spiral waves in reaction diffusion equations we consider the reaction diffusion system begin gathered r t nabla 2 r r left 1 r 2 vec nabla theta cdot vec nabla theta right hfill r theta t r nabla 2 theta 2 vec nabla r cdot vec nabla theta qr 3 hfill end gathered this system governs the solutions of reaction diffusion systems near a hopf bifurcation point in two spatial dimensions we use formal asymptotic expansions to contruct one armed and multi armed archimedean spiral waves for small values of the parameter q we then show that the one armed spiral waves are probably stable and the multi armed ones are unstable for q small next by numerical continuation methods we construct spiral waves for all q these calculations show that the one armed spiral waves are unstable when q 1 397 cdots we also find the explicit one dimensional analogues of spiral waves for all q and show that they are unstable for q small

time dependence of breakdown in a global fiber bundle model with continuous damage a time dependent global fiber bundle model of fracture with continuous damage is formulated in terms of a set of coupled nonlinear differential equations a first integral of this set is analytically obtained the time evolution of the system is studied by applying a discrete probabilistic method several results are discussed emphasizing their differences with the standard time dependent model the results obtained show that with this simple model a variety of experimental observations can be qualitatively reproduced

one point compactifications of ditopological texture spaces in this paper a one point compactification of a ditopological texture space is defined and a concept of local compactness introduced and shown to be additive in the class of ditopological texture spaces an application to hutton spaces is given here a compact extension of an hutton space is obtained and a notion of local compactness is defined and shown to be productive in the class of l topological spaces where l is a hutton algebra

an interpretation of membership functions and the properties of general probabilistic operators as fuzzy set operators part i case of type 1 fuzzy sets abstract the grade of membership is assumed to be determined as the relative size of evidence grounds supporting a given element s membership compared to all the necessary reference grounds relevant to the judgement of membership grade and is interpreted as conditional probability conditioned by the given element by assigning the dependence relations of the evidence grounds to those of the fuzzy subsets the set operators are defined as probabilistic operators with dependence relations the properties of the operators are studied and it is found that with type 1 fuzzy subsets they satisfy all the basic properties satisfied by the crisp set operators illustrative examples are given describing the construction of membership functions and the selection of set operators in relation to the situations to be modelled the proposed operators a kind of parametrized operators with an index value of the dependence relations as a parameter cover the entire operators ranging from the so called max min operators to the bold union intersection operators an extension of the above operator range is also discussed

membership function as an evaluation abstract after giving an overview of the different kinds of mathematical forms of the membership functions we extract the different demands and determine the rational class of the membership functions from the generalisation of our result we can determine it giving four parameters the internal a b the sharpness and the decision level we show the correspondence of this membership function to the zimmermann zysno model and using their empirical data we also test our mathematical model we also show the connections between the operators of the evaluation and membership functions which gives the generalisation of this concept in a more general form as a special case we can get a linear form

a review and comparison of six reasoning methods abstract five fuzzy reasoning methods are reviewed and their performance is compared with respect to a fuzzy control system model developed by an objective method based on three sets of real life data it is found from the investigation that the reasoning precision the calculation time and the number of possible input states to which a given reasoning method responds differ according to each reasoning method generally the point valued reasoning methods which are based on the assumption that connectives are crisp give better precision and shorter calculation time when the connectives are assumed to be linguistic reasoning with interval valued fuzzy sets are more appropriate to represent linguistic uncertainty for this reason type ii fuzziness generated with interval valued fuzzy sets are better handled with interval valued reasoning methods

fuzzy expert systems for ie or ms abstract fuzzy expert systems can be developed for the effective use of management within the domains of concern associated with industrial engineering ie operations research or and management science ms these models are designed with 1 expressive powers of representation embedded in linguistic variables and their linguistic values in natural language expressions and 2 improved methods of inference based on fuzzy logic which is a generalization of multi valued logic the results of these fuzzy expert system models are either 1 approximately good in comparison with their classical counterparts i e within a few percentage points of the optimal results of classical models as for example for the cases of production and spare parts planning or 2 much better than their counterparts as for example for the cases of job shop scheduling and consumer preference prediction in market share analysis in order to establish a sound basis for the preceding claims basic issues of representation and inference are first reviewed and then several prototype case studies are presented to support these claims

a model for the measurement of membership and the consequences of its empirical implementation representation and uniqueness theorems are presented for the fundamental measurement of the membership of a fuzzy set when the domain of discourse is order dense the conclusion that membership is on an interval scale is justified by the inapplicability of extensive measurement to fuzziness and the lack of a natural origin for membership some descriptive statistics are also presented from an empirical study currently in progress to construct membership functions they suggest that subjects differ in their perception of fuzziness and that the models in the literature for certain linguistic operators such as not very and antonym are not sufficiently general to account for the range of individual perceptions of vague attributes a more general mathematical model is proposed the question of the meaningfulness of statements about membership functions is also discussed in the light of the assertion that membership can be fundamentally measured at best on an interval scale some of the difficulties which arise in fuzzy set theory due to this property are illustrated and a solution is suggested involving the use of a function which is derived from membership but is on an absolute scale

pointed semi quantales and lattice valued topological spaces in a way more general than variable basis approach to lattice valued topological spaces the present paper introduces an alternative approach to lattice valued topological spaces direct product representation spaces extending the notion of quantal spaces in the sense of mulvey and pelletier to semi quantales recently proposed by rodabaugh this paper aims to give an answer to the main question whether there exists a categorical connection possibly a categorical equivalence between direct product representation spaces and variable basis lattice valued topological spaces small sources in the category of semi quantales which are called pointed semi quantales can be identified with direct product representation spaces for this reason the main problem will be handled in terms of pointed semi quantales generalized quasi lattice valued topological spaces extending variable basis quasi topological spaces into the present setting are introduced to be a suitable topological counterpart of pointed semi quantales to formalize and to solve the main problem categories of pointed semi quantales and of generalized quasi lattice valued topological spaces are constructed and the relations between these categories providing a satisfactory answer to the main problem are established in this paper

optimal design of laminated composite plates in a fuzzy environment the present study focuses on a fuzzy optimization approach to the optimal design of simply supported laminated composite plates the goal is minimum weight design of the composite plates the design constraints are the magnitude of center displacement and lamina failure criteria a procedure of two level optimization in a fuzzy environment is presented and this procedure is applied to the design of laminated composite plates to consider the influences of fiber direction and thickness of each lamina separately it is shown that the membership function in the case of failure can be deduced from continuum damage mechanics the membership function for failure criteria is the function of the internal state variable for degree of damage in the continuum damage mechanics the modified weibull membership function is chosen to be used as a simple case of damage progression the finite element method is used to calculate the displacement of the plate and the stresses of each lamina the fuzzy optimization formulation as a max min problem is transformed into a classical one this classical optimization problem is solved using the augmented lagrange multiplier method with the quasi newton method two examples are solved to demonstrate the procedure from the results it is shown that optimal design of laminated composite plates is more useful in a fuzzy environment and the modified weibull membership function characterizes the fuzziness of failure nomenclature bi upper limit of the inequality constraint d fuzzy decision f x objective function f x fuzzy goal

interacting damage models mapped onto ising and percolation models we introduce a class of damage models on regular lattices with isotropic interactions between the broken cells of the lattice quasistatic fiber bundles are an example the interactions are assumed to be weak in the sense that the stress perturbation from a broken cell is much smaller than the mean stress in the system the system starts intact with a surface energy threshold required to break any cell sampled from an uncorrelated quenched disorder distribution the evolution of this heterogeneous system is ruled by griffith s principle which states that a cell breaks when the release in potential elastic energy in the system exceeds the surfaceenergy barrier necessary to break the cell by direct integration over all possible realizations of the quenched disorder we obtain the probability distribution of each damage configuration at any level of the imposed external deformation we demonstrate an isomorphism between the distributions so obtained and standard generalized ising models in which the coupling constants and effective temperature in the ising model are functions of the nature of the quenched disorder distribution and the extent of accumulated damage in particular we show that damage models with global load sharing are isomorphic to standard percolation theory and that damage models with a local load sharing rule are isomorphic to the standard ising model and draw consequences thereof for the universality class and behavior of the autocorrelation length of the breakdown transitions corresponding to these models we also treat damage models having more general power law interactions and classify the breakdown process as a function of the power law interaction exponent last we also show that the probability distribution over configurations is a maximum of shannon s entropy under some specific constraints related to the energetic balance of the fracture process which firmly relates this type of quenched disorder based damage model to standard statistical mechanics

constructing membership functions using statistical data abstract determination of the membership functions is vital in practical applications of the fuzzy set theory this paper presents a guideline to construct the membership functions for fuzzy sets whose elements have a defining feature with a known probability density function pdf in the universe of discourse the method finds the smallest fuzzy set which assigns high average membership values to those objects with the defining features distributed according to the given pdf it is show that for any pdf the method is capable of generating membership functions in accordance with the possibility probability consistency principle membership functions derived from some of the well known pdfs and an application in solving noise contaminated linear system of equations are presented

elasticity and failure of a set of elements loaded in parallel the author studies the elasticity and failure characteristics of a system built by association in parallel of links with identical spring constant but random failure thresholds the occurrence of the first link rupture which is related to the theory of extreme order statistics is contrasted with the global failure for which a central limit theorem holds he also discusses the similarities and differences between the democratic and hierarchical models which differ in the mechanism by which the stress supported by links which have failed is transferred to the other stronger links this problem gives the simplest model of elastic non linear behaviour before global rupture occurs

thermodynamics of fiber bundles a recent theory that determines the properties of disordered solids as the solid accumulates damage is applied to the special case of fiber bundles with global load sharing and is shown to be exact in this case the theory postulates that the probability of observing a given emergent damage state is obtained by maximizing the emergent entropy as defined by shannon subject to energetic constraints this theory yields the known exact results for the fiber bundle model with global load sharing and holds for any quenched disorder distribution it further defines how the entropy evolves as a function of stress and shows definitively how the concepts of temperature and entropy emerge in a problem where all statistics derive from the initial quenched disorder a previously unnoticed phase transition is shown to exist as the entropy goes through a maximum in general this entropy maximum transition occurs at a different point in strain history than the stress maximum transition with the precise location depending entirely on the quenched disorder distribution

composite variety based topological theories motivated by the recent result of rodabaugh on categorical redundancy of lattice valued bitopology the paper considers another viewpoint on the topic based on the notion of composite variety based topological theory the new concept apart from providing a variable basis generalization of bitopology incorporates the most important approaches to topology currently developed in the fuzzy community bringing forward their categorically algebraic properties which are cleared from point set lattice theoretic dependencies dwelling on different ways of interaction between composite topology and topology e g embedding the former into the latter as a full bicoreflective subcategory we finally arrive at the conclusion that variable basis bitopological theories still deserve to be studied on their own

statistical aspects of the continuous damage theory abstract the present study addresses several fundamental aspects of a link connecting the continuous damage theory and the statistical strength theories the attention is focused on a simple but efficient way of devising rational damage laws based on the physical nature of the phenomenon the computed results evidence the remarkable flexibility of the suggested model in its application for a wide range of different materials

multivariate modeling and type 2 fuzzy sets this paper explores the link between type 2 fuzzy sets and multivariate modeling elements of a space x are treated as observations fuzzily associated with values in a multivariate feature space a category or class is likewise treated as a fuzzy allocation of feature values possibly dependent on values in x we observe that a type 2 fuzzy set on x generated by these two fuzzy allocations captures imprecision in the class definition and imprecision in the observations in practice many type 2 fuzzy sets are in fact generated in this way and can therefore be interpreted as the output of a classification task we then show that an arbitrary type 2 fuzzy set can be so constructed by taking as a feature space a set of membership functions on x this construction presents a new perspective on the representation theorem of mendel and john the multivariate modeling underpinning the type 2 fuzzy sets can also constrain realizable forms of membership functions because averaging operators such as centroid and subsethood on type 2 fuzzy sets involve a search for optima over membership functions constraining this search can make computation easier and tighten the results we demonstrate how the construction can be used to combine representations of concepts and how it therefore provides an additional tool alongside standard operations such as intersection and subsethood for concept fusion and computing with words

approximate reasoning for production planning abstract approximate reasoning for production planning could effectively be based on an interval valued representation of linguistic variables an interval valued representation provides a framework that i incorporates a dispersion about membership values and ii produces a robust result compared to classical results the proposed representation and inference is applied to a set of production problems in prototype studies the result of one such prototype study is summarized

on the qualitative necessity possibility measure i investigation in the framework of measurement theory abstract in this paper we try to investigate the qualitative possibility and or necessity measures introduced by d dubois computer and artificial intelligence 5 1986 403 416 and d dubois and h prade artificial intelligence 50 1991 223 239 as an extension of a qualitative or subjective probability studied by t fine theory of probability academic press new york 1973 we particularly review some relationship between these concepts and the basic qualitative possibility distribution as introduced by r r yager ieee trans fuzzy systems 1 3 1993 184 193 this will then be studied in the general framework of preference relations when the qualitative possibility necessity measures are real valued graded from 0 to 1 the justification of the proposal real valued relation will be carried out in the framework of measurement theory where a relationship between the difference measurement scale and our proposal will be established two kinds of relations will be proposed the first one is based on some appropriate exponential form and the second one is based on a more general form of r implication operators finally we briefly investigate some heuristic approach concerning the problem of how to obtain a real valued qualitative possibility from a quantitative possibility distribution

burst avalanches in solvable models of fibrous materials we review limiting models for fracture in bundles of fibers with statistically distributed thresholds for breakdown of individual fibers during the breakdown process avalanches consisting of simultaneous rupture of several fibers occur and the distribution d delta of the magnitude delta of such avalanches is the central characteristics in our analysis for a bundle of parallel fibers two limiting models of load sharing are studied and contrasted the global model in which the load carried by a bursting fiber is equally distributed among the surviving members and the local model in which the nearest surviving neighbors take up the load for the global model we investigate in particular the conditions on the threshold distribution which would lead to anomalous behavior i e deviations from the asymptotics d delta sim delta 5 2 known to be the generic behavior for the local model no universal power law asymptotics exists but we show for a particular threshold distribution how the avalanche distribution can nevertheless be explicitly calculated in the large bundle limit

time periodic spatial chaos in the complex ginzburg landau equation the phenomenon of time periodic evolution of spatial chaos is investigated in the frames of one and two dimensional complex ginzburg landau equations it is found that there exists a region of the parameters in which disordered spatial distribution of the field behaves periodically in time the boundaries of this region are determined the transition to the regime of spatiotemporal chaos is investigated and the possibility of describing spatial disorder by a system of ordinary differential equations is analyzed the effect of the size of the system on the shape and period of oscillations is investigated it is found that in the two dimensional case the regime of time periodic spatial disorder arises only in a narrow strip the critical width of which is estimated the phenomenon investigated in this paper indicates that a family of limit cycles with finite basins exists in the functional phase space of the complex ginzburg landau equation in finite regions of the parameters

measurement of membership functions and their acquisition abstract three basic views of the representation of membership functions are reviewed together with fundamental measurement of linguistic terms of linguistic variables the conclusion is that such measurements are either on an ordinal or an interval scale based on whether the appropriate axioms are validated by the empirical data with an allowance for stochastic variation the conjoint measurement is introduced for the case of multi dimensional linguistic variables whose linguistic terms are compositions of two or finitely many more component linguistic terms of distinct independent linguistic variables it is shown that any composition of distinct independent component linguistic terms of component linguistic variables by any t norm or s norm or any finite convext linear combination preserves the monotonic weak order property of the components in the composite once the scale properties of the measurement values of particular terms are validated composition procedures may be applied to the experimental data to obtain compound membership functions of fuzzy sets induced by meaningful representations of compositions of linguistic terms of linguistic variables finally four methods of membership acquisition and construction are reviewed from the perspective of fundamental measurement

equivalence and compositions of fuzzy rationality measures an axiomatic basis for fuzzy rationality measures has already been introduced by the authors in a previous paper 5 formalizing the fact that there exist degrees of consistency when preferences over a fixed set of alternatives are expressed in terms of fuzzy binary preference relations this paper deals with some practical consequences on the one hand similarities and compositions of fuzzy rationality measures are considered showing natural ways of deriving new measures on the other if basic stability properties are introduced in order to assure that small intensity measurement errors never lead to big changes in the associate rationality value it is shown that crisp i e binary rationality measures present serious difficulties when applied to fuzzy preference relations

paracompactness and full normality in ditopological texture spaces in this paper the authors lay the foundation for a theory of dicovers of ditopological texture spaces and use this to define notions of paracompactness and full normality some applications to fuzzy topology are also mentioned

a damage model based on failure threshold weakening abstract a variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions involving either critical phenomena or spinodal nucleation here we study a model for frictional sliding with long range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding we introduce a failure threshold weakening parameter into the cellular automaton slider block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event we show that a critical point is reached beyond which the probability of a system wide event scales with this weakening parameter we provide a mapping to the percolation transition and show that the values of the scaling exponents approach the values for mean field percolation spinodal nucleation as lattice size l is increased for fixed r we also examine the effect of the weakening parameter on the frequency magnitude scaling relationship and the ergodic behavior of the model

categorical foundations of variety based topology and topological systems the paper considers a new approach to fuzzy topology based on the concept of variety and developed in the framework of topological theories resembling those of rodabaugh as a result a categorical generalization of the notion of topological system of vickers is obtained and its theory unfolded which clarifies the relations between algebra and topology we also justify the use of semi quantales as the basic underlying structure for doing lattice valued topology as well as provide a categorical framework incorporating the theory of bitopological spaces

fuzzy sets as textures spaces ii subtextures and quotient textures in this paper the authors introduce the notions of subtexture and quotient texture of a complemented texture space conditions ensuring the existence of such textures are discussed and applied to show that certain natural subtextures of product textures may be defined these are used in particular to give representations of product l fuzzy sets and a representation involving quotient textures is also examined

a survey of fuzzifications of frames the papert papert isbell adjunction and sobriety this paper gives a survey of fuzzifications of frames the papert papert isbell adjunction between the categories of topological spaces and locales as well as the related concept of sobriety it then establishes categorical isomorphisms between yao l frames zhang liu l frames and l algebras lastly it studies the relationships between l sobriety modified l sobriety and i l sobriety the obtained results suggest that modified l sobriety is the most fruitful notion between the above concepts of lattice valued sobriety

a fuzzy c means variant for the generation of fuzzy term sets a fuzzy c means fcm variant is proposed for the generation of fuzzy term sets with overlap the proposed variant differs from the original mainly in two areas the first modification ensures that two end terms take the maximum and minimum domain values as their centers the second modification prevents the generation of non convex fuzzy terms that often occurs with the original algorithm the optimal number of terms and the optimal shape of the membership function associated with each term are determined based on the mean squared error criterion the exponential weight m used in the algorithm is found to greatly affect the shape of the membership function the effect of data size used for the generation of fuzzy terms is also discussed a generalized shaped function with a tunable parameter along with its complement is developed to fit all term sets generated by the fcm variant using various m values

synchronized disorder in a 2d complex ginzburg landau equation the phenomenon of spiral pair synchronization by oscillating strips nozaki bekki solution in a 2d cgle is investigated analytically the equations describing the interaction of the strips with one another and with spirals are derived analysis of the equations shows that under certain conditions the strips lead to frequency and phase locking of the spirals in this case the spiral pair dipole is aligned parallel to the strips with the position along the strips being arbitrary thus the interaction with strips may transform the spatio temporal chaos of spirals to the regime of periodically oscillating spatial disorder the dynamics of circular strips is investigated and their lifetime is estimated the behavior of the spirals bounded by circular stript is analysed

generalized fuzzy sets abstract this paper is concerned with a construction of fuzzy sets without depending on membership function algebraic properties of a family of fuzzy sets are investigated in this paper three notions are proposed 1 a ring of generalized fuzzy sets gf x of x a complete heyting algebra cha which contains the power set p x of x 2 an extension lattice b l where b p x and 3 the set of l fuzzy sets where l l x it is shown that these three notions are equivalent the mathematical structure of scgf x is studied and a ring of generalized fuzzy sets of type 2 is introduced

generalized fuzzy topology versus non commutative topology the paper introduces a modification of the notions of generalized fuzzy topological space of demirci and quantal space of mulvey and pelletier suitable to explore interrelations between point set lattice theoretic topology and non commutative topology developed in the framework of c algebras or more recently of quantales as a consequence of the new approach a generalization of the concept of topological system of vickers arises moreover the currently dominating variable basis topological setting in the fuzzy community due to rodabaugh appears to be fixed basis

interval valued fuzzy sets representation on multiple antecedent fuzzy s implications and reasoning abstract interval valued fuzzy sets are used to represent multiple antecedent s implications based on normal forms where linguistic connectives antecedents and consequents are assumed to be fuzzy these intervals are represented equivalently with their lower and upper bounds general forms are given for the bounds of multiple antecedent fuzzy s implications bounds for multiple antecedent reasoning are also investigated based on the bounds of multiple antecedent s implications it is suggested that modification functions utilized in approximation analogical reasoning aar be determined in such a way that consequents deduced by aar fall within the bounds of the reasoning an example is given to show how the bounds might be used to choose a modification scheme in aar

an efficient and flexible mechanism for constructing membership functions abstract this paper introduces a bezier curve based mechanism for constructing membership functions of convex normal fuzzy sets the mechanism can fit any given data set with a minimum level of discrepancy in the absence of data the mechanism can be intuitively manipulated by the user to construct membership functions with the desired shape some numerical experiments are included to compare the performance of the proposed mechanism with conventional methods

self organized criticality in a fibre bundle type model abstract the dynamics of a fibre bundle type model with equal load sharing rule is numerically studied the system formed by n elements is driven by a slow increase of the load upon it which is removed in a novel way through internal transfers to the elements broken during avalanches when an avalanche ends failed elements are regenerated with strengths taken from a probability distribution for a large n and certain restrictions on the distribution of individual strengths the system reaches a self organized critical state where the spectrum of avalanche sizes is a power law with an exponent 1 5

hierarchical scheduling based on approximate reasoning a comparison with isis abstract a hierarchical scheduling problem is considered the hierarchy consists of five levels each level has an associated rule base there are six basic input factors 1 the priority of a job 2 the earliness of the due date of a job 3 the likelihood of the availability of resources for the work station w s s 4 the capability of w s s to meet physical constraints 5 the capability of w s s to meet quality requirements and 6 work in progress inventory costs there are five consequents one for each level 1 suggested place of a job in the order of jobs 2 the suggested place of w s s in the order of w s s 3 the current suggested place of a w s s in the order of w s s 4 the next current suggested place of w s s in the order of w s s and 5 the suggested place of the queue arrangements both the input factors antecedents and the output factors consequents take on linguistic terms to express the qualitative assessments of a scheduling expert within the context of the specific factor an approximate reasoning framework based on interval valued fuzzy sets and a search tree heuristic with similarity measures is executed for the analysis of the hierarchical scheduling problem using a fuzzy tool box coded in lisp that interacts with kee for the representation of the knowledge base in a frame structure the software model is tested with real life data used in m fox s isis model a comparison of the two models based on tardiness measure shows that there are slight advantages to fuzzy set representation and approximate reasoning with respect to tardiness measure above and beyond the user friendly nature of knowledge representation available with fuzzy sets

spatiotemporal chaos in the one dimensional complex ginzburg landau equation the dynamical behavior of a large one dimensional system obeying the cubic complex ginzburg landau equation is studied numerically as a function of parameters near a supercritical bifurcation two types of chaotic behavior can be distinguished beyond the benjamin feir instability a phase turbulence regime with a conserved phase winding number and no phase dislocations space time defects and a defect regime with a nonzero density of defects the transition between the two can either be continuous or discontinuous hysteretic depending on parameters the spatial decay of the phase correlation function is inferred to be exponential in both regimes with a sharp decrease of the correlation length upon entering the defect phase the temporal decay of correlations is exponential in the defect regime

type i and type ii fuzzy system modeling abstract two system modeling approaches are proposed with a unification of fuzzy methodologies type i and type ii knowledge representation are reviewed together with their proposed approximate reasoning schemes type i representation and inference are based on boolean normal forms type i models are myopic because in these models either the disjunctive or the conjunctive boolean normal forms are selected rather arbitrarily for knowledge representation and inference and then they are fuzzified whereas in type ii models representation and inference are based on fuzzy disjunctive and conjunctive normal forms which are derived from the fuzzy truth tables