a new method for adding a parameter to a family of distributions with application to the exponential and weibull families summary a new way of introducing a parameter to expand a family of distributions is introduced and applied to yield a new two parameter extension of the exponential distribution which may serve as a competitor to such commonly used two parameter families of life distributions as the weibull gamma and lognormal distributions in addition the general method is applied to yield a new three parameter weibull distribution families expanded using the method introduced here have the property that the minimum of a geometric number of independent random variables with common distribution in the family has a distribution again in the family bivariate versions are also considered

existence of nonexpansive retractions for amenable semigroups of nonexpansive mappings and nonlinear ergodic theorems in banach spaces in this paper we study nonlinear ergodic properties for an amenable semigroup of nonexpansive mappings in a banach space we prove that ifsis an amenable semigroup and s tt t s is a nonexpansive semigroup on a closed convex subsetcin a uniformly convex banach spaceesuch that the setf s of common fixed points of s is nonempty then there exists a nonexpansive retractionpfromcontof s such thatptt ttp pfor eacht sandpx co ttx t s for eachx c in this case there exists a net a of finite averages of s such that for eacht sand for each bounded subsetbofc lim a ttx a x 0 and lim tta x a x 0 uniformly forx b also if the norm ofeis frechet differentiable then for eachx c pxis the unique common fixed point in s s co ttsx t s furthermore if is an asymptotically invariant net of means then for eachx c t x converges weakly topx

convergence theorems of implicit iterative sequences for a finite family of asymptotically quasi nonexpansive type mappings abstract in this paper we introduce a new implicit iteration process generated by a finite family of asymptotically quasi nonexpansive type mappings and prove the convergence theorems of the process in a banach space or uniformly convex banach spaces our results extend and improve some recent results

bidirectional approximate reasoning for rule based systems using interval valued fuzzy sets abstract in this paper we extend the work of chen et al fuzzy sets and systems 91 1997 339 353 to present a new method to deal with bidirectional approximate reasoning for rule based systems based on the direction of matching between interval valued fuzzy sets we also use some examples to illustrate the bidirectional approximate reasoning process because the proposed method can perform bidirectional approximate reasoning based on the direction of matching between interval valued fuzzy sets it is more reasonable and more powerful than the one presented in chen et al fuzzy sets and systems 91 1997 339 353 the proposed method can provide a useful way to deal with bidirectional approximate reasoning for rule based systems using interval valued fuzzy sets

ergodic retractions for amenable semigroups in banach spaces with normal structure abstract in this paper we discuss the existence of nonexpansive retraction onto the set of common fixed points assume that t s s s is an amenable semigroup of nonexpansive mappings on a closed convex subset c in a reflexive banach space e such that the set f of common fixed points of is nonempty among other things it is shown that if either c has normal structure or the t s s are affine then there exists a nonexpansive retraction p from c onto f such that p t t t t p p for each t s and every closed convex invariant subset of c is also p invariant in the case that the mappings are affine p is also affine and p x c o t t x t s for each x c and it is unique regarding the latter property our results extend corresponding results of t suzuki some remarks on the set of common fixed points of one parameter semigroups of nonexpansive mappings in banach spaces with the opial property nonlinear anal 58 2004 441 458 and r e bruck a common fixed point theorem for a commuting family of nonexpansive mappings pacific j math 53 1974 59 71

bidirectional approximate reasoning based on interval valued fuzzy sets abstract this paper proposes a bidirectional approximate reasoning method based on interval valued fuzzy sets where fuzzy production rules are used for knowledge representation and the fuzzy terms appearing in the fuzzy production rules of a rule based system are represented by interval valued fuzzy sets the proposed method is more flexible than the one presented in the paper by bien and chun ieee trans fuzzy systems 2 1994 177 due to the fact that it allows the fuzzy terms appearing in the fuzzy production rules of a rule based system to be represented by interval valued fuzzy sets rather than general fuzzy sets furthermore because the proposed method requires only simple arithmetic operations and because it allows bidirectional approximate reasoning it can be executed much faster and more flexible than the single input single output approximate reasoning scheme presented in the paper by gorzalczany fuzzy sets and systems 21 1981 10

moudafi s viscosity approximations with meir keeler contractions abstract in this paper we discuss moudafi s viscosity approximations with meir keeler contractions we first present very simple proofs of xu s theorems concerning moudafi s approximations we next prove that browder s and halpern s type convergence theorems imply moudafi s viscosity approximations using them we finally state several deduced theorems

asymptotic behavior of commutative semigroups of nonexpansive mappings in banachspaces on etablit des theoremes de convergence pour des semigroupes generaux d applications non dilatation dans le cadre des espaces de banach on demontre un theoreme ergodique non lineaire de type rode pour des semigroupes commutatifs

strong convergence of mann s type iterations for nonexpansive semigroups in general banach spaces abstract in this paper we prove a strong convergence theorem of mann s type for commutative nonexpansive semigroups in general banach spaces using this theorem we obtain some strong convergence theorems in general banach spaces

strong convergence of krasnoselskii and mann s type sequences for one parameter nonexpansive semigroups without bochner integrals abstract in this paper we prove krasnoselskii and mann s type convergence theorems for nonexpansive semigroups without using bochner integral and without assuming the strict convexity of banach spaces one of our main results is the following let c be a compact convex subset of a banach space e and let t t t 0 be a one parameter strongly continuous semigroup of nonexpansive mappings on c let t n be a sequence in 0 satisfying lim inf n t n lim sup n t n and lim n t n 1 t n 0 let 0 1 define a sequence x n in c by x 1 c and x n 1 t t n x n 1 x n for n n then x n converges strongly to a common fixed point of t t t 0

an ergodic theorem for semigroups of nonexpansive mappings in a hilbert space abstract j b baillon c r acad sci paris ser a 280 1975 1511 1514 proved an ergodic theorem for a single nonexpansive mapping in a hilbert space which is a nonlinear version of von neumann s mean ergodic theorem in this paper we study the ergodic behavior of a semigroup of nonexpansive mappings we try to find a sequence of means on the semigroup generalizing the cesaro means on n such that the corresponding sequence of nonexpansive mappings converges to a projection onto the set of common fixed points our method of proof is an appropriate modification of a pazy s proof israel j math 26 1977 197 204 of baillon s theorem

strong convergence to common fixed points of families of nonexpansive mappings abstract we introduce iteration schemes for families of nonexpansive mappings in hilbert spaces and prove that the iterates converge strongly to common fixed points of the mappings

on marshall olkin type distribution with effect of shock magnitude abstract in classical marshall olkin type shock models and their modifications a system of two or more components is subjected to shocks that arrive from different sources at random times and destroy the components of the system with a distinctive approach to the marshall olkin type shock model we assume that if the magnitude of the shock exceeds some predefined threshold then the component which is subjected to this shock is destroyed otherwise it survives more precisely we assume that the shock time and the magnitude of the shock are dependent random variables with given bivariate distribution this approach allows to meet requirements of many real life applications of shock models where the magnitude of shocks is an important factor that should be taken into account a new class of bivariate distributions obtained in this work involve the joint distributions of shock times and their magnitudes dependence properties of new bivariate distributions have been studied for different examples of underlying bivariate distributions of lifetimes and shock magnitudes the joint distributions of lifetimes of the components are investigated the multivariate extension of the proposed model is also discussed

fixed point set of semigroups of non expansive mappings and amenability abstract in this paper we study the fixed point set of a strongly continuous non expansive semigroup s t t t s of a semi topological semigroup s for which cb s is n extremely left amenable also we study the fixed point set of a strongly continuous semigroup of mappings when s is a semigroup which is a sub semigroup of a locally convex topological vector space with addition some applications to harmonic analysis are also provided

an implicit iteration process for nonexpansive semigroups let c be a closed convex subset of a banach space e let t t t 0 be a strongly continuous semigroup of nonexpansive mappings on c such that t 0f t t 0 let n and tn be sequences of real numbers satisfying appropriate conditions then for arbitrary x0 c the mann type implicit iteration process xn given by xn nxn 1 1 n t tn xn n 0 weakly strongly converges to an element of t 0f t t

stress strength reliability in the presence of fuzziness this paper investigates the stress strength reliability in the presence of fuzziness the fuzzy membership function is defined as a function of the difference between stress and strength values and the fuzzy reliability of single unit and multicomponent systems are calculated the inclusion of fuzziness in the stress strength interference enables the user to make more sensitive analysis illustrations are presented for various stress and strength distributions

approximate reasoning algorithm of interval valued fuzzy sets based on least square method in this paper we develop a new method for bidirectional approximate reasoning of interval valued fuzzy sets by employing least squares method and investigate some properties for our proposed approximate reasoning method furthermore we use four numerical examples to illustrate our proposed method reasonable

nonexpansive retractions and fixed point properties abstract among other results we prove that if a dual banach space e has the weak fixed point property then e has the weak fixed point property for commuting separable semitopological semigroups of nonexpansive mappings and study the existence of ergodic retractions for right amenable semigroups and commuting families of nonexpansive mappings this answers an open problem of lau and mah 1976 12 for commuting separable semi topological semigroups

iterative algorithms for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of families and semigroups of nonexpansive mappings abstract we introduce iterative algorithms for finding a common element of the set of solutions of a system of equilibrium problems and of the set of fixed points of a finite family and a left amenable semigroup of nonexpansive mappings in a hilbert space we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality which is the optimality condition for a minimization problem our results extend for example the recent result of v colao g marino h k xu an iterative method for finding common solutions of equilibrium and fixed point problems j math anal appl 344 2008 340 352 to systems of equilibrium problems

strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings in the present paper we prove that the modified implicit iteration sequence for a finite family of asymptotically quasi nonexpansive mappings converges strongly to a common fixed point of the family in a uniformly convex banach space requiring one member t in the family to be semi compact our results extend and improve some recent results

marshall olkin type copulas generated by a global shock a way to transform a given copula by means of a univariate function is presented the resulting copula can be interpreted as the result of a global shock affecting all the components of a system modeled by the original copula the properties of this copula transformation from the perspective of semi group action are presented together with some investigations about the related tail behavior finally the whole methodology is applied to model risk assessment

strong convergence theorems for nonexpansive semigroup in banach spaces abstract let k be a nonempty closed convex subset of a reflexive and strictly convex banach space e with a uniformly g teaux differentiable norm and f t t t 0 a nonexpansive self mappings semigroup of k and f k k a fixed contractive mapping the strongly convergent theorems of the following implicit and explicit viscosity iterative schemes x n are proved x n n f x n 1 n t t n x n x n 1 n f x n 1 n t t n x n and the cluster point of x n is the unique solution to some co variational inequality

the effects of membership function on fuzzy reasoning abstract fuzzy modus ponens has been considered a generalization of the classic modus ponens logic inference rule it has been expected to provide a more powerful and useful inference capability in the process of fuzzy reasoning the definitions of membership functions of fuzzy sets used in the reasoning process may however adversely affect the reasoning results if the insignificant parts of the membership functions are incompatible this paper explains these undesirable effects and proposes a method to resolve this problem in addition an algorithm for the compositional rule of inference is developed to perform the fuzzy modus ponens syllogism test results shown in this paper indicate that the algorithm and the underlying proposed methods are reasonable approaches to a robust fuzzy logic reasoning system

an extension of marshall and olkin s bivariate exponential distribution abstract this article extends marshall and olkin s bivariate exponential distribution such that it is absolutely continuous and need not be memoryless the new marginal distribution has an increasing failure rate and the joint distribution exhibits an aging pattern it offers an advantage in separately identifying the shock arrival rates and their impacts regarding estimation of the model both maximum likelihood and method of moments type estimation are considered the former is more efficient but computationally more demanding whereas the latter is simpler in computation but less efficient the trade off between computational burden and efficiency is gauged through monte carlo simulations and it turns out to be favorable for the method of moments type estimation

strong convergence theorems for fixed points of asymptotically pseudocontractive semi groups abstract let k be a nonempty closed convex and bounded subset of a real banach space e let t t t t r be a strongly continuous uniformly asymptotically regular and uniformly l lipschitzian semi group of asymptotically pseudocontractive mappings from k into k then for a given u k there exists a sequence y n k satisfying the equation y n 1 n t t n n y n n u for each n n where n 0 1 and t n 0 satisfy appropriate conditions suppose further that e is uniformly convex and has uniformly g teaux differentiable norm under suitable conditions on the mappings t the sequence y n converges strongly to a fixed point of t furthermore an explicit sequence x n generated from x 1 k by x n 1 1 n x n n t t n n x n n n x n x 1 for all integers n 1 where n n are positive real sequences satisfying appropriate conditions converges strongly to a fixed point of t

convergence theorem of common fixed points for lipschitzian pseudocontraction semigroups in banach spaces the purpose of this paper is to study the convergence problems of the implicity iteration process for an asymptotically nonexpansive semigroups in general banach spaces the results presented in this paper extend and improve the corresponding results announced by many authors

on strong convergence by the hybrid method for families of mappings in hilbert spaces abstract let c be a nonempty closed convex subset of a real hilbert space and let t n be a family of mappings of c into itself such that the set of all common fixed points of t n is nonempty we consider a sequence x n generated by the hybrid method in mathematical programming we give the new conditions of t n under which x n converges strongly to a common fixed point of t n and generalize the unified result for families of nonexpansive mappings k nakajo k shimoji w takahashi strong convergence theorems by the hybrid method for families of nonexpansive mappings in hilbert spaces taiwanese j math 10 2006 339 360 and the results for asymptotically nonexpansive mappings and semigroups t h kim h k xu strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups nonlinear anal 64 2006 1140 1152 s plubtieng and k ungchittrakool strong convergence of modified ishikawa iteration for two asymptotically nonexpansive mappings and semigroups nonlinear anal 67 2007 2306 2315

strong convergence theorem for nonexpansive semigroups in hilbert space abstract the purpose of this paper is to prove the strong convergence of a method combining the descent method and the hybrid method in mathematical programming for finding a point in the common fixed point set of a semigroup of nonexpansive mappings in hilbert space

an inference network for bidirectional approximate reasoning based on an equality measure an inference network is proposed as a tool for bidirectional approximate reasoning the inference network can be designed directly from the given fuzzy data knowledge if a fuzzy input is given for the inference network then the network renders a reasonable fuzzy output after performing approximate reasoning based on an equality measure conversely due to the bidirectional structure the network can yield its corresponding reasonable fuzzy input for a given fuzzy output this property makes it possible to perform forward and backward reasoning in the knowledge base system

a mean ergodic theorem for nonlinear semigroups which are asymptotically nonexpansive in the intermediate sense abstract let x be a uniformly convex banach space such that its dual x has the kadec klee property c a bounded closed convex subset of x and t t t t 0 a one parameter nonlinear semigroup which is asymptotically nonexpansive in the intermediate sense we show that every continuous almost orbit of t is weakly almost convergent to a common fixed point of t a discrete version of our main result is also included

convergence of a hybrid algorithm for a reversible semigroup of nonlinear operators in banach spaces abstract the purpose of this paper is to study hybrid iterative schemes of halpern types for a semigroup t s s s of relatively nonexpansive mappings on a closed and convex subset c of a banach space with respect to a sequence n of asymptotically left invariant means defined on an appropriate invariant subspace of l s we prove that given a certain sequence n in 0 1 x c we can generate an iterative sequence x n which converges strongly to f x where f x is the generalized projection from c onto the fixed point set f our main result is even new for the case of a hilbert space

predicting monthly streamflow using data driven models coupled with data preprocessing techniques 1 in this paper the accuracy performance of monthly streamflow forecasts is discussed when using data driven modeling techniques on the streamflow series a crisp distributed support vectors regression cdsvr model was proposed for monthly streamflow prediction in comparison with four other models autoregressive moving average arma k nearest neighbors knn artificial neural networks anns and crisp distributed artificial neural networks cdann with respect to distributed models of cdsvr and cdann the fuzzy c means fcm clustering technique first split the flow data into three subsets low medium and high levels according to the magnitudes of the data and then three single svrs or anns were fitted to three subsets this paper gives a detailed analysis on reconstruction of dynamics that was used to identify the configuration of all models except for arma to improve the model performance the data preprocessing techniques of singular spectrum analysis ssa and or moving average ma were coupled with all five models some discussions were presented 1 on the number of neighbors in knn 2 on the configuration of ann and 3 on the investigation of effects of ma and ssa two streamflow series from different locations in china xiangjiaba and danjiangkou were applied for the analysis of forecasting forecasts were conducted at four different horizons 1 3 6 and 1 2 month ahead forecasts the results showed that models fed by preprocessed data performed better than models fed by original data and cdsvr outperformed other models except for at a 6 month ahead horizon for danjiangkou for the perspective of streamflow series the ssa exhibited better effects on danjingkou data because its raw discharge series was more complex than the discharge of xiangjiaba the ma considerably improved the performance of ann cdann and cdsvr by adjusting the correlation relationship between input components and output of models it was also found that the performance of cdsvr deteriorated with the increase of the forecast horizon

a new image thresholding method based on gaussian mixture model in this paper an efficient approach to search for the global threshold of image using gaussian mixture model is proposed firstly a gray level histogram of an image is represented as a function of the frequencies of gray level then to fit the gaussian mixtures to the histogram of image the expectation maximization em algorithm is developed to estimate the number of gaussian mixture of such histograms and their corresponding parameterization finally the optimal threshold which is the average of these gaussian mixture means is chosen and the experimental results show that the new algorithm performs better

mosco convergence of the sets of fixed points for one parameter nonexpansive semigroups abstract we consider the mosco convergence of the sets of fixed points for one parameter strongly continuous semigroups of nonexpansive mappings one of our main results is the following let c be a closed convex subset of a hilbert space e let t t t 0 be a strongly continuous semigroup of nonexpansive mappings on c the set of all fixed points of t t is denoted by f t t for each t 0 let be a nonnegative real number and let t n be a sequence in r satisfying t n 0 and t n 0 for n n and lim n t n 0 then f t t n converges to t 0 f t t in the sense of mosco

nonexpansive retractions and nonlinear ergodic theorems in banach spaces on donne des theoremes ergodiques non lineaires pour des semigroupes commutatifs d applications non dilatation sans utiliser le concept de moyenne compacte

on n polygonal interval value fuzzy sets and numbers abstract the structure of interval valued fuzzy sets is complex in regard to their arithmetic operations to reduce the computational complexity of arithmetic operations on interval valued fuzzy sets we propose the notion of an n polygonal interval valued fuzzy set considering two 2 n 2 tuple ordered real numbers complete representation of n polygonal interval valued fuzzy sets and numbers is provided moreover we demonstrate that the n polygonal interval valued fuzzy numbers can approximate the general interval value fuzzy numbers with any precision next we introduce arithmetic operations on n polygonal interval valued fuzzy numbers by capitalizing on the good characteristics of n polygonal interval valued fuzzy numbers the properties of the introduced arithmetic operations are also addressed in addition with the aid of a concrete example we verify the effectiveness of the approximation ability of the n polygonal interval valued fuzzy set furthermore we study the properties of the topological space of n polygonal interval valued fuzzy numbers this proves that this space is a complete separable and local compact metric space when endowed with the newly defined distance between two n polygonal interval valued fuzzy numbers by product it shows that arithmetic operations introduced here on n polygonal interval valued fuzzy numbers are continuous finally the practicability of n polygonal interval valued fuzzy numbers is verified by an example

a new model of fuzzy reasoning abstract a new model of fuzzy reasoning is proposed a comparison of inference results using the new model and the linguistic synthesis approach is given

characterizations of common fixed points of one parameter nonexpansive semigroups and convergence theorems to common fixed points we first prove characterizations of common fixed points of one parameter nonexpansive semigroups we next present convergence theorems to common fixed points

convergence theorems for strongly continuous semi groups of asymptotically nonexpansive mappings abstract let k be a nonempty closed convex subset of a real banach space e let t t t t r be a strongly continuous semi group of asymptotically nonexpansive mappings from k into k with a sequence l t 1 suppose f t 0 then for a given u 0 k and t n 0 there exists a sequence u n k such that u n 1 n t t n u n n u 0 for n n such that n 0 1 and l t n 1 n where t n r suppose in addition that e is reflexive strictly convex with a uniformly g teaux differentiable norm and that lim n t n lim n n lim n l t n 1 n 0 then the sequence u n converges strongly to a point of f t moreover it is proved that an explicit sequence x n generated from x 1 k by x n 1 n u 1 n t t n x n n 1 converges to a fixed point of t

mean residual life and inactivity time of a coherent system subjected to marshall olkin type shocks we consider coherent systems subjected to marshall olkin type shocks coming at random times and destroying components of the system the paper combines two important models coherent systems and marshall olkin type shocks and studies the mean residual life mrl and the mean inactivity time mit functions of coherent systems that is subjected to random shocks the considered models and theoretical results are supported with examples and graphical representations

reliability analysis under marshall olkin run shock model abstract in this paper a new shock model called marshall olkin run shock model is defined and studied according to the model two components are subject to shocks that may arrive from three different sources and component i fails when it is subject to k consecutive critical shocks from source i or k consecutive critical shocks from source 3 i 1 2 reliability and mean residual life functions of such components are studied when the times between shocks follow phase type distribution

fixed points of non expansive mappings associated with invariant means in a banach space in this paper we study the fixed point set of the non expansive mapping t for a banach space with uniformly g teaux differentiable norm when is a multiplicative left invariant mean on l s as an application we establish nonlinear ergodic properties for an extremely amenable semigroup of non expansive mappings in a banach space with uniformly g teaux differentiable norm furthermore we improve a recent result of atsushiba and takahashi s atsushiba w takahashi weak and strong convergence theorems for non expansive semigroups in a banach spaces satisfying opial s condition sci math jpn in press on the fixed point set of non expansive mappings associated with a left invariant mean on a left amenable semigroup

the retractions onto the common fixed points of some families and semigroups of mappings abstract assume that c is a closed convex subset of a reflexive banach space e and t i i i is a family of self mappings on c of type such that f the common fixed point set of is nonempty from our results in this paper it can be derived that a if i i f t i is contained in a 3 dimensional subspace of e then f is a nonexpansive retract of c b if is commutative there exists a retraction r of type from c onto f such that r t i t i r r i and every closed convex invariant subset of c is r invariant the same result holds for a non commutative right amenable semigroup under some additional assumptions moreover the existence of a t i ergodic retraction r of type from c x i l e x i c i i onto f in l e for the family is discussed we also apply some of our results to find ergodic retractions for nonexpansive affine mappings