some notes on the paper cone metric spaces and fixed point theorems of contractive mappings abstract huang and zhang reviewed cone metric spaces in 2007 huang long guang zhang xian cone metric spaces and fixed point theorems of contractive mappings j math anal appl 332 2007 1468 1476 we shall prove that there are no normal cones with normal constant m 1 and for each k 1 there are cones with normal constant m k also by providing non normal cones and omitting the assumption of normality in some results of huang long guang zhang xian cone metric spaces and fixed point theorems of contractive mappings j math anal appl 332 2007 1468 1476 we obtain generalizations of the results

comprehensive analysis of a new fuzzy rule interpolation method the first published result in fuzzy rule interpolation was the spl alpha cut based fuzzy rule interpolation termed as kh fuzzy rule interpolation originally devoted for complexity reduction a modified version of the kh approach has been presented by yam et al 1999 which eliminates the subnormality problem while at the same time intending to maintain the advantageous computational properties of the original method this paper presents a comprehensive analysis of the new method which includes detailed comparison with the original kh fuzzy rule interpolation method concerning the explicit functions of the methods preservation of piecewise linearity and stability the fuzziness of the conclusion with respect to the fuzziness of the observation is also investigated in comparison with several interpolation techniques all these comparisons shows that the new method preserves the advantageous properties of the kh method and alleviates its most significant disadvantage the problem of subnormality

convergence theorems best approximation and best proximity for set valued dynamic systems of relatively quasi asymptotic contractions in cone uniform spaces abstract in cone uniform spaces x using the concept of the d family of cone pseudodistances the distance between two not necessarily convex or compact sets a and b in x is defined the concepts of cyclic and noncyclic set valued dynamic systems of d relatively quasi asymptotic contractions t a b 2 a b are introduced and the best approximation and best proximity point theorems for such contractions are proved also conditions are given which guarantee that for each starting point each generalized sequence of iterations of these contractions in particular each dynamic process converges and the limit is a best proximity point moreover d families are constructed characterized and compared the results are new for set valued and single valued dynamic systems in cone uniform cone locally convex and cone metric spaces various examples illustrating ideas methods definitions and results are constructed

on the vectoral ekeland s variational principle and minimal points in product spaces abstract phelps 13 noticed that the scalar ekeland s variational principle evp is equivalent to the existence of a minimal point of the epigraph of the corresponding function with respect to an appropriate order attouch and riahi 1 showed that evp is equivalent to the existence of maximal points with respect to cones satisfying some additional conditions taking these into account gopfert and tammer 6 7 established a maximal point theorem in a product space the aim of this paper is to obtain several minimal point theorems in product spaces and the corresponding variants of the vectorial evp

fuzzy interpolative reasoning via scale and move transformations interpolative reasoning does not only help reduce the complexity of fuzzy models but also makes inference in sparse rule based systems possible this paper presents an interpolative reasoning method by means of scale and move transformations it can be used to interpolate fuzzy rules involving complex polygon gaussian or other bell shaped fuzzy membership functions the method works by first constructing a new inference rule via manipulating two given adjacent rules and then by using scale and move transformations to convert the intermediate inference results into the final derived conclusions this method has three advantages thanks to the proposed transformations 1 it can handle interpolation of multiple antecedent variables with simple computation 2 it guarantees the uniqueness as well as normality and convexity of the resulting interpolated fuzzy sets and 3 it suggests a variety of definitions for representative values providing a degree of freedom to meet different requirements comparative experimental studies are provided to demonstrate the potential of this method

boyd wong type common fixed point results in cone metric spaces abstract some common fixed point results in cone metric spaces of c di bari and p vetro c di bari p vetro pairs and common fixed points in cone metric spaces rend cir mat palermo 57 2008 279 285 as well as p raja and s m vaezpour p raja s m vaezpour some extensions of banach s contraction principle in complete metric spaces fixed point theory appl 2008 doi 10 1155 2008 768294 are extended using generalized contractive type conditions and cones which may be nonnormal cone metric versions of several well known results such as boyd wong s theorem d w boyd j s wong on nonlinear contractions proc amer math soc 20 1969 458 464 are obtained as special cases

fixed point theorems for set valued contractions in complete metric spaces abstract the fixed point theory of set valued contractions which was initiated by nadler s b nadler jr multi valued contraction mappings pacific j math 30 1969 475 488 was developed in different directions by many authors in particular by s reich fixed points of contractive functions boll unione mat ital 5 1972 26 42 n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric spaces j math anal appl 141 1989 177 188 y feng s liu fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings j math anal appl 317 2006 103 112 in the present paper the concept of contraction for set valued maps in metric spaces is introduced and the conditions guaranteeing the existence of a fixed point for such a contraction are established one of our results essentially generalizes the nadler and feng liu theorems and is different from the mizoguchi takahashi result the second result is different from the reich and mizoguchi takahashi results the method used in the proofs of our results is inspired by mizoguchi takahashi and feng liu s ideas comparisons and examples are given

generalized fractal transforms and self similar objects in cone metric spaces we use the idea of a scalarization of a cone metric to prove that the topology generated by any cone metric is equivalent to a topology generated by a related metric we then analyze the case of an ordering cone with empty interior and we provide alternative definitions based on the notion of quasi interior points finally we discuss the implications of such cone metrics in the theory of iterated function systems and generalized fractal transforms and suggest some applications in fractal based image analysis

coincidence and fixed point theorems for generalized ψ φ weak nonlinear contraction in ordered k metric spaces in this paper we establish coincidence and fixed point theorems for a pair of mappings satisfying a new generalized j f weak nonlinear contraction type condition in ordered k metric spaces the presented results generalize and extend the very recent results of choudhury and metiya b s choudhury and n metiya the point of coincidence and common fixed point for a pair of mappings in cone metric spaces computers and mathematics with applications 60 2010 1686 1695

some new fixed point theorems of generalized nonlinear contractive multivalued maps in complete metric spaces in this paper we present some new fixed point theorems for generalized nonlinear contractive multivalued maps and these results generalize or improve the corresponding recent fixed point results in the literature

roughness of a fuzzy set an integration between the theories of fuzzy sets and rough sets has been attempted by providing a measure of roughness of a fuzzy set several properties of this new measure are established some of the possible applications for handling uncertainties in the field of pattern recognition are mentioned

cone metric spaces and fixed point theorems of contractive mappings in this paper we introduce cone metric spaces prove some fixed point theorems of contractive mappings on cone metric spaces

closed form fuzzy interpolation fuzzy interpolation enhances the robustness of fuzzy systems and helps to reduce systems complexity although a number of important fuzzy rule interpolation approaches have been proposed in the literature most of these approaches cannot be expressed in a closed form this is usually caused by the effort to avoid possible invalid interpolated results this paper proposes a different fuzzy rule interpolation approach it not only can be represented in a closed form but also guarantees that the interpolated results are valid fuzzy sets this approach is based on a direct use of the extension principle which has been widely utilised for the development of a variety of fuzzy systems the mathematical properties of the proposed approach are analysed by taking the advantage of the closed form representation this approach has been applied to a practical problem of predicting diarrhoeal disease rates in remote villages the results demonstrate the potential of the proposed work in enhancing the robustness of fuzzy interpolation

multi variable fuzzy forecasting based on fuzzy clustering and fuzzy rule interpolation techniques in this paper we present a new method for multi variable fuzzy forecasting based on fuzzy clustering and fuzzy rule interpolation techniques first the proposed method constructs training samples based on the variation rates of the training data set and then uses the training samples to construct fuzzy rules by making use of the fuzzy c means clustering algorithm where each fuzzy rule corresponds to a given cluster then we determine the weight of each fuzzy rule with respect to the input observations and use such weights to determine the predicted output based on the multiple fuzzy rules interpolation scheme we apply the proposed method to the temperature prediction problem and the taiwan stock exchange capitalization weighted stock index taiex data the experimental results show that the proposed method produces better forecasting results than several existing methods

existence and uniqueness of common fixed points for two multivalued operators in ordered metric spaces in this paper we discuss some new fixed point theorems for a pair of multivalued operators which satisfy weakly generalized contractive conditions our results are the extension and improvement of corresponding results of j harjani and k sadarangani fixed point theorems for weakly contractive mappings in partially ordered sets nonlinear analysis 71 2009 3403 3410 and x zhang common fixed point theorems for some new generalized contractive type mappings j math anal appl 333 2007 780 786 finally some examples are given to illustrate the usability of our results

mizoguchi takahashi s type fixed point theorem recently eldred a a eldred j anuradha p veeramani on equivalence of generalized multi valued contactions and nadler s fixed point theorem j math anal appl 2007 doi 10 1016 j jmaa 2007 01 087 claimed that nadler s s b nadler jr multivalued contraction mappings pacific j math 30 1969 475 488 fixed point theorem is equivalent to mizoguchi takahashi s n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric space j math anal appl 141 1989 177 188 fixed point theorem very recently suzuki t suzuki mizoguchi takahashi s fixed point theorem is a real generalization of nadler s j math anal appl 2007 doi 10 1016 j jmaa 2007 08 022 produced an example to disprove their claim and showed that mizoguchi takahashi s fixed point theorem is a real generalization of nadler s fixed point theorem we refine generalize mizoguchi takahashi s fixed point theorem our result improves a recent result by klim and wadowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 1 2007 132 139 and extends hicks and rhoades t l hicks b e rhoades a banach type fixed point theorem math japonica 24 1979 327 330 fixed point theorem to multivalued maps

dynamic processes and fixed points of set valued nonlinear contractions in cone metric spaces abstract investigations concerning the existence of dynamic processes convergent to fixed points of set valued nonlinear contractions in cone metric spaces are initiated the conditions guaranteeing the existence and uniqueness of fixed points of such contractions are established our theorems generalize recent results obtained by huang and zhang l g huang x zhang cone metric spaces and fixed point theorems of contractive maps j math anal appl 332 2007 1467 1475 for cone metric spaces and by klim and wardowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 1 2007 132 139 for metric spaces the examples and remarks provided show an essential difference between our results and those mentioned above

on some nonlinear problems induced by an abstract maximal element principle abstract in this paper by applying an abstract maximal element principle on quasi ordered sets established by lin and du we obtain a generalized brezis browder principle system vectorial versions of ekeland s variational principle and maximal element principle and a vectorial version of takahashi s nonconvex minimization theorem moreover we investigate the equivalence between scalar versions and vectorial versions of these results

fuzzy interpolative reasoning for sparse fuzzy rule based systems based on bm alpha cuts and transformations techniques in sparse fuzzy rule based systems the fuzzy rule bases are usually incomplete in this situation the system may not properly perform fuzzy reasoning to get reasonable consequences in order to overcome the drawback of sparse fuzzy rule based systems there is an increasing demand to develop fuzzy interpolative reasoning techniques in sparse fuzzy rule based systems in this paper we present a new fuzzy interpolative reasoning method via cutting and transformation techniques for sparse fuzzy rule based systems it can produce more reasonable results than the existing methods the proposed method provides a useful way to deal with fuzzy interpolative reasoning in sparse fuzzy rule based systems

ordered cone metric spaces and fixed point results in this paper we introduce a partial order on a cone metric space and prove a caristi type theorem furthermore we prove fixed point theorems for single valued nondecreasing and weakly increasing mappings and multi valued mappings on an ordered cone metric space

fuzzy interpolation and extrapolation a practical approach fuzzy interpolation does not only help to reduce the complexity of fuzzy models but also makes inference in sparse rule based systems possible it has been successfully applied to systems control but limited work exists for its applications to tasks like prediction and classification almost all fuzzy interpolation techniques in the literature make strong assumptions that there are two closest adjacent rules available to the observation and that such rules must flank the observation for each attribute also some interpolation approaches cannot handle fuzzy sets whose membership functions involve vertical slopes to avoid such limitations and develop a more practical approach this paper extends the work of huang and shen the result enables both interpolation and extrapolation which involve multiple fuzzy rules with each rule consisting of multiple antecedents two realistic applications namely truck backer upper control and computer activity prediction are provided in this paper to demonstrate the utility of the extended approach experiment based comparisons to the most commonly used mamdani fuzzy reasoning mechanism and to other existing fuzzy interpolation techniques are given to show the significance and potential of this research

multi valued nonlinear contraction mappings abstract two concepts of nonlinear contractions for multi valued mappings in complete metric spaces are introduced and three fixed point theorems are proved presented theorems are generalizations of very recent fixed point theorems due to klim and wardowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 2007 132 139 and feng and liu y feng s liu fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings j math anal appl 317 2006 103 112 as well as a fixed point theorem of mizoguchi and takahashi n mizoguchi w takahash fixed point theorems for multi valued mappings on complete metric spaces j math anal appl 141 1989 177 188 and several others an example is given to show that presented results are genuine generalizations our results are also some contribution to an open problem raised by reich s reich fixed points of contractive functions boll unione mat ital 5 1972 26 42 s reich some fixed point problems atti acad naz lincei 57 1974 194 198 s reich some problems and results in fixed point theory contemp math 21 1983 179 187

irreducible regular gaussian representations of the groups of the interval and circle diffeomorphisms abstract we define the analogue of the regular representations for infinite dimensional groups using quasi invariant measures on such groups and present the criterium of irreducibility and equivalence of constructed representations for groups of the interval and circle diffeomorphisms in a v kosyak funktsional anal i prilozhen 24 1990 82 a similar construction was done for a certain infinite dimensional matrix group

endpoints of set valued contractions in metric spaces abstract suppose x d be a complete metric space and suppose f x c b x be a set valued map satisfies h f x f y d x y for each x y x where 0 0 is upper semicontinuous t t for each t 0 and satisfies lim inf t t t 0 then f has a unique endpoint if and only if f has the approximate endpoint property

fixed point results for set valued contractions by altering distances in complete metric spaces nadler s contraction principle has led to fixed point theory of set valued contraction in non linear analysis inspired by the results of nadler the fixed point theory of set valued contraction has been further developed in different directions by many authors in particular by reich mizoguchi takahashi feng liu and many others in the present paper the concept of generalized contractions for set valued maps in metric spaces is introduced and the existence of fixed point for such a contraction are guaranteed by certain conditions our first result extends and generalizes the nadler feng liu and klim wardowski theorems and the second result is different from the reich and mizoguchi takahashi results as a consequence we derive some results related to fixed point of set valued maps satisfying certain conditions of integral type

fixed point theorems and the ulam hyers stability in non archimedean cone metric spaces abstract let x p be a metric space with a k valued non archimedean metric p in this paper we prove the existence and approximation of a fixed point for operators f x x satisfying the contractive condition in the form p f x f y q p x y where q k k is an increasing operator then we study the generalized ulam hyers stability of fixed point equations we next obtain an extension of the krasnoselskii fixed point theorem for the sum of two operators finally an application to functional equations is given

a note on cone metric fixed point theory and its equivalence abstract the main aim of this paper is to investigate the equivalence of vectorial versions of fixed point theorems in generalized cone metric spaces and scalar versions of fixed point theorems in general metric spaces in usual sense we show that the banach contraction principles in general metric spaces and in t v s cone metric spaces are equivalent our theorems also extend some results in huang and zhang 2007 l g huang x zhang cone metric spaces and fixed point theorems of contractive mappings j math anal appl 332 2007 1468 1476 rezapour and hamlbarani 2008 sh rezapour r hamlbarani some notes on the paper cone metric spaces and fixed point theorems of contractive mappings j math anal appl 345 2008 719 724 and others

a generalized concept for fuzzy rule interpolation the concept of fuzzy rule interpolation in sparse rule bases was introduced in 1993 it has become a widely researched topic in recent years because of its unique merits in the topic of fuzzy rule base complexity reduction the first implemented technique of fuzzy rule interpolation was termed as spl alpha cut distance based fuzzy rule base interpolation despite its advantageous properties in various approximation aspects and in complexity reduction it was shown that it has some essential deficiencies for instance it does not always result in immediately interpretable fuzzy membership functions this fact inspired researchers to develop various kinds of fuzzy rule interpolation techniques in order to alleviate these deficiencies this paper is an attempt into this direction it proposes an interpolation methodology whose key idea is based on the interpolation of relations instead of interpolating spl alpha cut distances and which offers a way to derive a family of interpolation methods capable of eliminating some typical deficiencies of fuzzy rule interpolation techniques the proposed concept of interpolating relations is elaborated here using fuzzy and semantic relations this paper presents numerical examples in comparison with former approaches to show the effectiveness of the proposed interpolation methodology

cone uniform cone locally convex and cone metric spaces endpoints set valued dynamic systems and quasi asymptotic contractions abstract the concepts of cone pseudometrics cone uniform spaces generated by these pseudometrics cone pseudodistances set valued quasi asymptotic contractions with respect to these pseudodistances and cone closed maps are introduced and studied conditions guaranteeing the existence and uniqueness of endpoints stationary points of these contractions and conditions ensuring that for each starting point each generalized sequence of iterations of these contractions in particular each dynamic process converges and then the limit is an endpoint are all established also the concept of the cone locally convex space as a special case of the cone uniform space is introduced and examples of quasi asymptotic contractions in cone metric spaces are constructed the definitions results ideas and methods are new for set valued dynamic systems in cone uniform cone locally convex and cone metric spaces and even for single valued maps in these spaces

fixed point theorems for multi valued contractions in complete metric spaces abstract in this paper the concept of a contraction for multi valued mappings in a metric space is introduced and the existence theorems for fixed points of such contractions in a complete metric space are proved presented results generalize and improve the recent results of y feng s liu y feng s liu fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings j math anal appl 317 2006 103 112 d klim d wardowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 2007 132 139 and several others the method used in the proofs of our results is new and is simpler than methods used in the corresponding papers two examples are given to show that our results are genuine generalization of the results of feng and liu and klim and wardowski

fuzzy interpolative reasoning for sparse fuzzy rule based systems based on the areas of fuzzy sets fuzzy interpolative reasoning is an inference technique for dealing with the sparse rules problem in sparse fuzzy rule based systems in this paper we present a new fuzzy interpolative reasoning method for sparse fuzzy rule based systems based on the areas of fuzzy sets the proposed method uses the weighted average method to infer the fuzzy interpolative reasoning results and has the following advantages 1 it holds the normality and the convexity of the fuzzy interpolative reasoning result 2 it can deal with fuzzy interpolative reasoning with complicated membership functions 3 it can deal with fuzzy interpolative reasoning when the fuzzy sets of the antecedents and the consequents of the fuzzy rules have different kinds of membership functions 4 it can handle fuzzy interpolative reasoning with multiple antecedent variables 5 it can handle fuzzy interpolative reasoning with multiple fuzzy rules and 6 it can handle fuzzy interpolative reasoning with logically consistent properties with respect to the ratios of fuzziness we use some examples to compare the fuzzy interpolative reasoning results of the proposed method with those of the existing fuzzy interpolative reasoning methods in terms of the six evaluation indices the experimental results show that the proposed method performs more reasonably than the existing methods the proposed method provides us a useful way to deal with fuzzy interpolative reasoning in sparse fuzzy rule based systems

a rademacher type theorem on l2 wasserstein spaces over closed riemannian manifolds abstract let p be any borel probability measure on the l 2 wasserstein space p 2 m w 2 over a closed riemannian manifold m we consider the dirichlet form e induced by p and by the wasserstein gradient on p 2 m under natural assumptions on p we show that w 2 lipschitz functions on p 2 m are contained in the dirichlet space d e and that w 2 is dominated by the intrinsic metric induced by e we illustrate our results by giving several detailed examples

common fixed points for self mappings on compact metric spaces in this paper we obtain a result of existence of points of coincidence and of common fixed points for two self mappings on compact metric spaces satisfying a contractive condition of suzuki type we also present some examples to illustrate our results moreover using the scalarization method of du we deduce a result of common fixed point in compact cone metric spaces

fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings abstract in this paper the famous banach contraction principle and caristi s fixed point theorem are generalized to the case of multi valued mappings our results are extensions of the well known nadler s fixed point theorem s b nadler jr multi valued contraction mappings pacific j math 30 1969 475 487 as well as of some caristi type theorems for multi valued operators see n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric spaces j math anal appl 141 1989 177 188 j p aubin optima and equilibria an introduction to nonlinear analysis grad texts in math springer verlag berlin 1998 p 17 s s zhang q luo set valued caristi fixed point theorem and ekeland s variational principle appl math mech 10 2 1989 111 113 in chinese english translation appl math mech english ed 10 2 1989 119 121 etc

the contraction principle for set valued mappings on a metric space with a graph let x d be a metric space and f x x be a set valued mapping we obtain sufficient conditions for the existence of a fixed point of the mapping f in the metric space x endowed with a graph g such that the set v g of vertices of g coincides with x and the set of edges of g is e g x y x y xxx

fixed points of multivalued operators in ordered metric spaces with applications abstract the purpose of this paper is to present some new hybrid fixed point theorems involving multivalued operators which satisfy weakly generalized contractive conditions in an ordered complete metric space an example of the existence of solutions for a perturbed impulsive hyperbolic differential inclusion with variable times is given to illustrate the usability of our results

coincidence and common fixed point results in partially ordered cone metric spaces and applications to integral equations abstract in this paper coincidence and common fixed point results are established in a partially ordered cone metric space an application of our results obtained to prove the existence of a common solution to integral equations is presented

some results on set valued contractions in abstract metric spaces abstract in this paper the concept of contractive set valued maps in the frame of abstract metric spaces is studied and the existence of fixed points for such maps is guaranteed under certain conditions consequently several known fixed point results are either generalized or extended including the corresponding recent fixed point results of wardowski d wardowski endpoints and fixed points of set valued contractions in cone metric spaces nonlinear anal 71 2009 512 516 as well as klim and wardowski d klim d wardowski dynamic process and fixed points of set valued nonlinear contractions in cone metric spaces nonlinear anal 71 2009 5170 5175 examples are given to show that our results are distinct from the existing ones

on circle diffeomorphisms with discontinuous derivatives and quasi invariance subgroups of malliavin shavgulidze measures abstract this note is devoted to construction of the domain of the regular representation of diff s 1 we consider a subgroup of diffeomorphism group such that the malliavin shavgulidze measure is quasi invariant with respect to the left action of the subgroup the measure appears to be quasi invariant with respect to the left action of diffeomorphisms with discontinuous second derivative we derive an expression for quasi invariance density and obtain an additional psl 2 r symmetry breaking term

interpolative reasoning with insufficient evidence in sparse fuzzy rule bases abstract rule based fuzzy approximate reasoning uses various techniques of modified modus ponens the observation is in most cases not identical with any of the antecedents in the rules however a conclusion still can be computed by using some combination of all consequents where an overlapping of observation and antecedent is present if the rule base is sparse i e it contains insufficient information on the total state space it might occur that an observation has absolutely no overlapping with any of the antecedents and so not even a single rule is fired i e no conclusion can be computed on the basis of modus ponens in such a case interpolative reasoning in the strict sense can be applied some kind of weighted average of the flanking rules is calculated this technique can be extended to a form of extrapolation when the observation is not flanked from both sides linear interpolation and extrapolation is presented and then the idea is extended to arbitrary approximation

weighted fuzzy interpolative reasoning for sparse fuzzy rule based systems based on piecewise fuzzy entropies of fuzzy sets in this paper we propose a new method for weighted fuzzy interpolative reasoning in sparse fuzzy rule based systems based on piecewise fuzzy entropies of fuzzy sets first the proposed method uses the representative values of antecedent fuzzy sets the representative values of observation fuzzy sets and the representative values of consequence fuzzy sets of fuzzy rules to get the characteristic points of the fuzzy interpolative result represented by a fuzzy set then it calculates the piecewise fuzzy entropies between any two characteristic points of the antecedent fuzzy sets the piecewise fuzzy entropies between any two characteristic points of the observation fuzzy sets and the piecewise fuzzy entropies between any two characteristic points of the consequence fuzzy sets of the fuzzy rules respectively then it calculates the weights of the antecedent fuzzy sets of each fuzzy rule respectively and calculates the weight of each fuzzy rule then it calculates the piecewise fuzzy entropies between any two characteristic points of the fuzzy interpolative result finally it uses the secant method to calculate the degree of membership of each obtained characteristic point of the fuzzy interpolative result the experimental results show that the proposed method outperforms the existing methods for dealing with the multivariate regression problems the mackey glass chaotic time series prediction problem and the time series prediction problems

fixed point theorems for multivalued mappings on complete metric spaces on obtient une version multivaluee du theoreme de point fixe de caristi qui est equivalent au principe e variationnel du a ekeland on utilise ce resultat pour obtenir un theoreme qui deduit le theoreme de nadler et un theoreme de point fixe commun pour une application a 1 valeur et une application multivaluee

adaptive fuzzy interpolation fuzzy interpolative reasoning strengthens the power of fuzzy inference by the enhancement of the robustness of fuzzy systems and the reduction of the systems complexity however after a series of interpolations it is possible that multiple object values for a common variable are inferred leading to inconsistency in interpolated results such inconsistencies may result from defective interpolated rules or incorrect interpolative transformations this paper presents a novel approach for identification and correction of defective rules in interpolative transformations thereby removing the inconsistencies in particular an assumption based truth maintenance system atms is used to record dependences between interpolations and the underlying technique that the classical general diagnostic engine gde employs for fault localization is adapted to isolate possible faulty interpolated rules and their associated interpolative transformations from this an algorithm is introduced to allow for the modification of the original linear interpolation to become first order piecewise linear the approach is applied to a realistic problem which predicates the diarrheal disease rates in remote villages to demonstrate the potential of this study

common fixed point results for noncommuting mappings without continuity in cone metric spaces the existence of coincidence points and common fixed points for mappings satisfying certain contractive conditions without appealing to continuity in a cone metric space is established these results generalize several well known comparable results in the literature

fixed point theorems for multi valued contractions with w distance some fixed point theorems for a few nonlinear multi valued contraction mappings in complete metric spaces with w distance are proved the results presented in this paper generalize the recent results due to ciric 2009 3 feng and liu 2006 4 klim and wardowski 2007 8 latif and abdou 2011 12 and liu et al 2010 14 seven examples are given to explain our results

fuzzy rules interpolation for sparse fuzzy rule based systems based on interval type 2 gaussian fuzzy sets and genetic algorithms in this paper we present a new method for fuzzy rules interpolation for sparse fuzzy rule based systems based on interval type 2 gaussian fuzzy sets and genetic algorithms first we present a method to deal with the interpolation of fuzzy rules based on interval type 2 gaussian fuzzy sets we also prove that the proposed method guarantees to produce normal interval type 2 gaussian fuzzy sets then we present a method to learn optimal interval type 2 gaussian fuzzy sets for sparse fuzzy rule based systems based on genetic algorithms we also apply the proposed fuzzy rules interpolation method and the proposed learning method to deal with multivariate regression problems and time series prediction problems the experimental results show that the proposed fuzzy rules interpolation method using the optimally learned interval type 2 gaussian fuzzy sets gets higher average accuracy rates than the existing methods

on cone metric spaces a survey abstract using an old m krein s result and a result concerning symmetric spaces from s radenovic z kadelburg quasi contractions on symmetric and cone symmetric spaces banach j math anal 5 1 2011 38 50 we show in a very short way that all fixed point results in cone metric spaces obtained recently in which the assumption that the underlying cone is normal and solid is present can be reduced to the corresponding results in metric spaces on the other hand when we deal with non normal solid cones this is not possible in the recent paper m a khamsi remarks on cone metric spaces and fixed point theorems of contractive mappings fixed point theory appl 2010 7 pages article id 315398 doi 10 1115 2010 315398 the author claims that most of the cone fixed point results are merely copies of the classical ones and that any extension of known fixed point results to cone metric spaces is redundant also that underlying banach space and the associated cone subset are not necessary in fact khamsi s approach includes a small class of results and is very limited since it requires only normal cones so that all results with non normal cones which are proper extensions of the corresponding results for metric spaces cannot be dealt with by his approach

multivalued generalized nonlinear contractive maps and fixed points abstract we introduce some notions of generalized nonlinear contractive maps and prove some fixed point results for such maps consequently several known fixed point results are either improved or generalized including the corresponding recent fixed point results of ciric l b ciric multivalued nonlinear contraction mappings nonlinear anal 71 2009 2716 2723 klim and wardowski d klim d wardowski fixed point theorems for set valued contractions in complete metric spaces j math anal appl 334 2007 132 139 feng and liu y feng s liu fixed point theorems for multivalued contractive mappings and multivalued caristi type mappings j math anal appl 317 2006 103 112 and mizoguchi and takahashi n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric spaces j math anal appl 141 1989 177 188

endpoints and fixed points of set valued contractions in cone metric spaces abstract in this paper we introduce the concept of set valued contractions in cone metric spaces and establish new endpoint and fixed point theorems for such contractions the paper includes examples

interpolation with function space representation of membership functions this paper generalizes a previous cartesian approach for interpolating fuzzy rules comprised of membership functions with finite number of characteristic points instead of representing membership functions as points in cartesian spaces they now become elements in the space of square integrable function interpolation is thus conducted between the antecedent and consequent function spaces the generalized representation allows an extended class of membership functions satisfying two monotonicity conditions to be accommodated in the interpolation process they include the popular bell shaped membership functions which were not possible before with the cartesian representation the work also extends the similarity triangle based interpolation technique from the previous cartesian representation to the new representation ensuing issues on computational complexity and nonunique conclusion are discussed other concepts such as spanning set and extensibility functions are also presented under the generalized framework examples to illustrate the extended approach and to compare with the cartesian approach are given

adaptive fuzzy interpolation based on general representative values of polygonal fuzzy sets and the shift and modification techniques abstract adaptive fuzzy interpolative reasoning afir can overcome the limitation of the conventional fuzzy interpolation techniques because it can find and solve the contradictions of the fuzzy interpolative reasoning fir results in order to ensure that the derived fir results are consistent in this paper we propose a new afir method to solve the inconsistencies occurring after the fir process the proposed afir method is based on the general representative values of polygonal fuzzy sets and the proposed shift and modification techniques the proposed afir method includes a new contradictions solving method to get a higher similarity degree between the afir results in order to demonstrate the higher consistency of the afir results obtained by the proposed afir method we apply the proposed afir method to deal with the diarrheal disease prediction problem the experimental results show that the proposed afir method outperforms yang and shen s afir method 2011 and cheng et al s afir method 2016 in terms of the degree of similarity between the afir results

weighted fuzzy interpolative reasoning systems based on interval type 2 fuzzy sets abstract in this paper we present a weighted fuzzy interpolative reasoning method for sparse fuzzy rule based systems based on interval type 2 fuzzy sets we also apply the proposed weighted fuzzy interpolative reasoning method to deal with the truck backer upper control problem the proposed method satisfies the seven evaluation indices for fuzzy interpolative reasoning the experimental results show that the proposed method outperforms the existing methods it provides us with a useful way for dealing with fuzzy interpolative reasoning in sparse fuzzy rule based systems

fuzzy interpolative reasoning based on the ratio of fuzziness of rough fuzzy sets in this paper we propose a method to construct a polygonal rough fuzzy set from a set of polygonal fuzzy sets representing the aggregation of multiple experts opinions and propose a new fuzzy interpolative reasoning method for sparse fuzzy rule based systems based on the ratio of fuzziness of the constructed polygonal rough fuzzy sets where the values of the antecedent variables and the consequence variable appearing in the fuzzy rules are represented by the constructed polygonal rough fuzzy sets the proposed fuzzy interpolative reasoning method can overcome the drawbacks of the existing method due to the fact that it can deal with fuzzy interpolative reasoning using polygonal rough fuzzy sets and it gets more reasonable fuzzy interpolative reasoning results than the existing method

common fixed point theorems for c distance in ordered cone metric spaces abstract recently cho et al y j cho r saadati s h wang common fixed point theorems on generalized distance in ordered cone metric spaces comput math appl 61 2011 1254 1260 introduced the concept of the c distance in a cone metric space and established some fixed point theorems on c distance the aim of this paper is to extend and generalize the main results of cho et al 20 and also show some examples to validate our main results

representing membership functions as points in high dimensional spaces for fuzzy interpolation and extrapolation this paper introduces a new approach for fuzzy interpolation and extrapolation of sparse rule base comprising of membership functions with finite number of characteristic points the approach calls for representing membership functions as points in high dimensional cartesian spaces using the locations of their characteristic points as coordinates hence a fuzzy rule base can be viewed as a set of mappings between the antecedent and consequent spaces and the interpolation and extrapolation problem becomes searching for an image in the consequent space upon given an antecedent observation the present approach divides observations into two groups 1 observations within the antecedent spanning set contain the same geometric properties as the given antecedents and 2 observations lying outside the antecedent spanning set contain new geometric properties beyond those of the given rules heuristic reasoning must therefore be applied in this case a two step approach with certain flexibility to accommodate additional criteria and design objectives is formulated

approximate reasoning on a basis of z number valued if then rules approximate reasoning is about reasoning with imperfect information nowadays a large diversity of approaches to approximate reasoning with fuzzy information and fuzzy type 2 information exists it should be stressed however that real world imperfect information is characterized by combination of fuzzy and probabilistic uncertainties which is referred to as bimodal information in view of this zadeh introduced the concept of a z number regarded as an ordered pair z a b of fuzzy numbers a and b where a is a linguistic value of a variable of interest and b is a linguistic value of probability measure of a playing a role of its reliability unfortunately up to day there is no research on approximate reasoning realized on the basis of if then rules with z number valued antecedents and consequents briefly z rules zadeh addressed this problem as related to an uncharted territory in this paper a new approach is developed to study approximate reasoning with z rules on a basis of linear interpolation we provide an application of the approach to job satisfaction evaluation and to students educational achievement evaluation problems related to psychological and perceptual issues naturally characterized by imperfect information the obtained results show applicability and validity of the proposed approach

fuzzy rule interpolation for multidimensional input spaces with applications a case study fuzzy rule based systems have been very popular in many engineering applications however when generating fuzzy rules from the available information this may result in a sparse fuzzy rule base fuzzy rule interpolation techniques have been established to solve the problems encountered in processing sparse fuzzy rule bases in most engineering applications the use of more than one input variable is common however the majority of the fuzzy rule interpolation techniques only present detailed analysis to one input variable case this paper investigates characteristics of two selected fuzzy rule interpolation techniques for multidimensional input spaces and proposes an improved fuzzy rule interpolation technique to handle multidimensional input spaces the three methods are compared by means of application examples in the field of petroleum engineering and mineral processing the results show that the proposed fuzzy rule interpolation technique for multidimensional input spaces can be used in engineering applications

weighted fuzzy rule interpolation based on ga based weight learning techniques in this paper we propose a weighted fuzzy interpolative reasoning method for sparse fuzzy rule based systems it is based on a genetic algorithm ga based weight learning technique the proposed method can deal with fuzzy rule interpolation with weighted antecedent variables it also can deal with fuzzy rule interpolation based on polygonal membership functions and bell shaped membership functions we also propose a ga based weight learning algorithm to automatically learn the optimal weights of the antecedent variables of the fuzzy rules furthermore we apply the proposed weighted fuzzy interpolative reasoning method and the proposed ga based weight learning algorithm to deal with the truck backer upper control problem the computer activity prediction problem multivariate regression problems and time series prediction problems based on statistical analysis techniques the experimental results show that the proposed weighted fuzzy interpolative reasoning method by the use of the optimally learned weights that were obtained by the proposed ga based weight learning algorithm has statistically significantly smaller error rates than the existing methods

endpoints of multi valued generalized weak contraction mappings abstract let x d be a complete metric space and let t x p cl bd x be a multi valued generalized weak contraction mapping then t has a unique endpoint if and only if t has the approximate endpoint property our results extend previous results given by ciric 1971 15 nadler 1969 11 daffer and kaneko 1995 9 and amini harandi 2010 8

coincidence and fixed points for multi valued mappings and its application to nonconvex integral inclusions in this paper we consider some problems on coincidence point and fixed point theorems for multi valued mappings applying the characterizations of p functions we establish some new existence theorems for coincidence point and fixed point distinct from nadler s fixed point theorem berinde berinde s fixed point theorem mizoguchi takahashi s fixed point theorem and du s fixed point theorem for nonlinear multi valued contractive mappings in complete metric spaces our results compliment and extend the main results given by some authors in the literature in the sequel we consider a nonconvex integral inclusion and prove the filippov type existence theorem by using an appropriate norm on the space of selection of a multi function and a multi valued contraction for set valued mappings

the point of coincidence and common fixed point for a pair of mappings in cone metric spaces in this paper the existence of a point of coincidence and a common fixed point for two weakly compatible maps on a cone metric space has been established the two mappings are assumed to satisfy certain weak inequalities supporting examples are also given