4 21 in this connection he introduced the notion of level subgroups of a fuzzy subgroup which is based on the notion of a level subset introduced earlier by zadeh for a finite group das showed that these level subgroups of a fuzzy subgroup form a chain 1 corollary 3 11 and also constructed a fuzzy subgroup whose chain of level subgroups is maximal in the following special cases when the group is i a direct product of cyclic groups of prime orders ii abelian l theorem 3 41 we analyze the level subgroups of a fuzzy subgroup in more detail and investigate whether the family of level subgroups of a fuzzy subgroup deter

homomorphisms and fuzzy fuzzy normal subgroups abstract using the idea of a level subgroup of a fuzzy subgroup an attempt is made to study the algebraic nature of fuzzy fuzzy normal subgroups under homomorphisms

observer with linear error dynamics for nonlinear multi output systems based upon nonlinear state coordinate transformations and a condensed dual brunovsk form for multi output systems a method for designing nonlinear state observers with linear error dynamics is presented necessary and sufficient conditions are provided for identifying the class of nonlinear systems for which state observers with linear error dynamics can be obtained

on the transformation of nonlinear dynamical systems into the extended nonlinear observable canonical form this article deals with the transformation of a class of nonlinear systems into an extended nonlinear observable canonical form enocf by dynamic extension the dynamic extension is obtained by adding auxiliary dynamics and virtual outputs to the original system thus giving rise to a higher dimensional system in an extended state space sufficient geometrical conditions to guarantee the existence of a local diffeomorphism which allow the transformation of the extended system into the enocf are given in particular an algorithm that permits us to compute such a diffeomorphism is derived

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

groups and fuzzy subgroups abstract the purpose of this paper is to deal with the following two problems 1 what can be said about the structure of a fuzzy subgroup a of a group g when information is known about the structure of g 2 what can be said about the structure of a group g when information is known about the structure of a fuzzy subgroup a of g