improving newton raphson method for nonlinear equations by modified adomian decomposition method in this paper we present some efficient numerical algorithms for solving nonlinear equations based on newton raphson method the modified adomian decomposition method is applied to construct the numerical algorithms some numerical illustrations are given to show the efficiency of algorithms

commutative stochastic games we are interested in the convergence of the value of n stage games as n goes to infinity and the existence of the uniform value in stochastic games with a general set of states and finite sets of actions where the transition is commutative this means that playing an action profile a1 followed by an action profile a2 leads to the same distribution on states as playing first the action profile a2 and then a1 for example absorbing games can be reformulated as commutative stochastic games when there is only one player and the transition function is deterministic we show that the existence of a uniform value in pure strategies implies the existence of 0 optimal strategies in the framework of two player stochastic games we study a class of games where the set of states is m and the transition is deterministic and 1 lipschitz for the l1 norm and prove that these games have a uniform value a similar proof shows the existence of an equilibrium in the nonzero sum case these results remain true if one co

a study of convergence on the newton homotopy continuation method the traditional newton method is a well known and popular method for solving non linear equation it has high efficient in the convergence speed however we always need to guess the initial value in the iteration process good initial guess value can solve the equation quickly bad initial guess value usually will yield divergence homotopy continuation method is a kind of perturbation method it can guarantee the answer by a certain path if we choose the auxiliary homotopy function or call start system well this paper presents some useful rules for the choice of the auxiliary homotopy function to avoid the problem of divergence of traditional newton method

multi granulation fuzzy preference relation rough set for ordinal decision system preference analysis is a class of important issues in multi criteria ordinal decision making rough set is an effective approach to handle preference analysis in order to solve the multi criteria preference analysis problem this work improves the fuzzy preference relation rough set model with additive consistent fuzzy preference relation and expands it to multi granulation case cost is also an important issue in decision analysis taking the cost into consideration we also expand the model to cost sensitive multi granulation fuzzy preference relation rough set some theorems are represented and the classification and sample condensation algorithms based on our model are investigated some experiments are complete and the experimental results show that our model and algorithms are effective for preference decision making of ordinal decision system

a measurement theory view on the granularity of partitions measurement of granularity is one of the foundational issues in granular computing this paper investigates a class of measures of granularity of partitions the granularity of a set is defined by a strictly monotonic increasing transformation of the cardinality of the set the granularity of a partition is defined as the expected granularity of all blocks of the partition with respect to the probability distribution defined by the partition many existing measures of granularity are instances of the proposed class new measures of granularity of partitions are also introduced

one point newton type iterative methods in this paper a unified point of view that includes the most of one point newton type iterative methods for solving nonlinear equations is introduced a simple idea to design iterative methods with quadratic or cubic convergence is also described this idea is extended to construct one point iterative methods of order four in addition several numerical examples are given to illustrate and compare different known methods and some introduced by using this unifying idea

solvability of concatenated runge kutta equations for second order nonlinear pdes in this paper we consider the solvability of concatenated runge kutta crk equations which are the nonlinear algebraic equations arising from crk methods applied to some kind of second order nonlinear partial differential equations to guarantee the existence and uniqueness of the solution of crk equations temporal and spatial step sizes of crk methods should be chosen appropriately under different assumptions with the homotopy continuation method we choose different step sizes to ensure the solvability of crk equations

reducts and constructs in classic and dominance based rough sets approach abstract the idea of the reduct as defined in the classic rough sets approach crsa has proven to be inspiring enough to get into closely related theories including the dominance based rough sets approach drsa the procedure of reduction is generally similar to that of feature selection but narrower as it is the descriptive rather than the predictive aspect of data exploration that constitutes its principal goal crsa reducts are thus defined as minimal subsets of attributes that retain sufficiently high quality of object description developed within crsa the crsa reducts have given rise to the generalized notion of crsa constructs which have turned out to be superior to reducts in numerous practical experiments with real life data sets the generalization process is continued in this paper in which a definition of constructs in the context of drsa is introduced the definition fully analogous to that of crsa constructs differs only in that it is context based in drsa while context free in crsa consequently the presented drsa constructs are expected to have analogous properties to that of crsa constructs including superiority to drsa reducts in experiments with real life data sets

the value of repeated games with an informed controller we consider the general model of zero sum repeated games or stochastic games with signals and assume that one of the players is fully informed and controls the transitions of the state variable we prove the existence of the uniform value generalizing several results of the literature a preliminary existence result is obtained for a particular class of stochastic games played with pure strategies

prediction of company acquisition in greece by means of the rough set approach abstract this paper presents a new approach to forecast the acquisition of a firm in greece based on the rough set theory a sample of acquired firms and a sample of equivalent non acquired firms are considered and the objective is to create patterns which would be able to distinguish between the two classes of firms based upon differences in their financial characteristics financial ratios for this purpose the rough set approach is used the information about the firms is organized in a financial information table in this table financial characteristics of the firms correspond to condition attributes and the classification is defined by a decision attribute telling if a firm has been acquired or not the rough set approach enables one to discover minimal subsets of condition attributes financial ratios ensuring an acceptable approximation of the classification of the firms analyzed and to derive decision rules from the financial information table which can be used to best distinguish in the future between acquired and non acquired firms a comparison of the rough set approach with the discriminant analysis on the same set of data shows an advantage of the new approach

third order iterative methods free from second derivatives for nonlinear equation in this paper we suggest and analyze a new two step iterative method for solving nonlinear equations which is called the modified householder method without second derivatives for nonlinear equation we also prove that the modified method has cubic convergence several examples are given to illustrate the efficiency and the performance of the new method new method can be considered as an alternative to the present cubic convergent methods for solving nonlinear equations

predictor corrector halley method for nonlinear equations abstract in this paper we suggest and analyze a new two step predictor corrector type iterative methods for solving nonlinear equations of the type f x 0 by using the technique of updating the solution this method can be viewed as a predictor corrector iterative halley s method we also consider the convergence analysis of the proposed method to illustrate the efficiency of this new method we give several examples and a comparison with the method of grau and diaz barrero m grau j l diaz barrero an improvement to ostrowski root finding method appl math comput 173 2006 450 456 is given this method can be considered as a refinement and improvement of the halley method

a new iteration method for solving algebraic equations in this paper a nonlinear algebraic equation f x 0 by applying taylor s theorem is converted into a coupled iteration systeml x n 1 g x n 0andg x n f x n l x n wherel x ax 2 bx c the formula is of high convergence some examples are given

a novel and better fitness evaluation for rough set based minimum attribute reduction problem the minimum attribute reduction mar problem in the context of rough set theory is known to be np hard one popular way of dealing with this problem is to first transform it into a fitness maximization problem over a multi dimensional boolean space and to then solve this problem using population based stochastic optimization algorithms it is therefore important to have an appropriate fitness function in this paper two examples are presented to show that existing fitness functions either do not guarantee optimality equivalence between the mar problem and the transformed fitness maximization problem or may produce the so called overemphasis phenomenon that affects the performance of population based stochastic optimization algorithms to overcome these drawbacks we propose a new fitness function that we prove both guarantees the optimality equivalence and reduces the overemphasis phenomenon experimental results show that the proposed fitness function is better than existing fitness functions in terms of solution quality

newton s method s basins of attraction revisited in this paper we revisit the chaotic number of iterations needed by newton s method to converge to a root here we consider a simple modified newton method depending on a parameter it is demonstrated using polynomiography that even in the simple algorithm the presence and the position of the convergent regions i e regions where the method converges nicely to a root can be complicatedly a function of the parameter

homotopy perturbation method a new nonlinear analytical technique in this paper a new perturbation method is proposed in contrast to the traditional perturbation methods this technique does not require a small parameter in an equation in this method according to the homotopy technique a homotopy with an imbedding parameter email protected 0 1 is constructed and the imbedding parameter is considered as a small parameter so the method is called the homotopy perturbation method which can take the full advantages of the traditional perturbation methods and homotopy techniques to illustrate its effectiveness and its convenience a duffing equation with high order of nonlinearity is used the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter and is more accurate than the perturbation solutions

a new iterative method to compute nonlinear equations the aim of this paper is to construct a new efficient iterative method to solve nonlinear equations the new method is based on the proposals of abbasbandy on improving the order of accuracy of newton raphson method s abbasbandy improving newton raphson method for nonlinear equations by modified adomian decomposition method applied mathematics and computation 145 2003 887 893 and on the proposals of babolian and biazar on improving the order of accuracy of adomian s decomposition method e babolian j biazar on the order of convergence of adomian method applied mathematics and computation 130 2002 383 387 the convergence of the new scheme is proved and at least the cubic order of convergence is established several examples are presented and compared to other methods showing the accuracy and fast convergence of this new method also it is shown in this paper that the modified adomian s method developed by babolian and biazar to solve nonlinear equations e babolian j biazar solution of nonlinear equations by modified adomian decomposition method applied mathematics and computation 132 2002 167 172 should be slightly modified due to the fact that convergence of adomian s method does not ensure convergence of the modified method an example illustrates this fact which unlike what is claimed by the authors does not converge with their method but with a simple different choice of the zero component becomes convergent

quick attribute reduction in inconsistent decision tables this paper focuses on three types of attribute reducts in inconsistent decision tables assignment reduct distribution reduct and maximum distribution reduct it is quite inconvenient to judge these three types of reduct directly according to their definitions this paper proposes judgment theorems for the assignment reduct the distribution reduct and the maximum distribution reduct which are expected to greatly simplify the judging of these three types of reducts on this basis we derive three new types of attribute significance measures and construct the q ara quick assignment reduction algorithm the q dra quick distribution reduction algorithm and the q mdra quick maximum distribution reduction algorithm these three algorithms correspond to the three types of reducts we conduct a series of comparative experiments with twelve uci machine learning data repository university of california at irvine data sets including consistent and inconsistent decision tables to evaluate the performance of the three reduction algorithms proposed with the relevant algorithm quickreduct 9 34 the experimental results show that quickreduct possesses weak robustness because it cannot find the reduct even for consistent data sets whereas our proposed three algorithms show strong robustness because they can find the reduct for each data set in addition we compare the q dra quick distribution reduction algorithm with the cebarknc conditional entropy based algorithm for reduction of knowledge without a computing core 43 because both find the distribution reduct by using a heuristic search the experimental results demonstrate that q dra runs faster than cebarknc does because the distribution function of q dra has a lower calculation cost instructive conclusions for these reduction algorithms are drawn from the perspective of classification performance for the c4 5 and rbf svm classifiers last we make a comparison between discernibility matrix based methods and our algorithms the experimental results indicate that our algorithms are efficient and feasible

rough set approach to multi attribute decision analysis abstract we review the methodology of the rough set analysis of multi attribute decision problems rough set theory proved to be a useful tool for analysis of a vague description of decision situations it answers two basic questions related to multi attribute decision problems one about explanation of a decision situation and another about prescription of some decisions basing on analysis of a decision situation we define four classes of multi attribute decision problems depending on the structure of their representation its interpretation and the kind of questions related then we characterize the rough set methodology for each particular class of decision problems we use simple practical examples to illustrate this presentation a review of related literature is made throughout the paper

generation of rough sets reducts and constructs based on inter class and intra class information the reduct originating from the classic rough set approach crsa is an inclusion minimal subset of attributes that provides discernibility between objects from different classes in at least the same degree as the set of all attributes it can be thus referred to as being consistent and minimal which are the two important characteristics of filter based feature selection these two characteristics have been also utilized to define reducts within the dominance based rough set approach drsa further the classic reduct here referred to as an inter class reduct has evolved into what is known as intra class reduct and construct in crsa the idea is that while inter class reducts utilize only one part of information generated from all pairs of objects intra class reducts utilize the remaining part while constructs utilize both the paper delivers a final unification of inter class reducts intra class reducts and constructs across crsa and drsa showing how they can be both defined and computed uniformly i e using basically the same concepts and algorithms it also presents an exact algorithm capable of generating all exact reduced subsets but of considerable complexity as well as a simple and fast heuristic designed to generate a single reduced subset finally it illustrates the computation process with examples and some experimental evaluation of crsa constructs which show how the use of both the inter class and the intra class information can assist the attribute reduction process and help obtaining useful insights into the analyzed data set

axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough set decision rules abstract utility or value functions play an important role of preference models in multiple criteria decision making we investigate the relationships between these models and the decision rule preference model obtained from the dominance based rough set approach the relationships are established by means of special cancellation properties used in conjoint measurement as axioms for representation of aggregation procedures we are considering a general utility function and three of its important special cases associative operator sugeno integral and ordered weighted maximum for each of these aggregation functions we give a representation theorem establishing equivalence between a very weak cancellation property the specific utility function and a set of rough set decision rules each result is illustrated by a simple example of multiple criteria decision making the results show that the decision rule model we propose has clear advantages over a general utility function and its particular cases

variable consistency dominance based rough set approach to preference learning in multicriteria ranking abstract we present a methodology for non statistical preference learning in multicriteria ranking based on variable consistency dominance based rough set approach vc drsa a finite set of objects to be ranked is evaluated by a set of criteria which are real valued functions with ordinal or cardinal scales given the statement of a multicriteria ranking problem the only objective information one can get is the dominance relation over the set of objects the dominance relation is however too poor because it leaves many objects incomparable to enrich this relation and make the objects more comparable a decision maker dm must supply some preference information revealing her his value system with respect to multicriteria evaluations we are considering a frequent case when the preference information has the form of pairwise comparisons of some objects relatively well known to the dm called reference objects this information is thus composed of some decision examples on the reference objects it is the input data for a method that learns the preferences of the dm since this information is prone to inconsistencies we propose to structure it using vc drsa then the pairs of objects that are sufficiently consistent serve as a basis for induction of a preference model this model has the form of a set of if then decision rules application of these rules on the whole set of objects to be ranked yields a fuzzy preference structure directed weighted graph this preference structure is then exploited using a ranking method so as to work out a final recommendation we propose a list of properties that helps to choose a proper ranking method the methodology is illustrated by an example

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

an iterative method for solving nonlinear equations an iterative method for finding a solution of the equation f x 0 is presented the method is based on some specially derived quadrature rules it is shown that the method can give better results than the newton method

perturbation theorems for estimating magnitudes of roots of polynomials two additional new theorems are posed and proven to estimate the magnitudes of roots of polynomials perturbation theory and the order of magnitude of terms are employed to develop the theorems the theorems may be useful to estimate the order of magnitudes of the roots of a polynomial a priori before solving the equation the theorems are developed for two special classes of polynomials of arbitrary order with their coefficients satisfying certain conditions numerical applications of the theorems are presented as examples it is shown that the theorems produce good estimates for the magnitudes of roots

a uniform tauberian theorem in dynamic programming we prove that in dynamic programming framework uniform convergence of v implies uniform convergence of vn and vice versa moreover both have the same limit

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

some numerical methods for solving nonlinear equations by using decomposition technique in this paper we use the system of coupled equations involving an auxiliary function together with decomposition technique to suggest and analyze some new classes of iterative methods for solving nonlinear equations these new methods include the halley method and its variant forms as special cases various numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations

uncertainly measures of rough set prediction abstract the main statistics used in rough set data analysis the approximation quality is of limited value when there is a choice of competing models for predicting a decision variable in keeping within the rough set philosophy of non invasive data analysis we present three model selection criteria using information theoretic entropy in the spirit of the minimum description length principle our main procedure is based on the principle of indifference combined with the maximum entropy principle thus keeping external model assumptions to a minimum the applicability of the proposed method is demonstrated by a comparison of its error rates with results of c4 5 using 14 published data sets

new iterative methods for solving nonlinear equation by using homotopy perturbation method in this paper we suggest and analyze a new class of iterative methods for solving nonlinear equations by using the homotopy perturbation method convergence of their method is also considered here we also discuss the efficiency index and computational order of convergence of new methods several numerical examples are given to illustrate the efficiency and performance of these new methods these new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations

high order iterative methods without derivatives for solving nonlinear equations the new second order and third order iterative methods without derivatives are presented for solving nonlinear equations the iterative formulae based on the homotopy perturbation method are deduced and their convergences are provided finally some numerical experiments show the efficiency of the theoretical results for the above methods

a two parameter third order family of methods for solving nonlinear equations in this paper we present a new two parameter family of iterative methods for solving nonlinear equations which includes as a particular case the classical potra and ptak third order method per iteration the new methods require two evaluations of the function and one evaluation of its first derivative it is shown that each family member is cubically convergent several examples are given to illustrate the performance of the family members

a third order newton type method for nonlinear equations based on modified homotopy perturbation method in this paper we present a new iterative method for solving nonlinear algebric equations by using modified homotopy perturbation method we also discuss the convergence criteria of the present method to assess its validity and accuracy the method is applied to solve several test problems

third order derivative free sph iterative method for solving nonlinear systems the majority of iterative methods to find roots of a function requires the evaluation of derivatives of this function in this paper based on the basic principle of the sph method s kernel approximation a kernel approximation was constructed to compute first and second order derivatives through taylor series expansion derivatives in our proposed method were replaced in a newton like iterative method to obtain a derivative free sph iterative method for solving nonlinear systems to illustrate that the new method has the same order of convergence as the considered iterative method some numerical examples are presented

a new formula of solving nonlinear equations by adomian and homotopy methods a new formula combining adomian and homotopy methods is presented the traditional newton raphson method is modified to a higher order form by adomian and homotopy methods and the rule for the choice of the auxiliary homotopy function in the new formula is also provided

blackwell optimality in markov decision processes with partial observation a blackwell epsilon optimal strategy in a markov decision process is a strategy that is epsilon optimal for every discount factor sufficiently close to 1 we prove the existence of blackwell epsilon optimal strategies in finite markov decision processes with partial observation

rough approximation of a preference relation by dominance relations an original methodology for using rough sets to preference modeling in multi criteria decision problems is presented this methodology operates on a pairwise comparison table pct including pairs of actions described by graded preference relations on particular criteria and by a comprehensive preference relation it builds up a rough approximation of a preference relation by graded dominance relations decision rules derived from the rough approximation of a preference relation can be used to obtain a recommendation in multi criteria choice and ranking problems the methodology is illustrated by an example of multi criteria programming of water supply systems

iterative methods with fourth order convergence for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations involving only first derive of the function using a new decomposition technique which is due to noor m aslam noor numerical analysis and optimization lecture notes comsats institute of information technology islamabad pakistan 2006 m aslam noor new iterative schemes for nonlinear equations appl math comput in press and noor and noor m aslam noor k inayat noor some iterative schemes for nonlinear equations appl math comput in press we show that this new iterative method has fourth order convergence several numerical examples are given to illustrate the efficiency and performance of the new method

set valued information systems set valued information systems are generalized models of single valued information systems incomplete information systems can be viewed as disjunctively interpreted set valued information systems since some objects in set valued information systems may have more than one value for an attribute so we define tolerance relation and use the maximal tolerance classes to classify the universe of discourse in order to derive optimal decision rules from set valued decision information systems we propose the concept of relative reduct of maximal tolerance classes and define a kind of discernibility function to compute the relative reduct by boolean reasoning techniques finally we define three kinds of relative reducts for set valued information systems and used them to evaluate the significance of attributes

on the solution of algebraic equations by the decomposition method abstract the decomposition method g adomian stochastic systems academic press new york 1983 developed to solve nonlinear stochastic differential equations has recently been generalized to nonlinear and or stochastic partial differential equations systems of equations and delay equations and applied to diverse applications as pointed out previously see reference above the methodology is an operator method which can be used for nondifferential operators as well extension has also been made to algebraic equations involving real or complex coefficients this paper deals specifically with quadratic cubic and general higher order polynomial equations and negative or nonintegral powers and random algebraic equations further work on this general subject appears elsewhere g adomian stochastic systems ii academic press new york in press

a family of methods for solving nonlinear equations we present a family of methods for solving nonlinear equations some well known classical methods and their modifications belong to our family for example newton potra ptak chebyshev halley and ostrowski s methods convergence analysis shows that our family contains methods of convergence order from 2 to 4 all our fourth order methods are optimal in terms of the kung and traub conjecture several examples are presented and compared

a new family of iterative methods for solving system of nonlinear algebric equations abstract homotopy perturbation method hpm is applied to construct a new iterative method for solving system of nonlinear algebric equations comparison of the result obtained by the present method with that obtained by revised adomian decomposition method hossein jafari varsha daftardar gejji appl math comput 175 2006 1 7 reveals that the accuracy and fast convergence of the new method

fifth order iterative methods for solving nonlinear equations abstract in this paper we suggest and analyze a new two step iterative method for solving nonlinear equation f x 0 by rewriting the given nonlinear equation as a coupled system of equations and using the taylor series it is shown that this new iterative method is of fifth order several examples are given to illustrate its performance and efficiency comparison with other methods is also given this method can be viewed as an improvement of the halley s method

a tauberian theorem for nonexpansive operators and applications to zero sum stochastic games we prove a tauberian theorem for nonexpansive operators and apply it to the model of zero sum stochastic game under mild assumptions we prove that the value of the discounted game converges uniformly when goes to zero if and only if the value of the n stage game converges uniformly when n goes to infinity this generalizes the tauberian theorem of lehrer and sorin lehrer e sorin s 1992 a uniform tauberian theorem in dynamic programming math oper res 17 2 303 307 to the two player zero sum case we also provide the first example of a stochastic game with public signals on the state and perfect observation of actions with finite state space signal sets and action sets in which for some initial state known by both players the value of the discounted game and the value of the n stage game starting at that initial state converge to distinct limits

multicriteria sorting using a valued preference closeness relation abstract to define a metric or a similarity relation with good properties is a crucial issue in most analogy and rule induction oriented methods for multicriteria sorting here we propose a valued indifference closeness relation which is inspired on concordance and discordance measures the criterion weights are obtained from the preferential information embedded in a reference set this proposal performs very well in several practical problems

using assignment examples to infer weights for electre tri method some experimental results given a finite set of alternatives a the sorting or assignment problem consists in the assignment of each alternative to one of the pre defined categories in this paper we are interested in multiple criteria sorting problems and more precisely in the existing method electre tri this method requires the elicitation of preferential parameters weights thresholds category limits in order to construct a preference model which the decision maker dm accepts as a working hypothesis in the decision aid study a direct elicitation of these parameters requiring a high cognitive effort from the dm v mosseau r slowinski journal of global optimization 12 2 1998 174 proposed an interactive aggregation disaggregation approach that infers electre tri parameters indirectly from holistic information i e assignment examples in this approach the determination of electre tri parameters that best restore the assignment examples is formulated through a nonlinear optimization program in this paper we consider the subproblem of the determination of the weights only the thresholds and category limits being fixed this subproblem leads to solve a linear program rather than nonlinear in the global inference model numerical experiments were conducted so as to check the behaviour of this disaggregation tool results showed that this tool is able to infer weights that restores in a stable way the assignment examples and that it is able to identify inconsistencies in the assignment examples

multi stage optimization of decision and inhibitory trees for decision tables with many valued decisions abstract we study problems of optimization of decision and inhibitory trees for decision tables with many valued decisions as cost functions we consider depth average depth number of nodes and number of terminal nonterminal nodes in trees decision tables with many valued decisions multi label decision tables are often more accurate models for real life data sets than usual decision tables with single valued decisions inhibitory trees can sometimes capture more information from decision tables than decision trees in this paper we create dynamic programming algorithms for multi stage optimization of trees relative to a sequence of cost functions we apply these algorithms to prove the existence of totally optimal simultaneously optimal relative to a number of cost functions decision and inhibitory trees for some modified decision tables from the uci machine learning repository

rough variables with values in measurable spaces an x valued rough variable is introduced as a measurable function from a rough space to a measurable space x based on the concept of x valued rough variables some properties of x valued rough variables are studied furthermore the concept of convergence is presented and convergence of x valued rough variables is discussed

the inverse kinematics problem of spatial 4p3r robot manipulator by the homotopy continuation method with an adjustable auxiliary homotopy function abstract in this paper the concept of an adjustable auxiliary homotopy function for the homotopy continuation method is presented by means of adjusting the auxiliary function we can solve non linear equations and guarantee the solutions exactly without divergence rather than the traditional numerical methods such as the newton raphson method and so on

fourth order convergent iterative method for nonlinear equation in this paper we suggest and analyze a new iterative method for finding approximate solution of the nonlinear equation f x 0 it is shown that proposed method has fourth order convergence several numerical examples are given to illustrate that the method developed in this paper give better results than the other methods including newton method

rough sets theory for multicriteria decision analysis the original rough set approach proved to be very useful in dealing with inconsistency problems following from information granulation it operates on a data table composed of a set u of objects actions described by a set q of attributes its basic notions are indiscernibility relation on u lower and upper approximation of either a subset or a partition of u dependence and reduction of attributes from q and decision rules derived from lower approximations and boundaries of subsets identified with decision classes the original rough set idea is failing however when preference orders of attribute domains criteria are to be taken into account precisely it cannot handle inconsistencies following from violation of the dominance principle this inconsistency is characteristic for preferential information used in multicriteria decision analysis mcda problems like sorting choice or ranking in order to deal with this kind of inconsistency a number of methodological changes to the original rough sets theory is necessary the main change is the substitution of the indiscernibility relation by a dominance relation which permits approximation of ordered sets in multicriteria sorting to approximate preference relations in multicriteria choice and ranking problems another change is necessary substitution of the data table by a pairwise comparison table where each row corresponds to a pair of objects described by binary relations on particular criteria in all those mcda problems the new rough set approach ends with a set of decision rules playing the role of a comprehensive preference model it is more general than the classical functional or relational model and it is more understandable for the users because of its natural syntax in order to workout a recommendation in one of the mcda problems we propose exploitation procedures of the set of decision rules finally some other recently obtained results are given rough approximations by means of similarity relations rough set handling of missing data comparison of the rough set model with sugeno and choquet integrals and results on equivalence of a decision rule preference model and a conjoint measurement model which is neither additive nor transitive

decision analysis based on fused double exponential possibility distributions abstract in this paper the possibility grades given by an expert are approximated by double possibility distributions called upper and lower possibility distributions to characterize uncertainty knowledge from this expert the upper and lower possibility distributions have some similarities to upper and lower approximations in rough set theory multi source knowledge from multiple experts is represented by a set of exponential possibility distributions based on the consistency index defined by the possibility measure of each pair of possibility distributions a fusion model is proposed to integrate multiple possibility distributions into a new one representing a refined knowledge as an application a portfolio selection problem with multiple experts is considered

solving the nonlinear equations by the newton homotopy continuation method with adjustable auxiliary homotopy function in this paper the concept of adjustable auxiliary homotopy function for the newton homotopy continuation method is presented by means of adjusting the auxiliary function we can solve the nonlinear equations and guarantee the solutions exactly without divergence rather than the traditional numerical methods such as the newton raphson method and so on

an optimal and efficient general eighth order derivative free scheme for simple roots abstract the main motivation of this study is to present an optimal scheme in a general way that can be applied to any existing optimal multipoint fourth order iterative scheme whose first substep employs steffensen s method or steffensen like method to further produce optimal eighth order iterative schemes a rational function approximation approach is used in the construction of proposed scheme in addition we also discussed the theoretical and computational properties of our scheme each member of the presented scheme satisfies the optimality conjecture for multipoint iterative methods without memory which was given by kung and traub in 1970 finally we also concluded on the basis of obtained numerical results that our methods have faster convergence in contrast to the existing methods of same order because they have minimum residual errors minimum error difference between two consecutive iterations and minimum asymptotic error constants corresponding to the considered test function

a modified formula of ancient chinese algorithm by the homotopy continuation technique a modified formula iteration representation of ancient chinese algorithm by combining the homotopy continuation technique is presented considering the convergence the new iteration formula and the technique for the choice of the auxiliary homotopy function are developed once we have the condition f x 1 f x 2 or f x is an even function we will diverge in traditional ancient chinese algorithm the paper provides some useful rules to overcome this defect

rough approximation of a preference relation by a multi attribute stochastic dominance for determinist and stochastic evaluation problems abstract let a be a set of actions evaluated by a set of attributes two kinds of evaluations will be considered in this paper determinist or stochastic in relation to each attribute the multi attribute stochastic dominance msd r for a reduced number of attributes will be suggested to model the preferences in this kind of problem the case of mixed data where we have the attributes of different natures is not well known in the literature although it is essential from a practical point of view to apply the msd r the subset r of attributes from which approximation of the global preference is valid should be known the theory of rough sets gives us an answer on this issue allowing us to determine a minimal subset of attributes that enables the same classification of objects as the whole set of attributes in our approach these objects are pairs of actions in order to represent preferential information we shall use a pairwise comparison table this table is built for subset b a described by stochastic dominance sd relations for particular attributes and a total order for the decision attribute given by the decision maker dm using a rough set approach to the analysis of the subset of preference relations a set of decision rules is obtained and these are applied to a set a b of potential actions the rough set approach of looking for the reduction of the set of attributes gives us the possibility of operating with msd r

rough sets analysis of diagnostic capacity of vibroacoustic symptoms abstract the paper refers to the problem of diagnostic classification of mechanical objects using vibroacoustic symptoms a new approach based on the rough sets theory is applied to evaluate the symptoms from the point of view of their diagnostic capacity i e the quality of estimation of a technical state of a mechanical object the approach enables reduction of the set of symptoms to a minimal subset ensuring a satisfactory estimation the minimal subset is then used to create a classifier of a technical state particular attention is paid to a comparison of different methods of calculation of symptom limit values which divide domains of symptoms into intervals corresponding to classes of technical states the analysed set of data concerns the technical state of rolling bearings installed in a laboratory stand they are described by a set of symptoms which result from measurements of noise and vibration of bearing housings the bearings are in good or bad technical states the paper presents particular steps of the rough sets methodology and gives as a final result a classifier of a technical state of bearings based on a minimal subset of symptoms with the greatest diagnostic capacity

bi criteria optimization of decision trees with applications to data analysis abstract this paper is devoted to the study of bi criteria optimization problems for decision trees we consider different cost functions such as depth average depth and number of nodes we design algorithms that allow us to construct the set of pareto optimal points pops for a given decision table and the corresponding bi criteria optimization problem these algorithms are suitable for investigation of medium sized decision tables we discuss three examples of applications of the created tools the study of relationships among depth average depth and number of nodes for decision trees for corner point detection such trees are used in computer vision for object tracking study of systems of decision rules derived from decision trees and comparison of different greedy algorithms for decision tree construction as single and bi criteria optimization algorithms

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

solution of nonlinear equations by modified adomian decomposition method in this paper we modify the standard adomian method for solution of the nonlinear equation f x 0 four examples are presented and compared using standard and modified adomian methods

evaluation functions and decision conditions of three way decisions with game theoretic rough sets abstract three way decisions have been used over the years in many application areas the rough sets and its extensions provide useful approaches for three way decisions typically these approaches employ a single evaluation function or criterion to induce three way decisions when extending the rough set based three way decisions to multiple criteria decision making mcdm two issues are encountered the first issue is related to the construction and definition of aggregation mechanisms for dealing with differences in results of evaluation functions the second issue is related to the setting of choice structure for selecting the three types of decision choices in this article we consider the role and use of game theoretic rough set gtrs model to resolve and address these two issues the issue related to differences in evaluation functions is addressed with gtrs by implementing a game that considers multiple evaluation functions as game players the game theoretic analysis in the gtrs is employed to resolve the differences by determining a tradeoff between evaluation functions the issue related to choice structure is addressed by considering the conditions under which different game outcomes could constitute a game solution in particular the equilibrium analysis within games is used to construct the rules for three way decisions a demonstrative example is used to explain the use of the proposed approach the relationship between the proposed approach and the probabilistic rough sets is also discussed