fuzzy non continuous mappings and fuzzy pre semi separation axioms the aim of the paper is mainly to introduce and study fuzzy pre semi open mapping fuzzy pre semi irresolute mapping fuzzy pre semi separation axioms and fuzzy pre semi connectedness in fuzzy topological spaces

a new algorithm for testing diagnosability of fuzzy discrete event systems failure diagnosis and detection of fuzzy discrete event systems play a significant role in the study of complex systems in this paper we investigate the diagnosability of fuzzy discrete event systems by proposing a new algorithm based on the concept of undistinguishable strings moreover a necessary and sufficient condition for fuzzy diagnosability is obtained in terms of certain properties of the diagnoser which is constructed with respect to the minimal observable event the computing process to check the diagnosability of fuzzy dess and some examples serving to illuminate the applications are developed and described

q convergence of nets and weak separation axioms in fuzzy lattices abstract in this paper we introduce the concept of q remote neighborhood and establish the q convergence theory of nets in fuzzy lattices next we introduce the st i i 1 0 1 2 separation axioms in fuzzy lattices and discuss some of their characterizations finally we introduce and study s irresolute order homomorphism and s homeomorphism discuss the application of q convergence of nets and show that the st i i 1 0 1 2 separability is preserved under s homeomorphism

the semi precompactness axiom a kind of new semi precompactness axiom is introduced in l topological spaces where l is a fuzzy lattice and its topological properties are systematically studied

fuzzy s irresolute mappings in this paper the concepts of fuzzy s irresolute semi s irresolute and s precontinuous mappings in fuzzy topological spaces in sostak sense are introduced and studied some of their characteristic properties are considered also fuzzy s connectedness is introduced and studied with the help of r fuzzy strongly semi open sets

on two weakers forms of continuous order homomorphisms the aim of this paper is to find further connections between two different current researches on fuzzy topology the one based on the concepts of neighborhood filter and zadeh function and the other based on the concepts of remote neighborhood ideal and order homomorphism on fuzzy lattices to approach this the paper studies two weaker forms of continuous order homomorphisms the semi continuous order homomorphism and the weakly semi continuous order homomorphism between l fuzzy topological spaces these order homomorphisms can be characterized in each of the notions remote neighborhood neighborhood ideal filter and molecular net in addition some relations connecting weakly semi continuous order homomorphisms semi hausdorff l fts and urysohn l fts have also been established

ps convergence theory of fuzzy nets and its applications the convergence theory not only is an significantly basic theory of fuzzy topology and fuzzy analysis but also has wide applications in fuzzy inference and some other aspects in this paper we introduce the concept of psc remote neighborhood of fuzzy points and establish the moore smith ps convergence theory of fuzzy nets also we discuss the applications of ps convergence of fuzzy nets

fµ strongly semiopen sets fµ strong semicontinuity and fµ strongly semiretracts throughout the literature if x d is an f ts and y x the induced f topological subspace y d y is defined so that d y n g y n d macho stadler and de prada vicente fuzzy sets and systems 58 1993 365 introduced a new concept of f topological subspaces which coincides with the usual definition in the case that m g y also they introduced the concepts of f m open sets and f m continuity in this paper using the previous concepts we introduce weaker forms of f m open sets and f m continuity the notion of an f retract was introduced by rodabough j math anal appl 79 1981 273 here we introduce the notion of a f m retract and weaker forms of it the basic properties of these notions are given many results are obtained

diagnosability of fuzzy discrete event systems in this paper discrete event systems dess are reformulated as fuzzy discrete event systems fdess and fuzzy discrete event dynamical systems fdedss these frameworks include fuzzy states events and if then rules in these frameworks all events occur at the same time with different membership degrees fuzzy states and events have been introduced to describe uncertainties that occur often in practical problems such as fault diagnosis applications to measure a diagnoser s fault discrimination ability a fuzzy diagnosability degree is proposed if the diagnosability of the degree of the system yields one a diagnoser can be implemented to identify all possible fault types related to a system for any degree less than one researchers should not devote their time to distinguish all possible fault types correctly thus two different diagnosability definitions fdeds and fdes are introduced due to the specialized fuzzy rule base embedded in the fdeds it is capable of representing a class of non linear dynamic system computationally speaking the framework of diagnosability of the fdeds is structurally similar to the framework of diagnosability of a non linear system the crisp des diagnosability has been turned into the term fuzzy diagnosability for the fdes the newly proposed diagnosability definition allows us to define a degree of diagnosability in a class of non linear systems in addition a simple fuzzy diagnosability checking method is introduced and some numerical examples are provided to illustrate this theoretical development finally the potential applications of the proposed method are discussed

the sr compactness in l fuzzy topological spaces abstract in this paper we introduce and study the sr compactness in l fuzzy topological spaces it possesses the following properties 1 sr compactness is defined for arbitrary subsets 2 sr compactness is hereditary for strongly semiclosed subsets 3 sr compactness is preserved under s irresolute mapping 4 every set with finite support is sr compact also the sr compact space is described with cover form and family of strongly semiclosed sets having a finite intersection property

diagnosability of fuzzy discrete event systems a fuzzy approach in order to more effectively cope with the real world problems of vagueness fuzzy discrete event systems fdess were proposed by lin and ying recently then we and cao and ying investigated the supervisory control of fdess independently in this paper we are concerned with another important issue of fdess the failure diagnosis more specifically 1 we propose a ldquofuzzy diagnosabilityrdquo approach by introducing a fuzzy diagnosability function to characterize the diagnosability degree which takes values in the interval 0 1 rather than 0 1 2 based on the observability of events we formalize the construction of the diagnosers that are used to perform fuzzy diagnosis 3 a number of basic properties of the diagnosers are investigated in particular we present a necessary and sufficient condition for failure diagnosis of fdess our results generalize the important consequences of the diagnosability for crisp discrete event systems dess introduced by sampath et al the newly proposed approach allows us to deal with the problem of diagnosability for both crisp dess and fdess 4 in addition a method for checking the fuzzy diagnosability for fdess is proposed also some examples are provided to illustrate the application of the diagnosability of fdess

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

bifuzzy discrete event systems and their supervisory control theory it is well known that type 1 fuzzy sets t1 fss have limited capabilities to handle some data uncertainties directly and type 2 fuzzy sets t2 fss can cover the shortcoming of t1 fss to a certain extent fuzzy discrete event systems fdess were proposed based on t1 fss theory hence fdes may not be a satisfactory model to characterize some high uncertainty systems in this paper we propose a new model called as bifuzzy discrete event systems bfdess by combining classical dess theory and t2 fss theory then we consider the supervisory control problem of bfdess the bifuzzy controllability theorem and nonblocking bifuzzy controllability theorem are demonstrated in addition an algorithm for checking the bifuzzy controllability condition is presented in addition two controllable approximations to an uncontrollable language are investigated in detail an illustrative example is provided to show the applicability and the advantages of the bfdes model

theory of generalized fuzzy discrete event systems there exist a large number of systems whose state variables are continuous signals and transit based on event driven mechanisms to model the transitions of these state variables the theory of extended fuzzy discrete event systems efdess was developed by extending the fuzzy discrete event system fdes theory however the efdes theory remains limited in modeling these event driven systems a primary reason for this is that the efdes theory allows every event to be characterized by one variable only and thus every event can be modeled by a fuzzy set fs only although the efdes theory provides the steps for computing the next states of the state variables how to compute their next states remains unknown when any event is modeled by multiple fss to overcome this limitation this paper will present the theory of generalized fuzzy discrete event systems gfdess by generalizing the efdes theory in the proposed gfdes theory events are characterized by their multiple attributes which may determine the transitions of the state variables and are modeled by representing each of their attributes using one fs to establish the gfdes theory models for gfdess will be presented by extending the concepts of efdess to make this theory complete the procedures for computing the next states of the state variables will also be provided in addition numerical examples will be presented to further illustrate the proposed gfdes theory

a belief evolution based approach for online control of fuzzy discrete event systems under partial observation in this paper we investigate the partially observed supervisor synthesis problem in the framework of fuzzy discrete event systems dess the goal is to synthesize a fuzzy supervisor such that the behavior of the closed loop system is within a given fuzzy language a new approach for solving this problem is proposed based on the idea of belief evolution specifically we propose an algorithm that can be implemented in an online manner we show that the proposed algorithm is both sound and complete i e it effectively solves the supervisor synthesis problem to the best of our knowledge this is the first algorithm with such a property for fuzzy dess as previous works on this topic mostly focus on the supervisor existence condition rather than the supervisor synthesis problem

fuzzy weak totally semicontinuous and fuzzy weak totally precontinuous mappings abstract the aim of this paper is to introduce some new classes of mappings called fuzzy weak totally continuous fuzzy totally precontinuous fuzzy weak totally semicontinuous fuzzy totally m precontinuous fuzzy totally m precontinuous and fuzzy totally irresolute mappings their compositions their relationships with other mappings preservations of some fuzzy spaces under these mappings and some examples are studied we also prove that the property that the mapping is fuzzy totally semicontinuous and fuzzy totally precontinuous is equivalent to the property that the mapping is fuzzy totally continuous

on some weaker forms of fuzzy continuous and fuzzy open mappings on fuzzy topology spaces abstract the purpose of the present paper is to study some weaker forms of fuzzy continuous and fuzzy open maps between fuzzy topological spaces along with the introduction and investigations of a new class of non fuzzy continuous maps this latter type of mappings is seen to be independent of the other non continuous functions discussed here all these functions are characterized and certain properties concerning them are proved finally a comparative study as to their mutual dependence and interrelations under different conditions is taken up

theory of extended fuzzy discrete event systems for handling ranges of knowledge uncertainties and subjectivity in 2001 we originated a theory of fuzzy discrete event systems fdess that generalized the conventional crisp discrete event systems dess vagueness and imprecision concerning states and event transitions of dess were represented by membership grades and computed via fuzzy logic our application of the fdes theory to computerized human immunodeficiency virus acquired immune deficiency syndrome treatment regimen selection although preliminarily successful suggests that a more comprehensive fdes theory is needed to address two general issues critically important not only to biomedical applications but also to real world problems in other industries first domain experts should have means other than point estimates and type 1 fuzzy sets mandated in the current framework to describe uncertainties subjectivity and imprecision in their complex knowledge and experience second when a group of experts with distinct opinions is involved they should not be forced to reach consensus for the sake of system development this is because collective consensus may not be achievable which is often the case in medicine where individual expertspsila opinions should be equally respected since the underlying ground truth is unknown most of the time the theory of extended fdes presented in this paper addresses both the problems and contains the fdes theory as a special case experts are now allowed to use interval numbers and type 1 and type 2 fuzzy sets to intuitively and quantitatively express their diverse knowledge and experience which will then be processed by the new theory to form fuzzy state vectors and fuzzy event transition matrices accordingly we have established mathematical operations that cover the computations of fuzzy states fuzzy event transitions and parallel composition numerical examples are provided

semi interior and semi closure of a fuzzy set on definit le semi interieur et la semi fermeture d un ensemble flou d une facon semblable a celle utilisee dans les espaces topologiques ordinaires

irresolute and lmost open functions between fuzzy topological spaces abstract the aim of this paper is to introduce and characterize the concept of fuzzy irresolute functions which is strictly stronger than the concept of fuzzy semi continuous functions and independent of the concept of fuzzy continuous functions the independence of the two definitions of fuzzy almost open functions as introduced in 5 and 3 and some of their characterizations are also established

fuzzy weak semicontinuity abstract in this paper we introduce the fuzzy weakly semicontinuous mapping which is the weaker form of both fuzzy semicontinuous and fuzzy almost continuous mappings in fuzzy topological spaces however fuzzy weakly semicontinuous mapping and fuzzy weakly continuous mapping are independent notions then we discuss some characteristic properties of fuzzy semicontinuous fuzzy semiopen fuzzy semiclosed and fuzzy pre semi open mappings

safe diagnosability of fuzzy discrete event systems and a polynomial time verification since fuzzy discrete event systems fdess were significantly brought forward the study of fdess has received increasing attention recently this paper addresses the safe diagnosability under the framework of fdess the contributions are threefold first the notion of safe diagnosability for fuzzy systems is formalized a safe diagnosable fdes means that not only each failure can be detected in terms of fuzziness as well as the detection must be completed before any unsafe operation is executed then a necessary and sufficient condition of safe diagnosability of fdess is proposed by constructing the safe diagnoser finally we present an algorithm for verifying the safe diagnosability of fdess based on a constructive nondeterministic automaton namely verifier it is worth noting that both constructing the verifier and verifying the safe diagnosability of fdess can be realized with a polynomial complexity

reliable decentralized supervisory control of fuzzy discrete event systems decentralized supervisory control has been introduced to deal with a class of fuzzy discrete event systems des in which state transitions are uncertain in this paper we develop the work on fuzzy des to consider the reliable decentralized supervisor problem with possible failures of some local supervisors by presenting a new definition of co observable language the reliable decentralized supervisory control problem is solved since the co observable languages are not closed under union a new normal language that is co observable is defined to solve the synthesis problem finally a numerical example is given

q convergence of ideals in fuzzy lattices and its applications abstract in this paper we study q convergence and q convergence of ideals in fuzzy lattices by the concept of q remote neighborhood then we introduce the strong s irresoluteness s irresoluteness and s strong semicontinuity on fuzzy lattices we also study some properties of the notions above and strong semicontinuity 2 3 and s irresoluteness 3 4 with the aid of the q convergence q convergence of ideals

f γ open sets and f γ continuity in fuzzy bitopological spaces in this paper we firstly introduce the concept of d i d j f c open resp d i d j f c closed set which is weaker than each of the concepts of d i d j f semiopen d i d j f semiclosed set or d i d j f preopen d i d j f preclosed set we study their properties and discuss the relationships between these concepts and relevant concepts in f bitopological spaces using this new notion we define the f p c continuity as a generalization of f pairwise semicontinuity fuzzy sets syst 64 1994 421 and f pairwise precontinuity fuzzy sets syst 62 1994 231 and establish their various characteristic properties

bisimulations for fuzzy transition systems there has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems however the comparison at this level is too coarse recently a finer behavioral measure i e bisimulation has been introduced to fuzzy finite automata however the results obtained are applicable only to finite state systems in this paper we consider bisimulation for general fuzzy systems which may be infinite state or infinite event by modeling them as fuzzy transition systems ftss to help understand and check bisimulation we characterize it in three ways by enumerating whole transitions comparing individual transitions and using a monotonic function in addition we address composition operations subsystems quotients and homomorphisms of ftss and discuss their properties connected with bisimulation the results presented here are useful to compare the behavior of general fuzzy systems in particular this makes it possible to relate an infinite fuzzy system to a finite one which is easier to analyze with the same behavior

a note on the article fuzzy less strongly semiopen sets and fuzzy less strong semicontinuity abstract in this note we show that some results in the article by fang jing ming are incorrect

the near sr compactness axiom in l topological spaces a kind of new fuzzy compactness called near sr compactness is defined for an arbitrary l subset and for l a complete demorgan algebra this kind of fuzzy compactness is between lowen s strong fuzzy compactness and the second author s sr compactness characterizations and examples of near sr compact l subsets are given and its topological properties are systematically investigated

fuzzy discrete event systems under fuzzy observability and a test algorithm in order to more effectively cope with the real world problems of vagueness impreciseness and subjectivity fuzzy discrete event systems fdess were proposed recently notably fdess have been applied to biomedical control for human immunodeficiency virus hiv acquired immune deficiency syndrome aids treatment planning and sensory information processing for robotic control qiu independently developed supervisory control theory of fdess we note that the controllability of events in qiu s work is fuzzy but the observability of events is crisp and the observability of events in cao and ying s work is also crisp although the controllability is not completely crisp since the controllable events can be disabled with any degrees motivated by the necessity to consider the situation that the events may be observed or controlled with some membership degrees in this paper we establish the supervisory control theory of fdess with partial observations in which both the observability and controllability of events are fuzzy instead we formalize the notions of fuzzy controllability condition and fuzzy observability condition in addition controllability and observability theorem of fdess is set up in a more generic framework in particular we present a detailed computing flow to verify whether the controllability and observability conditions hold thus this result can decide the existence of supervisors also we use this computing method to check the existence of supervisors in the controllability and observability theorem of classical discrete event systems dess which is a new method and different from classical case a number of examples are elaborated on to illustrate the presented results

fuzzy discrete event systems for multiobjective control framework and application to mobile robot navigation fuzzy discrete event systems fdess have been introduced in recent years to model systems whose discrete states or discrete state transitions can be uncertain and are hence determined by a possibility degree this paper develops an fdes framework for the control of sampled data systems that have to fulfill multiple objectives the choice of a fuzzy system representation is justified by the assumption of a controller realization that depends on various potentially imprecise sensor measurements the proposed framework consists of three basic steps that are performed at each sampling instant first the current fuzzy state of the system is determined by a sensor evaluation second the fuzzy state in the future sampling instant is predicted for all possible control actions of the system finally an original multiobjective weighting strategy is proposed to determine the control action to be applied in the current sampling instant the features of the proposed approach are demonstrated by a detailed mobile robot example which includes a simulation study

fuzzy strongly semiopen sets and fuzzy strong semicontinuity abstract in this paper we first introduce and study the fuzzy strongly semiopen and fuzzy strongly semiclosed sets in fuzzy space then we introduce the strong semi interior and strong semiclosure of a fuzzy set and kuratowski s 14 sets theorem of general topology is generalized finally we introduce the fuzzy strongly semicontinuous fuzzy strongly semiopen and fuzzy strongly semiclosed mappings on fuzzy topological spaces and also establish some of their characteristic properties and discuss relations between fuzzy continuous fuzzy semicontinuous and fuzzy strongly semicontinuous mappings

analysis and control of fuzzy discrete event systems using bisimulation equivalence in order to more effectively cope with the real world problems of vagueness impreciseness and subjectivity fuzzy discrete event systems fdess were proposed recently in this paper we deal with the analysis and control of fuzzy discrete event systems by using bisimulation equivalence in practice we design a supervisor such that the controlled system is bisimilar to the specification also a model theorem showing that a supervisor exists over a certain finite fuzzy state space is obtained furthermore the notion of fuzzy state controllability is introduced as part of a necessary and sufficient condition for the existence of a supervisor

supervisory control of fuzzy discrete event systems for simulation equivalence the supervisory control theory of fuzzy discrete event systems fdess for fuzzy language equivalence has been developed however in a way language equivalence has limited expressiveness therefore if the given specification can not be expressed by language equivalence then the control for language equivalence does not work in this paper we further establish the supervisory control theory of fdess for fuzzy simulation equivalence whose expressiveness is stronger than that of fuzzy language equivalence first we formalize the notions of fuzzy simulation and fuzzy simulation equivalence between two fdess then we present a method for deciding whether there is a fuzzy simulation or not in addition we also show several basic properties of fuzzy simulation relations afterward we put forward the notion of fuzzy simulation based controllability and in particular show that it serves as a necessary and sufficient condition for the existence of the fuzzy supervisors of fdess moreover we study the range control problem of fdess some examples are given to illustrate the main results obtained