application of fuzzy soft set in decision making problems based on grey theory there are many uncertain problems in practical production and life which need decisions made with soft sets and fuzzy soft sets however the basis of evaluation of the decision method is single and simple the same decision problem can obtain different results from using a different evaluation basis in this paper in order to obtain the right result we discuss fuzzy soft set decision problems a new algorithm based on grey relational analysis is presented the evaluation bases of the new algorithm are multiple there is more information in a decision result based on multiple evaluation bases which is more easily accepted and logical to one s thinking for the two cases examined the results show that the new algorithm is efficient for solving decision problems

a comparative study of adjoint triples adjoint triples are helpful as basic operators used in several domains for example adjoint triples play an important role in two important frameworks multi adjoint logic programming and multi adjoint concept lattices this paper shows that adjoint triples are an interesting generalization of t norms and their residuated implications since they preserve their main properties as well as they help to increase the flexibility of the operators used for computation in the considered framework furthermore these operators will be related to other important general triples specifically implication triples and the definition of these latter operators will be improved

critical heights on the moduli space of polynomials abstract let m d be the moduli space of one dimensional degree d 2 complex polynomial dynamical systems the escape rates of the critical points determine a critical heights map g m d r d 1 for generic values of g we show that each connected component of a fiber of g is the deformation space for twist deformations on the basin of infinity we analyze the quotient space t d obtained by collapsing each connected component of a fiber of g to a point the space t d is a parameter space analog of the polynomial tree t f associated to a polynomial f c c studied in demarco and mcmullen 2008 6 and there is a natural projection from t d to the space of trees t d we show that the projectivization p t d is compact and contractible further the shift locus in p t d has a canonical locally finite simplicial structure the top dimensional simplices are in one to one correspondence with topological conjugacy classes of structurally stable polynomials in the shift locus

isotone fuzzy galois connections with hedges we study isotone fuzzy galois connections and concept lattices parameterized by particular unary operators the operators represent linguistic hedges such as very rather more or less etc isotone fuzzy galois connections and concept lattices provide an alternative to their antitone counterparts which are the fundamental structures behind formal concept analysis of data with fuzzy attributes we show that hedges enable us to control the number of formal concepts in the associated concept lattice we also describe the structure of the concept lattice and provide a counterpoint to the main theorem of concept lattices

formal concept analysis via multi adjoint concept lattices several fuzzifications of formal concept analysis have been proposed to deal with uncertain information in this paper we focus on concept lattices under a multi adjoint paradigm which enriches the language providing greater flexibility to the user in that he she can choose from a number of different connectives multi adjoint concept lattices are shown to embed different fuzzy extensions of concept lattices found in the literature the main results of the paper being the representation theorem of this paradigm and the embedding of other well known approaches

on the solvability of bipolar max product fuzzy relation equations with the product negation abstract this paper studies the solvability of the max product fuzzy relation equations in which a negation operator is considered specifically the residuated negation of the product t norm has been introduced in these equations in order to increase the flexibility of the standard fuzzy relation equations introduced by sanchez in 1976 the solvability and the set of solutions of these bipolar equations have been studied in different scenarios depending on the considered number of variables and equations

a simple lemma on greedy approximation in hilbert space and convergence rates for projection pursuit regression and neural network training a general convergence criterion for certain iterative sequences in hilbert space is presented for an important subclass of these sequences estimates of the rate of convergence are given under very mild assumptions these results establish an 0 1 f4n nonsampling convergence rate for projection pursuit regression and neural network training where n represents the number of ridge functions neurons or coefficients in a greedy basis expansion

numerical solution of two dimensional nonlinear hammerstein fuzzy integral equations based on optimal fuzzy quadrature formula in this paper our aim is to provide an efficient iterative method of successive approximations to approximate solution of linear and nonlinear two dimensional hammerstein fuzzy integral equations by defining and developing an optimal quadrature formula for classes of two dimensional fuzzy number valued functions of lipschitz type after the introduction of the optimal formula we prove the convergence of the method of successive approximations used to approximate the solution of two dimensional hammerstein fuzzy integral equations and investigate the numerical stability of the presented method with respect to the choice of the first iteration finally some illustrative numerical experiments confirm the theoretical results and demonstrate the accuracy of the method

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

characterizing reducts in multi adjoint concept lattices abstract the construction of reducts that is minimal sets of attributes containing the main information of a database is a fundamental task in different frameworks such as in formal concept analysis fca and rough set theory rst this paper will be focused on a general fuzzy extension of fca called multi adjoint concept lattice and we present a study about the attributes generating meet irreducible elements and on the reducts in this framework from this study we introduce interesting results on the cardinality of reducts and the consequences in the classical case

minimization of error functionals over perceptron networks supervised learning of perceptron networks is investigated as an optimization problem it is shown that both the theoretical and the empirical error functionals achieve minima over sets of functions computable by networks with a given number n of perceptrons upper bounds on rates of convergence of these minima with n increasing are derived the bounds depend on a certain regularity of training data expressed in terms of variational norms of functions interpolating the data in the case of the empirical error and the regression function in the case of the expected error dependence of this type of regularity on dimensionality and on magnitudes of partial derivatives is investigated conditions on the data which guarantee that a good approximation of global minima of error functionals can be achieved using networks with a limited complexity are derived the conditions are in terms of oscillatory behavior of the data measured by the product of a function of the number of variables d which is decreasing exponentially fast and the maximum of the magnitudes of the squares of the l1 norms of the iterated partial derivatives of the order d of the regression function or some function which interpolates the sample of the data the results are illustrated by examples of data with small and high regularity constructed using boolean functions and the gaussian function

relating attribute reduction in formal object oriented and property oriented concept lattices attribute reduction is an important step in reducing computational complexity in order to extract information from relational systems three of these systems are the formal object oriented and property oriented concept lattices attribute reduction in the last two concept lattices has recently been studied the relation with the first concept lattice is very important since two important independent tools to extract information from databases the formal concept analysis and rough set theory will be related this paper studies attribute reduction in these three frameworks the main results are that the classification of each attribute into absolutely necessary relatively necessary and absolutely unnecessary attributes is independent of the framework considered and that an attribute reduct in one of these relational systems is also an attribute reduct in the others

attribute and size reduction mechanisms in multi adjoint concept lattices attribute reduction and size reduction in concept lattices are key research topics in formal concept analysis fca this paper combines both strategies in the multi adjoint concept lattice framework in order to simplify the information provided by the original context specifically we present three procedures which merge the attribute reduction and the size reduction by means of an irreducible cut concept lattice analyzing the obtained properties

reducing concept lattices by means of a weaker notion of congruence abstract attribute and size reductions are key issues in formal concept analysis in this paper we consider a special kind of equivalence relation to reduce concept lattices which will be called local congruence this equivalence relation is based on the notion of congruence on lattices with the goal of losing as less information as possible and being suitable for the reduction of concept lattices we analyze how the equivalence classes obtained from a local congruence can be ordered moreover different properties related to the algebraic structure of the whole set of local congruences are also presented finally a procedure to reduce concept lattices by the new weaker notion of congruence is introduced this procedure can be applied to the classical and fuzzy formal concept analysis frameworks

an aggregated fuzzy naive bayes data classifier in this study an aggregated fuzzy naive bayes classifier is proposed for decision making problems where both linguistic and numerical information are available in the solution process of such problems all attributes are considered as fuzzy numbers and a procedure based on 2 tuple fuzzy linguistic representation model is generated for combining them this procedure and subsequent fuzzy naive bayes classification are performed based on arithmetic operations defined by chen s function principle the proposed method was demonstrated on 2 well known examples from the literature in which both numerical and linguistic attributes were considered the results show that the proposed aggregated fuzzy naive bayes classifier is notably efficient in decision making where the attributes are in more realistic forms

rough set driven approach for attribute reduction in fuzzy formal concept analysis abstract the reduction of the set of attributes is an important preliminary challenge in order to obtain information from knowledge systems two remarkable formal tools for extracting such information are rough set theory rst and formal concept analysis fca as well as their fuzzy generalizations this work introduces a new method to reduce attributes in fuzzy fca considering the reduction philosophy given in rst and studies its main properties this method allows us to carry out a deeper study of the relation between these two theories moreover the proposed methodology has been compared with other existing reduction mechanisms

simultaneous approximations of polynomials and derivatives and their applications to neural networks we have constructed one hidden layer neural networks capable of approximating polynomials and their derivatives simultaneously generally optimizing neural network parameters to be trained at later steps of the bp training is more difficult than optimizing those to be trained at the first step taking into account this fact we suppressed the number of parameters of the former type we measure degree of approximation in both the uniform norm on compact sets and the lp norm on the whole space with respect to probability measures

attribute reduction in multi adjoint concept lattices knowledge reduction is one of the key issues in formal concept analysis and there have been many studies on this topic the irreducible elements in a lattice are also very important since they form the basic information of a relational system moreover they are also important from the viewpoint of attribute reduction both topics are notably more complicated in a fuzzy setting since not only the size of the sets of attributes and objects influence the size of the fuzzy concept lattice but the truth value sets where the sets of objects attributes and the relation are evaluated are important this paper presents in the general fuzzy framework of multi adjoint concept lattices a characterization of the meet irreducible elements from which a classification of attributes and its application to attribute reduction is introduced

dependence of computational models on input dimension tractability of approximation and optimization tasks the role of input dimension d is studied in approximating in various norms target sets of d variable functions using linear combinations of adjustable computational units results from the literature which emphasize the number n of terms in the linear combination are reformulated and in some cases improved with particular attention to dependence on d for worst case error upper bounds are given in the factorized form d n where is nonincreasing typically n n 1 2 target sets of functions are described for which the function is a polynomial some important cases are highlighted where decreases to zero as d for target functions extent e g the size of domains in rd where they are defined scale e g maximum norms of target functions and smoothness e g the order of square integrable partial derivatives may depend on d and the influence of such dimension dependent parameters on model complexity is considered results are applied to approximation and solution of optimization problems by neural networks with perceptron and gaussian radial computational units

on stability of fuzzy formal concepts over randomized one sided formal context abstract we propose a probabilistic approach to the issue of one sided fuzzy formal concepts stability the modified rice siff algorithm represents a crisp index how to select the relevant concepts from the set of all one sided fuzzy formal concepts we suggest to explore the formal concepts stability affected by the random fluctuation of values in a formal context we describe the algorithm and study the properties of the concept stability using random variables with the gaussian normal distribution in combination with the modified rice siff algorithm the gaussian probabilistic index improves the analysis of the most relevant one sided formal concepts from the original one sided formal context the connections to recent works in the related directions are presented