on stability in possibilistic linear equality systems with lipschitzian fuzzy numbers abstract linear equality systems with fuzzy parameters and crisp variables defined by the extension principle are called possibilistic linear equality systems the study focuses on the problem of stability with respect to perturbations of fuzzy parameters of the solution in these systems

on the steepest descent approximation method for the zeros of generalized accretive operators abstract in this paper we present certain characteristic conditions for the convergence of the generalized steepest descent approximation process to a zero of a generalized strongly accretive operator defined on a uniformly smooth banach space our study is based on an important result of reich s reich an iterative procedure for constructing zeros of accretive sets in banach spaces nonlinear anal 2 1978 85 92 and given results extend and improve some of the earlier results which include the steepest descent approximation method

applications of fuzzy chaos to fuzzy simulation in this paper we wish to use fuzzy chaos to generate fuzzy simulation we first discuss how fuzzy chaos can produce a chaotic sequence of fuzzy numbers we apply this technique to fuzzily simulate a solution to a simple fuzzy optimization problem other applications of fuzzy simulation to fuzzy mathematical programming fuzzy max flow fuzzy regression and tuning a fuzzy controller are also presented

fuzzy plane geometry i points and lines abstract we introduce a comprehensive study of fuzzy geometry in this paper by first defining a fuzzy point and a fuzzy line in fuzzy plane geometry we consider the fuzzy distance between fuzzy points and show it is a weak fuzzy metric we study various definitions of a fuzzy line develop their basic properties and investigate parallel fuzzy lines

convergence theorems for strongly pseudo contractive and strongly accretive maps supposeeis an arbitrary real banach space andkis a nonempty closed convex and bounded subset ofe supposet k kis a uniformly continuous strong pseudo contraction with constantk 0 1 suppose an bn cn a n b n and c n are sequences in 0 1 satisfying the following conditions i an bn cn 1 a n b n c n integersn 0 ii lim bn lim b n lim c n 0 iii bn iv cn for arbitraryx0 u0 v0 k define the sequence xn n 0iteratively byxn 1 anxn bntyn cnun yn a nxn b ntxn c nvn n 0 where un vn are arbitrary sequences ink then xn converges strongly to the unique fixed point oft related results deal with the iterative solutions of nonlinear equations involving set valued strongly accretive operators

a new i vector topology generated by a fuzzy norm this paper is devoted to the research for a topological structure for i vector on the fuzzy normed linear space in the sense of felbin by using a natural method a new i vector topology on the fuzzy normed linear space is constructed we study some of its properties and prove that the fuzzy normed linear space is a locally convex i topological vector space with respect to the i topology under a proper condition we give a necessity and sufficienct condition for a fuzzy normed linear space to be hausdorff and weakly hausdorff with respect to the i vector topology respectively in addition we also discuss the relations between this i vector topology and other two known i vector topologies on the fuzzy normed linear space lastly we give some canonical examples of fuzzy normed linear spaces using this i vector topology

benchmarking in linguistic importance weighted aggregations in this work we concentrate on the issue of weighted aggregations and provide a possibilistic approach to the process of importance weighted transformation when both the importances interpreted as benchmarks and the ratings are given by symmetric triangular fuzzy numbers we will show that using the possibilistic approach i small changes in the membership function of the importances can cause only small variations in the weighted aggregate ii the weighted aggregate of fuzzy ratings remains stable under small changes in the nonfuzzy importances iii the weighted aggregate of crisp ratings still remains stable under small changes in the crisp importances whenever we use a continuous implication operator for the importance weighted transformation we illustrate the proposed method by some simple examples

embedding problem of fuzzy number space part ii abstract using a concrete structure into which we embed the fuzzy number space e1 several necessary and sufficient conditions of fuzzy set valued functions are given by means of abstract function theory

iterative solutions of nonlinear accretive operator equations in arbitrary banach spaces suppose e is an arbitrary real banach space and k is a nonempty closed convex and bounded subset of e suppose t k k is a uniformly continuous strong pseudocontraction it is proved that the mann and the ishikawa iteration methods converge strongly to the unique fixed point of t furthermore our results also hold for the slightly more general class of strictly hemicontractive maps related results deal with the iterative approximation of solutions of accretive operator equations in arbitrary real banach spaces miramare trieste april 1996 permanent address department of mathematics university of nigeria nsukka nigeria

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

iterative process with errors to locally strictly pseudocontractive maps in banach spaces abstract let k be a nonempty subset of a uniformly smooth banach space x and a k x be a locally strickly pseudocontractive map with bounded range the mann and ishikawa iterative sequences with errors which strongly converge to the unique fixed point of a are given under weaker conditions these results answer positively the open problems mentioned by deng and ding 1 p 122 and chidume 2 p 550 the related results deal with the problems that the mann and ishikawa iterative sequences with errors strongly converge to the unique solution of the equation tx f when t x x is locally strongly accretive such that the range of i t is bounded

platform type fuzzy number and separability of fuzzy number space abstract in this paper we introduce the notions of the rectangular fuzzy set and step type fuzzy number it is shown that the family of all platform type fuzzy numbers e t 1 is dense in fuzzy numbers space e 1 about l p metric d p and the family of all rational type step fuzzy numbers e qg 1 e qg 1 e t 1 and e qg 1 is a countable set is dense in e t 1 d p further as corollaries we obtain that e 1 d p is a separable metric space and several separable metric spaces about p mean symmetric difference metric d p

convergence of iterative processes with errors for set valued pseudocontractive and accretive type mappings in banach spaces abstract in this paper some new results on convergence of iterative processes with errors for set valued pseudocontractive and accretive mappings in banach spaces are obtained our results extend and improve a number of the recent results

a generalized steepest descent approximation for the zeros of m accretive operators a necessary and sufficient condition is proved for a generalized steepest descent approximation to converge to the zeros of m accretive operators related results deal with the convergence of the scheme to fixed points of pseudocontractive maps

iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo contractive mappings in banach spaces abstract in this article we prove some new convergence theorems of the ishikawa and mann iteration sequences for strongly accretive and strongly pseudo contractive mappings by using the new inequality and the new approximation methods our main results improve and extend the corresponding results of j math anal appl 151 1990 453 461 proc amer math soc 120 1994 545 551 j math appl 192 1995 502 518 j math anal appl 174 1993 441 449 acta appl math 32 1993 183 196 nonlinear anal tma 24 1995 981 987 j math anal appl 178 1993 9 21 proc amer math soc 125 6 1997 1705 1709

representations with fuzzy darts abstract fuzzy information is organized by partitioning the fuzzy interval 0 1 into layers of fuzzy strata at each level fuzzy information is approximated by a fuzzy dart information at all levels is combined and recorded as an n tuple of fuzzy darts from this perspective fuzzy numbers with continuous boundaries are approximated by pn fuzzy numbers then within the framework of fuzzy level sets the problem of comparing pn fuzzy numbers is addressed for applications differentiably smooth fuzzy maps which are either expansive or contractive are characterized by their derivatives finally anti fuzzy numbers are introduced and discussed

the topological structure of fuzzy sets with endograph metric for a non degenerate convex subset y of the n dimensional euclidean space r n let k y be the family of all fuzzy sets of r n which are upper semicontinuous fuzzy convex and normal with compact supports contained in y we show that the space k y with the topology of endograph metric is homeomorphic to the hilbert cube q 1 1 w iff y is compact and the space k y is homeomorphic to x n q sup x n 1 iff y is non compact and locally compact

approximating solutions for the systems of strongly accretive operator equations the purpose of this paper is to study a strong convergence of multi step iterative scheme to a common fixed point for a finite family of strongly pseudo contractive mappings as a consequence the strong convergence theorems for the modified multi step iterative sequence to a solution of systems of strongly accretive operator equations are obtained in real uniformly smooth banach spaces the results presented in this paper improve and extend the corresponding xu y xu ishikawa and mann iterative processes with errors for nonlinear strongly accretive operator equations j math anal appl 224 1998 91 101 and noor rassias and huang m a noor t m rassias z huang three step iterations for nonlinear accretive operator equations j math anal appl 274 2002 59 68 and many others

error bounds for approximation solutions to nonlinear equations of strongly accretive operators in uniformly smooth banach spaces abstract let x be a uniformly smooth banach space and t x x a strongly accretive operator in this paper we give the error bounds for the approximation solutions of the nonlinear equation tx f generated by both the mann and the ishikawa iteration process on the other hand let k be a nonempty convex subset of x and t k k a strictly pseudocontractive mapping the related results deal with the error bounds for the iterative approximation of the fixed point of t generated by these two processes

topological properties of the spaces of regular fuzzy sets abstract by identifying the space f 0 x of regular fuzzy sets with a subspace t 0 x of some compact set valued function space we define a uniform topology on f 0 x and discuss several topological properties such as first countability separability connectedness etc when x is a reflexive banach space f 0 x is imbedded into a locally convex topological vector space and a definition of integration and differentiation for f 0 x valued functions is given

the solution by iteration of nonlinear equations in uniformly smooth banach spaces abstract letebe a uniformly smooth banach space and lett d t e ebe a strong pseudocontraction with an open domaind t ineand a fixed pointx d t we establish the strong convergence of the mann and ishikawa iterative processes with errors to the fixed point oft related results deal with the iterative solution of operator equations of the formsf txandf x tx 0 whentis a set valued strongly accretative operator our theorems include the cases in which the operatortis defined only locally explicit error estimates are also given

duality theory in fuzzy mathematical programming problems with fuzzy coefficients in this paper the notions of subgradient subdifferential and differential with respect to convex fuzzy mappings are investigated which provides the basis for the fuzzy extremum problem theory we consider the problems of minimizing or maximizing a convex fuzzy mapping over a convex set and develop the necessary and or sufficient optimality conditions furthermore the concept of saddle points and minimax theorems under fuzzy environment is discussed the results obtained are used to formulate the lagrangian dual of fuzzy programming under certain fuzzy convexity assumptions kkt conditions for fuzzy programming are derived and the perturbed convex fuzzy programming is considered finally these results are applied to fuzzy linear programming and fuzzy quadratic programming

comparison of topological and uniform structures for fuzzy numbers and the fixed point problem abstract the goal of this paper is to compare certain topological and uniform structures on sets of fuzzy numbers since fuzzy sets can be viewed as a kind of subsets they can be endowed with uniform structures in ways similar to those used for classic subsets the hausdorff construction is one such approach the structures we study are the myope structure the uniform convergence of the cuts in the sense of hausdorff and a structure induced by a metric defined by goetschel and voxman we show how these structures are related to fixed point problems for some classes of fuzzy numbers

dynamic topologies and their applications to crisp topologies fuzzifications of crisp topologies and fuzzy topologies on the crisp real line abstract we introduce and develop topologies whose members are dynamic sets a la zeleny this development spawns the notions of phase and co phase spaces fuzzy dual dynamic dual and co fuzzy dual with the following results being obtained result a the notion of fuzzy dual provides a unifying framework for the diverse fuzzification schemes of hutton gantner steinlage warren klein and lowen result b the dynamic duals of the fuzzy real lines are both homeostatic and coheterostatic result c the fuzzy real lines re interpreted as fuzzy duals of r with the usual euclidean topology t induce on r via the notion of co fuzzy dual a class of canonical stratified fuzzy topologies co r l e g if l is a demorgan algebra and lc 1 then the compactness of a r is equivalent to the ordinary compactness of a w r t t and if l is a hutton algebra r l co r l is metrizable in the sense of hutton and erceg with erceg metric d l such that d l p r 1 p s 1 r s where pr is the crisp point or impulse with support r i e d l extends the euclidean metric on r

a representation of fuzzy numbers abstract each fuzzy number can be written in a unique way as the sum of a symmetric and a skew fuzzy number these two kinds of fuzzy numbers correspond bijectively to certain functions on the unit interval that are of bounded variation these bijections give rise to a representation of fuzzy numbers by pairs of functions of bounded variation as application mathematical structures on the set of functions of bounded variation are transported to that of fuzzy numbers making the set of fuzzy numbers into a complete metric space a commutative semiring and a commutative residuated lattice

the solution by iteration of nonlinear equations of hammerstein type let e be a real uniformly smooth banach space suppose n is a set valued locally accretive map with open domain d n c e k is a single valued map with domain d k c e such that im n c d k and k exists and is locally strongly accretive on im k if the equation f e x knx has a solution x e d n the strong convergence of iteration methods of the ishikawa and mann types to this solution is established related theorems deal with the iterative solution of nonlinear equations of the form f g x tx for the case where t is accretive explicit convergence rates are established miramare trieste november 1996 permanent address department of mathematics and computer science nnamdi azikiwe university p m b 5025 awka anambra state nigeria

convex and strongly convex fuzzy sets abstract properties of the support and of the core of convex and strongly convex fuzzy sets are considered the convex and strongly convex fuzzy sets in the real line are characterized by means of the piece wise monotonic functions

topological properties of fuzzy numbers fuzzy numbers are defined and a metric is assigned to this class of fuzzy sets topological properties of the resulting metric space are studied the notion of q crisp fuzzy numbers is introduced and in particular it is shown that this class of fuzzy numbers is homeomorphic to the hilbert cube

equations with fuzzy numbers abstract assuming that is any operation defined in the real number set it can be extended to the fuzzy sets by zadeh s extension principle in this paper we study which conditions have to be verified by the cuts of the fuzzy numbers f and g in order that the equation f x g has a solution by the way we study some properties of the function h g f considered by e sanchez

on the convergence of fuzzy sets three kind of convergences are defined on a space of fuzzy sets relationships between these convergences are studied some comments on the fixed point property are represented

a perturbed iterative procedure for multivalued pseudo contractive mappings and multivalued accretive mappings in banach spaces abstract the main purpose of this paper is to introduce and study a new perturbed iteration method for multivalued mappings some strong convergence theorems of perturbed iteration sequences for multivalued pseudo contractive mappings and strongly accretive mappings are obtained

can fuzzy neural nets approximate continuous fuzzy functions abstract we first argue that regular fuzzy neural nets based on standard fuzzy arithmetic and the extension principle cannot be universal approximators this negative result is surprising since regular neural nets are universal approximators we then argue that hybrid fuzzy neural nets not necessarily based on standard fuzzy arithmetic can be universal approximators

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

ishikawa iteration process for nonlinear lipschitz strongly accretive mappings abstract let e lp p 2 and let t e e be a lipschitzian and strongly accretive mapping let s e e be defined by sx tx x it is proved that under suitable conditions on the real sequences n n 0 and n n 0 the iteration process x0 e xn 1 1 n xn ns 1 n xn nsxn n 0 converges strongly to the unique solution of tx a related result deals with the iterative approximation of fixed points for lipschitz strongly pseudocontractive mappings in e a consequence of our result gives an affirmative answer to a problem posed by c e chidume j math anal appl 151 no 2 1990 453 461

stable iteration procedures for strong pseudo contractions and nonlinear operator equations of the accretive type it is proved that certain mann and ishikawa iteration procedures arestable with respect to strongly pseudo contractive mappingsin real banach spaces which areq uniformly smooth 1 q a related result deals with stable iteration procedures forsolutions of nonlinear equations of the accretive type

convergence theorems for φ strongly accretive and φ hemicontractive operators suppose that x is an arbitrary real banach space and t x x is a continuous strongly accretive operator it is shown that the nonlinear equation tx f has a unique solution and under certain conditions both the mann and ishikawa iteration methods with errors introduced by y xu 1998 j math anal appl 224 91 101 converge strongly to the solution a related result deals with the approximation of fixed points of hemicontractive operators

some remarks on the topological properties of fuzzy numbers in r n abstract the space of normal upper semicontinuous fuzzy convex and compactly supported fuzzy numbers in r b are considered endowed with different metrics generated by the hausdorff metric a subspace is introduced and properties of the metrics restricted to the subspace are investigated

steepest descent method for equilibrium points of nonlinear systems with accretive operators let e be a real normed linear space and let a e 2e be a bounded uniformly continuous strongly accretive multi valued map with nonempty closed values such that the inclusion 0 ax has a solution x e it is proved that both the ishikawa and the mann iteration processes are bounded and converge strongly to x related results deal with the convergence of the iteration processes to fixed points of strongly pseudocontractive maps and the iterative solution of the equation 0 x fx for an accretive map f furthermore the ishikawa and mann iteration methods with errors are discussed and proofs are sketched on how our theorems extend to these methods our method of proof is of independent interest

l metric on the space of l fuzzy numbers abstract in this article a natural l topology is constructed on the set of l fuzzy numbers which is called the standard l topology it is proved that the standard l topology can be induced by an l metric the space of trapezoidal fuzzy numbers can be regarded as a subspace of the space of l fuzzy numbers an l metric on the set of trapezoidal fuzzy numbers is presented

contributions to fuzzy analysis in some sense fuzzy analysis deviates highly from classical analysis needing its own specific notions the main reason which causes this situation consists in the different algebraic and structure theoretic properties of the usual real numbers and fuzzy numbers the paper which is an extended version of 4 is devoted to this problem presenting some of these specific notions in particular examples of proper fuzzy normed vector spaces and proper fuzzy normed algebras are given

strong convergence of iterative methods by strictly pseudocontractive mappings in banach spaces abstract in this paper we deal with fixed point computational problems by strongly convergent methods involving strictly pseudocontractive mappings in smooth banach spaces first we prove that the s iteration process recently introduced by sahu in 14 converges strongly to a unique fixed point of a mapping t where t is strongly pseudocontractive mapping from a nonempty closed and convex subset c of a smooth banach space into itself it is also shown that the hybrid steepest descent method converges strongly to a unique solution of a variational inequality problem with respect to a finite family of i strictly pseudocontractive mappings from c into itself our results extend and improve some very recent theorems in fixed point theory and variational inequality problems particularly the results presented here extend some theorems of reich 1980 1 and yamada 2001 15 to a general class of strictly pseudocontractive mappings in uniformly smooth banach spaces

on chidume s open questions and approximate solutions of multivalued strongly accretive mapping equations in banach spaces abstract some new convergence theorems of the ishikawa iteration process for multi valued pseudo contractive mappings and multi valued accretive mappings are obtained which affirmatively answer the open questions put forth by 4

on the level convergence of a sequence of fuzzy numbers abstract in this paper we first give a simplified proof of the existence theorem of supremum and infimum in fuzzy number space e 1 established by wu and wu j math anal appl 210 1997 499 and improve the expressions of the supremum and infimum as a straightforward corollary of this result we obtain a necessary and sufficient condition under which for a bounded sequence of fuzzy numbers u n the pair of functions sup n u n and sup n u n can determine a fuzzy number secondly we give a necessary and sufficient condition for a sequence of fuzzy numbers u n to be levelwise convergent in e 1 and generalize some important theorems in real number spaces to fuzzy number spaces finally we prove the existence of supremum and infimum for the level continuous fuzzy valued function on a closed interval and give a necessary and sufficient condition under which its supremum and infimum can be attained

ishikawa and mann iteration methods with errors for nonlinear equations of the accretive type abstract let e be an arbitrary banach space and t e e a lipschitz strongly accretive operator it is proved that for a given f e the ishikawa and the mann iteration methods with errors introduced by 18 converge strongly to the solution of the equation tx f furthermore if e is a uniformly smooth banach space and t e e is demicontinuous and strongly accretive it is also proved that both the ishikawa and the mann iteration methods with errors converge strongly to the solution of the equation tx f related results deal with the iterative approximation of fixed points of strongly pseudocontractive operators and the solution of the equation x tx f f e when t e e is m accretive

fuzzy plane geometry ii circles and polygons abstract this paper continues our research in fuzzy plane geometry previously we studied fuzzy points and fuzzy lines now we investigate fuzzy circles and fuzzy polygons we show that the fuzzy area of a fuzzy circle or a fuzzy polygon is a fuzzy number we also argue that the fuzzy perimeter of a fuzzy circle or a fuzzy polygon is a fuzzy number

an experimental study on fuzzy distances for skull face overlay in craniofacial superimposition abstract skull face overlay is the most time consuming and error prone stage in craniofacial superimposition an important skeleton based forensic identification technique this task focuses on achieving the best possible overlay of an unknown skull found and a single ante mortem image of a candidate missing person the process is influenced by some sources of uncertainty since two objects of different nature are involved i e a skull and a face in previous works we have developed a computer aided craniofacial superimposition system aimed to assist forensic anthropologists in obtaining the best possible skull and face overlay the system has successfully allowed us to reduce the processing time simplify the forensic anthropologists work and make the process more objective and reproducible our approach is based on automatically overlaying a skull three dimensional model onto a facial photograph by minimizing the distance between two subsets of corresponding cranial and facial landmarks the proposed method properly deals with the inherent uncertainty sources to the skull face overlay process by considering fuzzy sets to model imprecise landmark location and imprecise cranial and facial landmarks spatial correspondence resulting from the presence of soft tissues in the face accordingly our methodology requires computing two kinds of distance metrics between a point and a fuzzy set and between two fuzzy sets this contribution is devoted to study the performance and influence of the most significant and suitable fuzzy distances proposed in the specialized literature as well as other new ones proposed on our skull face overlay system in particular we have tested the behavior of our automatic method when considering eight different distance measurements the system performance has been objectively evaluated considering 18 case studies resulting from a ground truth dataset following a rigorous statistical experimental setup the fact that the choice of a good distance metric is crucial to our method has been demonstrated since it significantly affects the quality of the final solutions it has been shown that our skull face overlay approach presents the best performance using the weighted mean distance in most of the cases and that the results are both more accurate and robust than the other studied metrics

iterative and approximate solutions of general parameter dependent nonlinear operator equations in hilbert spaces iterative solutions of a general nonlinear operator equation of the form ax tx f where a and t are in general nonlinear operators in an appropriate space have not been developed so far in this paper the three well known banach mann and ishikawa iteration processes are used to find solutions of this equation in the hilbert space case an error estimate in each case is given the established results generalize many of the known results in literature

iterative approximation of solutions to nonlinear equations involving m accretive operators in banach spaces let e be an arbitrary real banach space and t e e be a lipschitz continuous accretive operator under the lack of the assumption limn n limn n 0 we prove that the ishikawa iterative sequence with errors converges strongly to the unique solution of the equation x tx f moreover this result provides a convergence rate estimate for some special cases of such a sequence utilizing this result we imply that if t e e is a lipschitz continuous strongly accretive operator then the ishikawa iterative sequence with errors converges strongly to the unique solution of the equation tx f our results improve generalize and unify the ones of liu chidume and osilike and to some extent of reich

solving fuzzy equations a new solution concept abstract we have previously shown 2 that many fuzzy equations do not have solutions when the solution concept is based on the extension principle we therefore introduce two new solution procedures one based on the unified extension 6 and the other based on possibility theory after we solve the non fuzzy equation for the unknown variable we show for many types of equations that 1 the two new solutions are identical 2 the solution is either a real or generalized complex fuzzy number all uncertain parameters are modeled as real fuzzy numbers and 3 the previous solution based on the extension principle when it exists is a subset of the new solution in particular we show that the fuzzy quadratic equation with real fuzzy number coefficients always has a new solution

iterative solution of nonlinear equations of the φ strongly accretive type abstract letq 1 and letebe a realq uniformly smooth banach space lett e ebe a lipschitz strongly accretive operator and suppose the equationtx f f e has a solution it is proved that under suitable conditions on the real sequences n n 0 and n n 0 the iteration process formula converges strongly to the unique solution of the equationtx f a related result deals with the approximation of fixed points of hemicontractive operators a class of operators which is much more general than the important class of strongly pseudocontractive operators

the problem of completeness for p mean symmetric difference metric in this paper by applying lebesgue s measure on the symmetric difference of sets the p mean symmetric difference metric d p is established to measure the difference between fuzzy numbers the basic properties of cauchy sequences of e1 d p are discussed and we show e1 k d p is complete where e1 k a a e1anda0 k k is a closed interval a0 is the closure of support set of a further an example where the space e1 d p is not complete is given

stability of the mann and ishikawa iteration procedures for φ strong pseudocontractions and nonlinear equations of the φ strongly accretive type abstract we study the stability of the mann and ishikawa iteration procedures for the class of lipschitz strongly pseudocontractive maps in arbitrary real banach spaces as a consequence we study the stability of these iteration procedures for the iterative approximation of solutions of nonlinear equations of the strongly accretive type furthermore we prove that the t stability of the mann iteration procedure leads to the strong convergence to the fixed point of t of the so called mann iteration method with errors introduced by liu j math anal appl 194 1995 114 125

ishikawa and mann iterative processes with errors for nonlinear strongly accretive operator equations abstract the purpose of this paper is to revise the definitions of ishikawa and mann iterative processes with errors by using a new inequality to study the unique solution of the nonlinear strongly accretive operator equationtx fand the convergence problem of ishikawa and mann iterative sequences for strongly pseudo contractive mappings without the lipschitz condition the results presented in this paper improve and extend the corresponding results in 4 5 7 10 12 15 16 in the more general setting in particular the open problem mentioned by chidume in 5 has been given an affirmative answer

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

study on fuzzy optimization methods based on principal operation and inequity degree fuzzy optimization is a well known optimization problem in artificial intelligence manufacturing and management so establishing general and operable fuzzy optimization methods are important in both theory and application in this paper by distinguishing principal indices and secondary indices we give a method for comparing fuzzy information based on synthesizing effect and an operation for achieving fuzzy optimization based on a principal indices transformation further we propose an axiomatic system for fuzzy inequity degree based on the essence of constraint and give an instructive metric method for fuzzy inequity degree then by combining with genetic algorithm we give some fuzzy optimization methods based on principal operation and inequity degree denoted by bpo id fga for short finally we consider the convergence of our algorithm using the theory of markov chains and analyze its performance through two concrete examples all these indicate that bpo id fga can effectively merge decision preferences into the optimization process and that it also possesses better global convergence so it can be applied to many fuzzy optimization problems

a novel visual codebook model based on fuzzy geometry for large scale image classification the codebook model has been developed as an effective means for image classification however the inherent operation of assigning visual words to image feature vectors in traditional codebook approaches causes serious ambiguities in image classification in particular the nearest word may not be the best fit to a feature and multiple words may be equally appropriate for one specific feature to resolve these ambiguities we propose a novel visual codebook model based on the n dimensional fuzzy geometry n d fg theory where all visual words and features are modeled as fuzzy points in the n d fg space and appropriate uncertainty is introduced to each fuzzy point to enhance the representation capacity this n d fg codebook model not only inherits advantages from the fuzzy set theory but also facilitates the analysis and determination of the relationship between visual words and features in geometric form by explicitly taking into account the ambiguities we propose a novel measure of similarity between the visual words and fuzzy features following the proposed codebook model and the novel similarity measure we develop two useful image classification algorithms by modifying popular image coding algorithms i e spm and llc finally experimental results demonstrate that the classification accuracy of the proposed algorithms is dramatically improved for a standard large scale image database for example with a codebook size of 256 the proposed algorithms achieve similar performance as traditional algorithms with a codebook size of 1024 indicating that the proposed algorithms reduce the computational cost by 75 while achieving almost identical classification accuracy to traditional algorithms thus the proposed algorithms represent a more efficient and appropriate scheme for big image data this paper aims to overcome the drawbacks of traditional visual words fuzzy visual word and fuzzy feature are defined using n dimensional fuzzy geometry a new similarity measure between fuzzy features and fuzzy visual words is designed two modified image classification frameworks based on fuzzy codebook are proposed experimental results demonstrated their advantages against traditional algorithms

solving fuzzy equations we start in the next section 10 2 with looking at possible solutions to the simple fuzzy linear equation overline a cdot overline x overline b overline c we discuss three different types of solution which we have studied before in solving fuzzy equations then we present a fourth type of solution based on our fuzzy monte carlo method in section 10 2 2 this new solution is based on random fuzzy numbers in section 10 3 we look at only classical solutions to the fuzzy quadratic equation and apply our fuzzy monte carlo method to obtain new solutions then in section 10 4 we consider the fuzzy matrix equation overline a cdot overline x overline b and a number of solution types for overline x and then another solution based on fuzzy monte carlo techniques the last section contains a brief summary and our conclusions

extending lattice structures on essaie d etendre des operations d une structure reticulee et de definir une sous classe d ensembles flous sur lesquels les extensions induisent un treillis

iterative process with errors to nonlinear ф strongly accretive operator equations in arbitrary banach spaces abstract let x be an arbitrary banach space and t d t x x be a lipschitz strongly accretive operator with domain d t and range r t the mann and ishikawa type iterative sequences with errors which strongly converge to the unique solution of the equation tx f under weaker conditions are given the related results deal with the problems that the mann and ishikawa iterative sequences with errors strongly converge to the unique fixed point of lipschitz hemicontractive operators

iterative solution of nonlinear equations involving strongly accretive operators without the lipschitz assumption abstract letebe a real banach space with a uniformly convex dual spacee supposet e eis a continuous not necessarily lipschitzian strongly accretive map such that i t has bounded range whereidenotes the identity operator it is proved that the ishikawa iterative sequence converges strongly to the unique solution of equationtx f f e our results extend and complement the recent results obtained by chidume

hybrid projective synchronization of chaotic fractional order systems with different dimensions abstract the hybrid projective synchronization of different dimensional fractional order chaotic systems is investigated in this paper it is shown that the slave system can be synchronized with the projection of the master system generated through state transformation based on the stability theorem of linear fractional order systems a suitable controller for achieving the synchronization is given the hybrid projective synchronization between the fractional order chaotic system and hyperchaotic system is successfully achieved in both reduced order and increased order the corresponding numerical results verify the effectiveness of the proposed method