system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

subjective valuations in a production model abstract this paper is devoted to a model of economic dynamics first a definition of fuzzy mapping some of its properties and economic interpretations are presented next a model of economic dynamics is defined and problems of optimization are considered

lpv system analysis via quadratic separator for uncertain implicit systems this paper considers a class of linear systems containing time varying parameters whose behavior is not known exactly we assume that the parameters vary within known intervals and there are known bounds on their rates of variation our objective is to give a computationally verifiable condition that guarantees stability of the system for all possible parameter variations we first point out that the information on the rate bounds can be exploited by considering an augmented system described by an implicit model we then develop a tool called the quadratic separator for stability analysis of uncertain implicit systems using this tool a sufficient stability condition is obtained for the original linear parameter varying system moreover we show that the stability condition obtained is equivalent to the existence of a lyapunov function that depends on the parameters in a linear fractional manner finally the computational aspects of the proposed stability conditions are addressed

stabilization of uncertain systems via linear control this note considers the problem of stabilizing a linear dynamical system whose state equation includes a time varying uncertain parameter vector q cdot given the dynamics dot x t a q t x t b q t u t and a bounding set q for the values q t the objective is to choose a control law u t p x t guaranteeing uniform asymptotic stability for all admissible variations of q cdot our results differ from previous work in one fundamental way that is we show that when working with linear controllers it is possible to dispense with all assumptions on b cdot which have been made by previous authors e g see 1 9 this elimination of hypotheses on b cdot is accomplished roughly as follows the system sigma underline underline delta a q b q is shown to be equivalent to another system sigma underline underline delta a q b as far as stabilization is concerned since b is a constant matrix independent of q the desired result is readily obtained

structural analysis of robust control systems in this paper a necessary and sufficient condition for well posedness is presented using the inclusion condition of uncertainty and a set of all the systems corresponding to the uncertainty with which a closed loop system is well posed is given furthermore we analyze the topology of the set of systems based on the well posedness property we give the number of connected components in the set of uncertainty in the cases of complex matrix uncertainty and 2 spl times 2 real matrix uncertainty

fixed points for fuzzy mappings in this paper the problem of the existence and computation of fixed points for fuzzy mappings is approached a fuzzy mapping r over a set x is defined to be a function attaching to each x in x a fuzzy subset r of x an element x of x is called fixed point of r iff its membership degree to r is at least equal to the membership degree to r of any y x i e r r y y x two existence theorems for fixed points of a fuzzy mapping are proved and an algorithm for computing approximations of such a fixed point is described the convergence theorem of our algorithm is proved under the restrictive assumption that for any x in x the membership function of r has a complementary function examples of fuzzy mappings having this property are given but the problem of proving general criteria for a function to have a complementary remain open

dynamical system design from a control perspective finite frequency positive realness approach nonminimum phase zeros are well known to limit the best achievable control performance when the control gain is allowed to be arbitrarily high on the other hand the phase crossover appears to be a limiting factor for performance when high gain controllers are not allowed in particular the positive realness in a finite frequency range seems crucial for achieving good performance in the presence of control constraints this paper will first give multiple reasons to support this conjecture and then develop a systematic method for designing mechanical systems to achieve the finite frequency positive real ffpr property specifically we present a state space characterization of the ffpr property by generalizing the well known kalman yakubovich popov lemma to deal with a class of frequency domain inequalities that are required to hold within a finite frequency interval the result is further extended for uncertain systems to give a sufficient condition for satisfaction of a robust ffpr property the nominal ffpr result is interpreted in the time domain in terms of input output signals finally we show that certain sensor actuator placement problems to achieve the ffpr property can be reduced to finite dimensional convex problems involving linear matrix inequalities the method is applied to the shape design of a swing arm for magnetic storage devices with the objective of maximizing the control bandwidth achievable with a limited actuator power

common fixed point theorems in fuzzy metric spaces in this paper we prove common fixed point theorems for six mappings in fuzzy metric space our main results extend generalize and fuzzify some known results in fuzzy metric spaces probabilistic metric spaces and uniform spaces

a dilated lmi approach to robust performance analysis of linear time invariant uncertain systems this paper studies robust performance analysis problems of linear time invariant systems affected by real parametric uncertainties in the case where the state space matrices of the system depend affinely on the uncertain parameters it is know that recently developed extended or dilated linear matrix inequalities lmis are effective to assess the robust performance in a less conservative fashion this paper further extends those preceding results and propose a unified way to obtain numerically verifiable dilated lmi conditions even in the case of rational parameter dependence in particular it turns out that the proposed dilated lmis enable us to assess the robust performance via multiaffine parameter dependent lyapunov variables so that less conservative analysis results can be achieved connections among the proposed conditions and existing results are also discussed concretely several existing results can be viewed as particular cases of the proposed conditions

coincidence theorems and variational inequalities for fuzzy mappings abstract in this paper some coincidence theorems and existence theorems of solutions of variational inequalities for fuzzy mappings are established

coincidence degree and coincidence theorems for fuzzy mappings abstract in this paper the concept of coincidence degree and some coincidence theorems for fuzzy mappings have been introduced and established the results presented in this paper generalize and unify some results of 2 3 4 5 8 and give a fuzzy generalization of the famous kakutani ky fan theorem

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

improved upper bounds for the mixed structured singular value in this paper we take a new look at the mixed structured singular value problem a problem of finding important applications in robust stability analysis several new upper bounds are proposed using a very simple approach which we call the multiplier approach these new bounds are convex and computable by using linear matrix inequality lmi techniques we show most importantly that these upper bounds are actually lower bounds of a well known upper bound which involves the so called d scaling for complex perturbations and g scaling for real perturbations

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

convergence of sequences of fuzzy numbers and fixed point theorems for increasing fuzzy mappings and application in this paper we discuss some properties of the convergence of sequences of fuzzy numbers and obtain some fixed point theorems for increasing fuzzy mappings and as applications we give two examples one is about fishery production which discusses the balance problems between the quantity of catching fish and the increase in the quantity of fish that is produced by the reproduction and growth of fish another is about the solvability of the equation of fuzzy numbers

fixed point theorems for fuzzy mappings in complete metric spaces in this paper we are concerned with mathematical properties of the previous contractive types of set valued maps or fuzzy mappings on a metric space see for instance nadler pacific j math 30 1969 475 488 heilpern j math anal appl 83 1981 566 569 papageorgiou nonlinear anal theory methods appl 7 1983 763 770 bose and sahani fuzzy sets and systems 21 1987 53 58 som and mukherjee fuzzy sets and systems 33 1989 213 219 park and jeong fuzzy sets and systems 59 1993 231 235 87 1997 111 116 lee et al fuzzy sets and systems 101 1999 143 152 and we prove some crucial theorems relating fixed points of fuzzy mappings on complete metric spaces first we prove a theorem by using the concept of w distance kada et al math japonica 44 1996 381 391 which generalizes the results of amemiya and takahashi fuzzy sets and systems 114 2000 469 476 and kada et al 1996 next we prove two theorems for fuzzy mappings which are connected with fixed point theorems for set valued maps then we shall observe that our theorems can be used to obtain almost all results proved so far concerning fixed points of fuzzy mappings or set valued maps on complete metric spaces and therefore that our results imply the existence of fixed points of various contractive types of fuzzy mappings or set valued maps on complete metric spaces

singular schemes of hypersurfaces let y be the singular locus of a hypersurface x in a smooth variety m with the scheme structure defined by the jacobian ideal of x we will say then that y is the singular scheme of x to emphasize that the scheme structure of y is important for our considerations in this note we consider a class in the chow group of y which arises naturally in this setup and which captures much intersection theoretic information about the situation the guiding question we have in mind is which schemes y can arise as singular schemes of hypersurfaces we will obtain strong constraints showing for instance that the only hypersurfaces in p whose singular schemes are positive dimensional linear subspaces of p are quadrics and that no reduced nodal curve can be the singular scheme of a hypersurface in a non singular variety many more statements of this sort can be found in section 3 a different type of application is in section 2 we show how our class relates to other invariants of the singularity of a hypersurface the class can be used to recover results of holme and parusi ski on degree and multiplicity of dual varieties and leads naturally to a generalization of the notion of ranks of a smooth projective variety also we obtain a strengthening of landman s parity result and a new proof of a result of zak on the dimension of the dual of a smooth variety the duality results follow by applying the framework to hyperplane sections of m the singular scheme of a section is supported on the locus of contact of the hyperplane with m and the class can be used to measure this contact for example the class measures how general a given section is we show corollary 2 6 that if the contact scheme is a linear subspace pr 1 then the corresponding hyperplane is a smooth point of the dual variety of m and the dual variety has codimension r the main general results are in section 1 where we prove corollary 1 7 that the class we introduce depends in fact only on y and on the line bundle l o x y and not on the ambient variety m provided that y is the singular scheme of a

a note on fixed point theorems for fuzzy mappings by p vijayaraju and m marudai in this paper a result on common fixed point theorem for a pair of contractive type fuzzy mappings in a metric space is established which improves the result of vijayaraju and marudai fixed point theorems for fuzzy mappings fuzzy sets and systems 135 2003 401 408

fixed degree and fixed point theorems for fuzzy mappings in probabilistic metric spaces abstract this paper introduces the concept and properties of fixed degrees for fuzzy mappings in probabilistic metric spaces by virtue of this concept some theorems about common fixed degree of a sequence of fuzzy mappings in probabilistic metric spaces are obtained these new results are a unified approach to generalize several fixed point theorems for fuzzy mappings

generalized fuzzy games and fuzzy equilibria abstract in this paper we define the concepts of generalized fuzzy game and fuzzy equilibrium next we shall prove new existence theorems of equilibrium in generalized fuzzy games with uncountable number of agents our results generalize the corresponding results due to arrow debreu kim lee and yannelis prabhakar in several aspects

simultaneous parametric uncertainty modeling and robust control synthesis by lft scaling given a set of experimental data points in the plant parameter space the objective of this paper is to give a systematic method for designing a controller to achieve a prescribed level of robust performance for the closed loop system a standard procedure would be to model the data first and then to design a controller our focus here instead is to complete these two tasks simultaneously eliminating the conservatism caused by the fact that the data is modeled independently of the closed loop objective to this end integral quadratic constraints iqcs are used as a tool for uncertainty modeling we propose the lft scaling to integrate the iqc modeling with the control synthesis it is shown that the lft scaling provides a condition dual to the standard iqc for linear time invariant systems and this duality result is essential for solving the simultaneous modeling and synthesis problem a solution is given in terms of matrix inequalities and its computational aspects are discussed the proposed method is applied to the control design for an ac linear servo motor and experimental results demonstrate that our method achieves the performance superior to that achieved by existing methods

fuzzy homomorphism and algebraic structures abstract the object of this paper is to prove an analogue of the fundamental theorem of homomorphism and the second isomorphism theorem for fuzzy homomorphisms we also study the fuzzy subgroup generated by a fuzzy subset

constantly scaled h sub spl infin control problems for pseudofull information problems this paper proposes a class of the constantly scaled h sub spl infin control problem where the class is characterized by an assumption also proposed in this paper in general the scaled h sub spl infin control problem leads to nonconvex solvability conditions on the other hand for the problems in the proposed class we show that a convex but sufficient solvability condition can be given moreover the convexity of the state feedback and the full information problems can be regarded as the extreme cases of the sufficient condition this fact motivates us to call the assumption the pseudofull information condition

fuzzy closed graph fuzzy multifunctions we study certain properties of fuzzy closed valued fuzzy compact valued and fuzzy closed graph fuzzy multifunctions defined on a fuzzy topological space fuzzy closed graph theorem for fuzzy multifunctions is also obtained and an application to fixed point is shown

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

the theory of approximate prices analytical foundations of experimental cost benefit analysis in a fuzzy decision space abstract the essay presents a theory of efficient prices for cost benefit analysis in a fuzzy space the approach proceeds by taking consumers income and producers outputs and costs as given the price preferences of consumers and producers are elicited and then embedded in a fuzzy space through fuzzy mappings to obtain a fuzzy compact price space where fuzzy price decisions are constructed solutions to the fuzzy price decision problems are abstracted through fuzzy mathematical programming to obtain fuzzy equilibrium prices from the fuzzy price space measures of price disagreement fuzzy consumer surplus and fuzzy producer surplus are advanced theorems of existence and uniqueness are stated the total result is a theory of fuzzy prices for cost benefit analysis for decision problem in general including cases where market imputations of prices may not be available to us as well as those cases where market failure may yield price distortions the theory is not only compactible with either contigent variation method direct information elicitation and revealed preference method market based evaluation but provides a direction for cases where problems may exist in both a computational example is provided to illustrate the working mechanism of the theory

fixed point theorems for fuzzy numbers abstract in this paper we study the problem of the existence of fixed points for fuzzy maps we first define uniform structures on sets of fuzzy subsets and describe the closed convergence and myope convergence structures which have properties close to the corresponding traditional ones we then give two ways in order to obtain fixed point results we finally give applications of these results particularly to fuzzy markov processes

a natural interpretation of fuzzy mappings in this paper we present a new and natural interpretation of fuzzy mappings which is a direct extension of the natural interpretation of fuzzy sets and fuzzy relations shown in our previous paper a natural interpretation of fuzzy sets and fuzzy relations fuzzy sets and systems 128 2002 135 we interpret fuzzy mappings as mappings in a heyting valued model for intuitionistic set theory and present a characterization of fuzzy mappings with membership functions which seems to be different from all kinds of known definitions this interpretation is quite natural for it deduces naturally various properties of fuzzy mappings and it makes clear the meaning of the famous extension principle by zadeh which is said to be very important in fuzzy theory

continuity of fuzzy multivalued mappings continuity of multivalued mappings is characterized by two types of semi continuity lower and upper semi continuity in this paper different equivalent ways in which these concepts can be expressed are investigated and then used to define lower and upper semi continuous fuzzy multivalued mappings some shortcomings in existing definitions of upper semi continuous multivalued mappings are addressed several relationships between the lower semi continuity of fuzzy multivalued mappings and the classical lower semi continuity of their cuts or the lower semi continuity w r t the level topologies are established in the setting of stratified fuzzy topological spaces two different types of upper semi continuity of fuzzy multivalued mappings are introduced inspired by the two equivalent ones in the crisp case the relationships between these two types are studied completely many interesting properties of lower and upper semi continuous fuzzy multivalued mappings are presented including the composition and union of lower and upper semi continuous fuzzy multivalued mappings and the compactness preserving property of upper semi continuous and compact valued fuzzy multivalued mappings

on fuzzy multi valued functions part 2 some topological properties abstract in this paper new topological concepts connected with fuzzy multi valued functions theory as presented in the first part of this work are introduced and their properties are investigated as will be shown in future papers these concepts and properties are indispensable in connection with the analysis of fuzzy economic systems

on fuzzy multi valued functions part 1 introduction and general properties abstract in this paper a concept of fuzzy multi valued function is introduced and other related objects are defined next their properties that assume no topological structure are presented

generalization of shadows and fixed point theorems for fuzzy sets in this paper we define a fuzzy set concerning shadows without assuming the existence of the metric projection and extend a well known result in a hilbert space to that in a normed linear space we shall observe that the fuzzy set presented here is in essence a generalization of shadows further we study fuzzy mappings in the framework of fixed point theory we first prove two theorems extending nadler s fixed point theorem lots of fixed point theorems for fuzzy mappings have been proved however the method used here is completely different from those in the previous results next we prove a theorem by applying fan s fixed point theorem and conversely we show that this is a generalization of this theorem

milnor number at infinity topology and newton boundary of a polynomial function in this paper we show that the euler characteristic of the generic fibre of a complex polynomial function f c n c can be easily computed using the newton number of f we apply this result to study polynomials with a finite number of critical points

milnor classes of local complete intersections let v be a compact local complete intersection defined as the zero set of a section of a holomorphic vector bundle over the ambient space for each connected component s of the singular set sing v of v we define the milnor class v s in the homology of s the difference between the schwartz macpherson class and the fulton johnson class of v is shown to be equal to the sum of v s over the connected components s of sing v this is done by proving poincare hopf type theorems for these classes with respect to suitable tangent frames the 0 degree component 0 v s coincides with the milnor numbers already defined by various authors in particular situations we also give an explicit formula for v s when s is a non singular component and v satisfies the whitney condition along s

chern classes for singular hypersurfaces we prove a formula expressing the chern schwartz macpherson class of a hypersurface in a nonsingular variety as a variation on another definition of the homology chern class of singular varieties introduced by w fulton and we discuss the relation between these classes and others such as mather s chern class and the l class we introduced in previous work 0 introduction there are several candidates for a notion of homology chern class of a possibly singular algebraic variety x agreeing with the class obtained as dual of the total chern class of the tangent bundle of x if x is nonsingular one such notion was introduced by r macpherson macpherson agreeing as it was later understood with a class introduced earlier by m ij schwartz and enjoying good functorial properties a different class was defined by w fulton fulton 4 2 6 in a different and somewhat more general setting the main purpose of this paper is to prove a precise relation between the schwartz macpherson and the fulton class of a hypersurface x of a nonsingular variety we denote these two classes by csm x cf x respectively a summary of the context and essential definitions is given in 1 where we present several different statements of the result the version which expresses most directly the link between the two classes mentioned above goes as follows fulton s class for a subscheme x of a nonsingular variety m is defined by cf x m c tmix n s x m that is by capping the total chern class of the ambient space against the segre class of the subscheme it is proved in fulton 4 2 6 that this definition does not depend on the choice of the ambient variety m for a hypersurface x of a nonsingular variety m let y be the singular subscheme of x locally defined by the partial derivatives of an equation of x for an integer k 0 we can consider the k th thickening x k of x along y and then consider its fulton class cf x k it is easily seen that cf x k is a polynomial in k with coefficients in the chow group a x so it can be formally evaluated at negative k s we can then define a class c x cf x 1 the main result of this paper is theorem c x is equal to the chern schwartz macpherson class of x received by the editors june 3 1997 1991 mathematics subject classification prinmary 14c17 32s60 supported in part by nsf grant dms 9500843 1999 american mathbemiatical society 3989 this content downloaded from 157 55 39 136 on thu 01 dec 2016 05 45 16 utc all use subject to http about jstor org terms

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

on the structure of the classes of stable and pure fuzzy sets in this paper two interesting classes of sets with respect to a multivalued mapping are considered the class of stable sets and the class of pure sets in addition to the results existing in the literature several new properties of stable and pure sets are established a generalization of the concepts of stable and pure sets to fuzzy multivalued mappings is developed the properties of stable and pure fuzzy sets are studied extensively it is obtained that the stable resp pure fuzzy sets with respect to a normalized fuzzy multivalued mapping constitute a complete lattice and also a stratified fuzzy topology the notions of level stable and level pure fuzzy sets are introduced interactions between stability resp purity and level stability resp level purity are established and expressed in terms of relationships between particular stratified fuzzy topologies some additional relationships between the stability resp purity of a fuzzy set with respect to a multivalued mapping and the stability resp purity of its cuts with respect to this mapping are established by imposing certain conditions on the triangular norm and the implication operator involved a one to one correspondence between the class of stable fuzzy sets and the class of pure fuzzy sets with respect to a normalized fuzzy multivalued mapping that has a normalized inverse is obtained in the last section it is shown that a normalized fuzzy multivalued mapping is continuous with respect to the stratified fuzzy topologies constituted by the stable fuzzy sets and the pure fuzzy sets with respect to this fuzzy multivalued mapping

on the existence of maximal elements fixed points and equilibria of generalized games in a fuzzy environment we give new sufficient conditions for the existence of fuzzy maximal elements fuzzy fixed points and equilibria of generalized fuzzy games in our results a key role is played by the existence of upper semicontinuous selection maps of set valued functions that we obtain for the class of generalized transfer open lower sections maps

from fuzzy set theory to non additive probabilities how have economists reacted abstract in this paper we are going to try to conduct a comparative review of the two programmes devoted to the application of fuzzy sets theory in economics for the first and to nonadditive probabilities for the second while putting forward some explanations and conjecture as to their development and their future in section 1 we defend the thesis which claims that the first programme has only had a global focus on the approach in terms of generalization and we shall go deeper into the analysis of the particular area of general equilibrium as it is the programme on which ponsard worked the most in section 2 we shall seek to show that the second programme devoted to the introduction of nonadditive probabilities in decision theory on the contrary has attempted to come up with independent findings this would explain why this last programme has managed to fit into topics at a standstill or in crisis easily which is undeniably the case of the standard theory of decision making while the first programme was only envisaged as a kind of mathematical game involving the application of new rules to an old model in the case of the first programme one might thus speak of an extension principle and in the second case of a resolution principle

fuzzy mathematical models in economics abstract this paper is a survey of three fuzzy mathematical models dealing with economic choice economic calculation and general economic equilibrium they are the elements of a fuzzy theory of value the aim is to test the efficiency of the application of fuzzy subsets theory to the analysis of the foundations of economics and thus to legitimate its use in the area

nash fuzzy equilibrium theory and application to a spatial duopoly abstract consider a non cooperative n persons game each gambler has a set of mixed strategies at his disposal the payoffs are some physical or immaterial objects the game is a fuzzy game because 1 gamblers have more or less precise preferences for the payoffs and 2 the outcoming of payoffs is uncertain the uncertainty can be expressed either by a distribution of possibility or by a distribution of probability the product set of a gambler s mixed strategies is convex and compact and the payoff functions are continuous then a closed and convex fuzzy point to set mapping is defined on the product set of strategies and by using a butnariu theorem the existence of a fixed point for this fuzzy point to set mapping is proved the issue allows us to generalize a famous nash result a n persons non cooperative fuzzy game with mixed strategies has at least one equilibrium point in the second part of the paper an economic application is devoted to the statement of the equilibrium existence conditions in a spatial duopoly the model is not only more general than the classical ones but also more relevant because new results are obtained

fuzzy topology and fuzzy multifunctions the fundamental concept of a fuzzy set was first introduced by zadeh in his classical paper 141 since then work has been done by many authors in several directions which has resulted in the formation of a new mathematical field called fuzzy mathematics the theory of fuzzy topological spaces is a branch of such mathematics chang in 2 was the first to introduce the notion of fuzzy topology several others continued the work in this area for example see 12 131 we remark that general point set topology can be regarded as a special case of fuzzy topology where all membership functions are just characteristic functions in this paper we introduce several fuzzy topological concepts and examine their properties our basic tool in that process is the notion of the fuzzy neighborhood of a point introduced by warren in ill we also introduce the notion of fuzzy multifunctions which we strongly believe will be useful in the study of fuzzy games and general fuzzy optimization problems we study the continuity and measurability properties of these multifunctions also we introduce linear fuzzy multifunctions and study their properties in the light of the recent work of katsaras 5 katsaras and liu s and lowen 9 on fuzzy vector spaces

fixed point theorems for fuzzy mappings abstract this paper presents some new fixed point theorems for fuzzy mappings the results given in this paper improve and extend some recent results

optimal constant i o similarity scaling for full information and state feedback control problems abstract in robust control problems capturing all robustness and performance objectives in a single h norm cost function is impossible an alternative approach still untilizing the h norm involves diagonal similarity scaling of certain closed loop transfer functions the set of allowable diagonal scalings is problem dependent and reflects assumptions about the uncertainty and desired performance objectives the scaling set considered here is a prescribed convex set of positive definite matrices we consider the optimal constant scaling problem for the full information h control problem the solution is obtained by transforming the original problem into a convex feasibility problem specifically a structured linear matrix inequality in special cases solvability of the full information problem is equivalent to solvability of the state feedback problem

on fixed degree theorems for fuzzy mappings in menger pm spaces in this paper we establish a new common fixed degree theorem for a sequence of fuzzy mappings in menger pm spaces as an immediate consequence of this theorem we obtain an improvement of a corresponding result of chang et al fuzzy sets and systems 87 1997 325 334 in addition we also obtain some fixed degree and fixed point theorems for fuzzy mappings in fuzzy metric spaces our results unify and generalize the results of heilpern j math anal appl 83 1981 566 569 butnariu fuzzy sets and systems 7 1982 191 207 hadzic fuzzy sets and systems 29 1989 115 125 fang fuzzy sets and systems 48 1992 391 395 lee et al fuzzy sets and systems 61 1994 309 312 j fuzzy math 2 1994 859 870 and chang et al math japon 40 1994 289 293 fuzzy sets and systems 87 1997 325 334

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

on l multifunctions and their applications abstract in this paper a concept of l multifunction is introduced and other related objects are defined next the l economic model is introduced moreover the technological trajectories and their optimality are here presented

on almost continuous and weakly continuous fuzzy multifunctions abstract the paper deals with the study of almost continuous and weakly continuous multifunctions in fuzzy setting several characterizations and certain properties of these fuzzy multifunctions along with their mutal relationships are established attempts are also made to correlate them with fuzzy lower and upper semi continuous multifunctions

numerical solutions of fuzzy differential and integral equations using the embedding method numerical procedures for solving fuzzy differential equations fdes and fuzzy integral equations fies with arbitrary kernels have been investigated sufficient conditions for convergence of the proposed algorithms are given and their applicability is illustrated with examples this work and its conclusions may narrow the gap between the theoretical research on fdes and fies and the practical applications already existing in the design of various fuzzy dynamical systems

an application of fuzzy subsets theory to the analysis of the consumer s spatial preferences abstract this paper discards to usual assumptions of the classical theory of consumer behaviour in mathematical economics first that the consumer is capable of perfectly discriminating between different goods second that the goods capable of satisfying needs are all supplied at a unique point actually consumer behaviour is by nature fuzzy and goods are scattered in a supply space and are transportable in this model the consumer is located at a given point of demand first a general study is made of the structures of spatial preferences in a fuzzy context next the particular properties are introduced in order to define a behaviour of attainable choice then the conditions which guarantee the existence of a completely preordered topological space are imposed in order to verify that the consumer s fuzzy behaviour is coherent these conditions permit to define the existence and continuity of a fuzzy utility as a numerical representation of the imprecise preference the resulting economic theory is neither ordinal nor cardinal but a valuation theory of preference

a note on fuzzy subgroups and fuzzy homomorphism on introduit la notion d homomorphisme flou entre deux groupes et on etudie son effet sur des sous groupes flous

on fuzzy multi valued functions part 4 fuzzy economic models abstract an application to fuzzy economic systems of the fuzzy multi valued functions theory elaborated by both of us in our previous papers is presented first stationary and dynamic fuzzy economic models are defined next the optimality of fuzzy trajectories of these models is introduced and investigated

a fixed point theorem for contractive type fuzzy mappings abstract in this paper we define a contractive type fuzzy mapping and show that a contractive type fuzzy mapping has a fixed point on a complete metric linear space