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

constructing symmetric boolean functions with maximum algebraic immunity symmetric boolean functions with even variables 2k and maximum algebraic immunity ai f k have been constructed in braeken s thesis 2006 in this paper we show more constructions of such boolean functions including the generalization of a result and prove a conjecture raised in braeken s thesis 2006

an efficient newton barrier method for minimizing a sum of euclidean norms a new newton barrier method is proposed for minimizing a sum of euclidean norms msn f x sum i 1 k a i t x b i 2 msn is a nonsmooth problem because f is not differentiable at any point x where any of the norms is zero the method used is based on approximating f with a smooth function which in the limit has the same optimal value as f msn is shown to have a dual problem with properties very similar to duality theory in linear programming this is used in the development of the method and to give a proof of when an optimal solution for the smooth approximation is epsilon optimal measured in the duality gap for the original problem an implementation of the algorithm is described for large sparse problems and numerical results are presented for problems with more than 270 000 nonlinear variables these problems arise from plastic collapse analysis

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

interpolation of fuzzy data analytical approach and overview we propose a general framework for the interpolation problem our framework stems from the classical elaboration of the problem we introduce the notion of an interpolating fuzzy function and show how this function can be characterized we examine and analyze previously published fuzzy interpolation algorithms to choose those algorithms that can be represented analytically we also propose an analytic solution of the interpolation problem that unifies various algorithmic approaches

constructions of balanced odd variable rotation symmetric boolean functions with optimal algebraic immunity and high nonlinearity abstract rotation symmetric boolean functions have been used as components of different cryptosystems in this paper two classes of balanced rotation symmetric boolean functions having optimal algebraic immunity on odd number of variables are constructed we give a lower bound on the algebraic degree of the first class of functions and prove that the n variable functions in the second class has optimal algebraic degree if n 2 m 1 for m 2 moreover it is shown that both classes of functions have much better nonlinearity than all the previously obtained rotation symmetric boolean functions with optimal algebraic immunity and have good behavior against fast algebraic attacks at least for small numbers of input variables

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

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

a note on reasoning conditions of ko czy s interpolative reasoning method abstract in this note we analyze continually the interpolative reasoning method by koczy and hirota and prove that the reasoning conditions given by the authors are also necessary conditions to guarantee the fuzzy inference consequence to be of triangular type if the fuzzy rules and an observation are defined by triangular type membership functions

two classes of symmetric boolean functions with optimum algebraic immunity construction and analysis this paper discusses two classes of symmetric boolean functions for each class a necessary and sufficient condition for having optimum algebraic immunity is proposed the algebraic degree and nonlinearity of the boolean functions are also completely determined and then we prove several of braeken s conjectures about the algebraic degree and nonlinearity of the boolean functions with optimum algebraic immunity in the two classes

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

on 2k variable symmetric boolean functions with maximum algebraic immunity k given a positive even integer n it is found that the weight distribution of any n variable symmetric boolean function with maximum algebraic immunity ai n 2 is determined by the binary expansion of n based on the foregoing all n variable symmetric boolean functions with maximum ai are constructed the amount is 2 wt n 1 2 log2n

on minimizing the lengths of checking sequences a general model for constructing minimal length checking sequences employing a distinguishing sequence is proposed the model is based on characteristics of checking sequences and a set of state recognition sequences some existing methods are shown to be special cases of the proposed model and are proven to construct checking sequences the minimality of the resulting checking sequences is discussed and a heuristic algorithm for the construction of minimal length checking sequences is given

test generation for multiple state table faults in finite state machines a test generation procedure to detect multiple state table faults in finite state machines is proposed the importance of multiple state table faults and their advantages as test generation objectives to avoid the need for checking experiments are considered the proposed procedure is based on a new method for implicit enumeration of large numbers of multiple faults by using incompletely specified faulty machines experimental results are presented to demonstrate the effectiveness of implicit fault enumeration in detecting large numbers of multiple faults and in guaranteeing detection of all the faults or all the faults up to a specific multiplicity

optimal hedge algebras based controller design and application in previous papers we introduced a new reasoning method based on quantifying linguistic domains established a new fuzzy control algorithm called hedge algebras based controller hac and applied it to solve some fuzzy control problems the hac does not require fuzzy sets to provide the semantics of the linguistic terms used in the fuzzy rule system rather the semantics is obtained through the semantically quantifying mappings sqms it was shown that the new method is very effective i e for these problems it is always able to efficiently control the process toward the stable state in the algebraic approach the design of an hac leads to the determination of the parameters of sqms which are the fuzziness measure of primary terms and linguistic hedges occurring in the fuzzy model and the weights of a weighted averaging operator however there exists another problem namely how one can determine the optimal parameters of the method in the present paper we improved the hac s design by adding an optimal step that aims to find the optimal parameters of hac using a genetic algorithm ga to show the effectiveness of the proposed method we apply it to solve again the inverted pendulum problem and the problem of holding an object on a hill the results demonstrate the good performance of the designed hac

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

an efficient primal dual interior point method for minimizing a sum of euclidean norms the problem of minimizing a sum of euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature this nonsmooth optimization problem arises in many different kinds of modern scientific applications we derive a primal dual interior point algorithm for the problem by applying newton s method directly to a system of nonlinear equations characterizing primal and dual feasibility and a perturbed complementarity condition the main work at each step consists of solving a system of linear equations the schur complement equations this schur complement matrix is not symmetric unlike in linear programming we incorporate a mehrotra type predictor corrector scheme and present some experimental results comparing several variations of the algorithm including as one option explicit symmetrization of the schur complement with a skew corrector term we also present results obtained from a code implemented to solve large sparse problems using a symmetrized schur complement this has been applied to problems arising in plastic collapse analysis with hundreds of thousands of variables and millions of nonzeros in the constraint matrix the algorithm typically finds accurate solutions in less than 50 iterations and determines physically meaningful solutions previously unobtainable

a quadratically convergent method for minimizing a sum of euclidean norms we consider the problem of minimizing a sum of euclidean norms f x sum nolimits i 1 m r i x here the residuals r i x are affine functions fromr n tor 1 n 1 2 m 2 this arises in a number of applications including single and multi facility location problems the functionf is in general not differentiable atx if at least oner i x is zero

computing the shortest network under a fixed topology we show that in any given uniform orientation metric plane the shortest network interconnecting a given set of points under a fixed topology can be computed by solving a linear programming problem whose size is bounded by a polynomial in the number of terminals and the number of legal orientations when the given topology is restricted to a steiner topology our result implies that the steiner minimum tree under a given steiner topology can be computed in polynomial time in any given uniform orientation metric with spl lambda legal orientations for any fixed integer spl lambda spl ges 2 this settles an open problem posed by brazil thomas and weng 2000

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

on the convergence of a hyperboloid approximation procedure for the perturbed euclidean multifacility location problem for the euclidean single facility location problem e weiszfeld proposed a simple closed form iterative algorithm in 1937 later numerous authors proved that it is a convergent descent algorithm in 1973 j eyster j white and w wierwille extended weiszfeld s idea and proposed a hyperboloid approximation procedure hap for solving the euclidean multifacility location problem they believed based on considerable computational experience that the hap always converges in 1977 ostresh proved that the hap is a descent algorithm under certain conditions in 1981 morris proved that a variant of the hap always converges however no convergence proof for the original hap has ever been given in this paper we prove that the hap is a descent algorithm and that it always converges to the minimizer of the objective function from any initial point

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

reasoning conditions on ko czy s interpolative reasoning method in sparse fuzzy rule bases abstract in our pre work the two sufficient and necessary conditions have been given on koczy s interpolative reasoning method in sparse fuzzy rule bases to guarantee that the reasoning consequence is of triangular type if the fuzzy rules and an observation are defined by triangular type membership functions however the two conditions are too strong to use the reasoning method on practical applications in this paper we analyze the properties of the reasoning method in detail and give several applicable sufficient conditions on it in order to make the reasoning consequence always a normal and convex fuzzy set

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 symmetric boolean functions with high algebraic immunity on even number of variables in this paper we put forward an efficient method to study the symmetric boolean functions with high algebraic immunity on even number of variables we obtain some powerful necessary conditions for symmetric boolean functions to achieve high algebraic immunity by studying the weight support of some specific types of boolean functions of low degrees with these results we prove that the algebraic immunity of a large class of symmetric correlation immune boolean functions namely the symmetric palindromic functions is not high besides we construct all symmetric boolean functions with maximum algebraic immunity and give a description for those with submaximum algebraic immunity we also determine the hamming weight degrees and nonlinearity of the symmetric boolean functions with maximum algebraic immunity

on some distance problems in fixed orientations in vlsi design technology requirements often dictate the use of only two orthogonal orientations determining both the shape of objects and the distance function the l 1 metric to be used for wiring objects more recent vlsi fabrication technology is capable of creating edges and wires in both the orthogonal and diagonal orientations we generalize the distance concept to the case where any fixed set of orientations is allowed and introduce a family of naturally induced metrics and the subsequent generalization of geometrical concepts a shortest connection between two points is in this case a path composed of line segments with only the given orientations we derive optimal solutions for various basic planar distance problems in this setting such as the computation of a voronoi diagram a minimum spanning tree and the minimum and maximum distance between two convex polygons many other theoretically interesting and practically relevant problems remain to be solved in particular the new famil

an efficient algorithm for minimizing a sum of euclidean norms with applications in recent years rich theories on polynomial time interior point algorithms have been developed these theories and algorithms can be applied to many nonlinear optimization problems to yield better complexity results for various applications in this paper the problem of minimizing a sum of euclidean norms is studied this problem is convex but not everywhere differentiable by transforming the problem into a standard convex programming problem in conic form we show that an epsilon optimal solution can be computed efficiently using interior point algorithms as applications to this problem polynomial time algorithms are derived for the euclidean single facility location problem the euclidean multifacility location problem and the shortest network under a given tree topology in particular by solving the newton equation in linear time using em gaussian elimination on leaves of a tree we present an algorithm which computes an epsilon optimal solution to the shortest network under a given full steiner topology interconnecting n regular points in o n sqrt n log bar c epsilon log n arithmetic operations where bar c is the largest pairwise distance among the given points the previous best known result on this problem is a graphical algorithm which requires o n2 arithmetic operations under certain conditions

a note on symmetric boolean functions with maximum algebraic immunity in odd number of variables in this note it is proved that for each odd positive integer n there are exactly two n variable symmetric boolean functions with maximum algebraic immunity

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

rough fuzzy rule interpolation abstract fuzzy rule interpolation forms an important approach for performing inference with systems comprising sparse rule bases even when a given observation has no overlap with the antecedent values of any existing rules fuzzy rule interpolation may still derive a useful conclusion unfortunately very little of the existing work on fuzzy rule interpolation can conjunctively handle more than one form of uncertainty in the rules or observations in particular the difficulty in defining the required precise valued membership functions for the fuzzy sets that are used in conventional fuzzy rule interpolation techniques significantly restricts their application in this paper a novel rough fuzzy approach is proposed in an attempt to address such difficulties the proposed approach allows the representation handling and utilisation of different levels of uncertainty in knowledge this allows transformation based fuzzy rule interpolation techniques to model and harness additional uncertain information in order to implement an effective fuzzy interpolative reasoning system final conclusions are derived by performing rough fuzzy interpolation over this representation the effectiveness of the approach is illustrated by a practical application to the prediction of diarrhoeal disease rates in remote villages it is further evaluated against a range of other benchmark case studies the experimental results confirm the efficacy of the proposed work

fuzzy interpolative reasoning based on ranking values of polygonal fuzzy sets and automatically generated weights of fuzzy rules in this paper we propose a new fuzzy interpolative reasoning method for sparse fuzzy rule based systems based on ranking values of polygonal fuzzy sets and automatically generated weights of fuzzy rules first the proposed method gets the characteristic points of the observation polygonal fuzzy sets and the characteristic points of the antecedent polygonal fuzzy sets of the fuzzy rules respectively by using the cut operations respectively where 0 1 then it calculates the ranking value of each observation polygonal fuzzy set and the ranking value of each antecedent polygonal fuzzy set respectively then it calculates the difference between the ranking value of each observation polygonal fuzzy set and the ranking value of each antecedent polygonal fuzzy set then it calculates the weight of each fuzzy rule based on the obtained differences between the ranking values of the observation polygonal fuzzy sets and the ranking values of the antecedent polygonal fuzzy sets then based on the obtained characteristic points of the observation polygonal fuzzy sets the obtained characteristic points of the antecedent polygonal fuzzy sets and the obtained weights of the fuzzy rules it gets the characteristic points of the fuzzy interpolative reasoning result represented by a polygonal fuzzy set the experimental results show that the proposed method can overcome the drawbacks of the existing methods for fuzzy interpolative reasoning in sparse fuzzy rule based systems

generalized adaptive fuzzy rule interpolation as a substantial extension to fuzzy rule interpolation that works based on two neighboring rules flanking an observation adaptive fuzzy rule interpolation is able to restore system consistency when contradictory results are reached during interpolation the approach first identifies the exhaustive sets of candidates with each candidate consisting of a set of interpolation procedures which may jointly be responsible for the system inconsistency then individual candidates are modified such that all contradictions are removed and thus interpolation consistency is restored it has been developed on the assumption that contradictions may only be resulted from the underlying interpolation mechanism and that all the identified candidates are not distinguishable in terms of their likelihood to be the real culprit however this assumption may not hold for real world situations this paper therefore further develops the adaptive method by taking into account observations rules and interpolation procedures all as diagnosable and modifiable system components in addition given the common practice in fuzzy systems that observations and rules are often associated with certainty degrees the identified candidates are ranked by examining the certainty degrees of its components and their derivatives from this the candidate modification is carried out based on such ranking this study significantly improves the efficacy of the existing adaptive system by exploiting more information during both the diagnosis and modification processes

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

an efficient algorithm for minimizing a sum of p norms we study the problem of minimizing a sum of p norms where p is a fixed real number in the interval 1 infty several practical algorithms have been proposed to solve this problem however none of them has a known polynomial time complexity in this paper we transform the problem into standard conic form unlike those in most convex optimization problems the cone for the p norm problem is not self dual unless p 2 nevertheless we are able to construct two logarithmically homogeneous self concordant barrier functions for this problem the barrier parameter of the first barrier function does not depend on p the barrier parameter of the second barrier function increases with p using both barrier functions we present a primal dual potential reduction algorithm to compute an epsilon optimal solution in polynomial time that is independent of p computational experiences with a matlab implementation are also reported

weighted fuzzy interpolative reasoning based on weighted increment transformation and weighted ratio transformation techniques in this paper we present a new weighted fuzzy interpolative reasoning method for sparse fuzzy rule based systems the proposed method uses weighted increment transformation and weighted ratio transformation techniques to handle weighted fuzzy interpolative reasoning in sparse fuzzy rule based systems it allows each variable that appears in the antecedent parts of fuzzy rules to associate with a weight between zero and one moreover we also propose an algorithm that automatically tunes the optimal weights of the antecedent variables appearing in the antecedent parts of fuzzy rules we also apply the proposed weighted fuzzy interpolative reasoning method to handle the truck backer upper control problem the proposed weighted fuzzy interpolative reasoning method performs better than the ones obtained by the traditional fuzzy inference system 2000 huang and shen s method 2008 and chen and ko s method 2008 the proposed method provides us with a useful way to deal with weighted fuzzy interpolative reasoning in sparse fuzzy rule based systems

comparison of fuzzy reasoning methods l a zadeh e h mamdani and m mizumoto et al have proposed methods for fuzzy reasoning in which the antecedent involves a fuzzy conditional proposition if x is a then y is b with a and b being fuzzy concepts mizumoto et al have investigated the properties of their methods in the case of generalized modus ponens this paper deals with the properties of their methods in the case of generalized modus tollens and investigates the other new fuzzy reasoning methods obtained by introducing the implication rules of many valued logic systems finally the properties of syllogism and contrapositive are investigated under each fuzzy reasoning method

fast algebraic attacks and decomposition of symmetric boolean functions in this correspondence first we give a decomposition of symmetric boolean functions then we show that almost all symmetric boolean functions including these functions with good algebraic immunity behave badly against fast algebraic attacks besides we improve the relations between algebraic degree and algebraic immunity of symmetric boolean functions

testing finite state machines state identification and verification we study the complexity of two fundamental problems in the testing of finite state machines 1 distinguishing sequences state identification we show that it is pspace complete to determine whether a finite state machine has a preset distinguishing sequence there are machines that have distinguishing sequences but only of exponential length we give a polynomial time algorithm that determines whether a finite state machine has an adaptive distinguishing sequence the previous classical algorithms take exponential time furthermore if there is an adaptive distinguishing sequence then we give an efficient algorithm that constructs such a sequence of length at most n n spl minus 1 2 which is the best possible where n is the number of states 2 unique input output sequences state verification it is pspace complete to determine whether a state of a machine has a unique input output sequence there are machines whose states have unique input output sequences but only of exponential length

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

algebraic immunity for cryptographically significant boolean functions analysis and construction recently algebraic attacks have received a lot of attention in the cryptographic literature it has been observed that a boolean function f used as a cryptographic primitive and interpreted as a multivariate polynomial over f sub 2 should not have low degree multiples obtained by multiplication with low degree nonzero functions in this paper we show that a boolean function having low nonlinearity is also weak against algebraic attacks and we extend this result to higher order nonlinearities next we present enumeration results on linearly independent annihilators we also study certain classes of highly nonlinear resilient boolean functions for their algebraic immunity we identify that functions having low degree subfunctions are weak in terms of algebraic immunity and we analyze some existing constructions from this viewpoint further we present a construction method to generate boolean functions on n variables with highest possible algebraic immunity spl lceil n 2 spl rceil this construction first presented at the 2005 workshop on fast software encryption fse 2005 has been the first one producing such functions these functions are obtained through a doubly indexed recursive relation we calculate their hamming weights and deduce their nonlinearities we show that they have very high algebraic degrees we express them as the sums of two functions which can be obtained from simple symmetric functions by a transformation which can be implemented with an algorithm whose complexity is linear in the number of variables we deduce a very fast way of computing the output to these functions given their input

adaptive fuzzy interpolation based on ranking values of polygonal fuzzy sets and similarity measures between polygonal fuzzy sets after the fuzzy interpolative reasoning processes if two unequal fuzzy interpolative reasoning results are derived or one derived and another observed for a consequence variable of a fuzzy rule then it is called a contradiction in the fuzzy interpolative reasoning process in recent years some adaptive fuzzy interpolation methods for sparse fuzzy rule based systems have been presented to solve contradictions after fuzzy interpolative reasoning processes in this paper a new adaptive fuzzy interpolation method is proposed for sparse fuzzy rule based systems based on ranking values and similarity measures of polygonal fuzzy sets which can solve contradictions occurred in fuzzy interpolative reasoning processes we also apply the proposed adaptive fuzzy interpolation method to predict the diarrheal disease rates in roadless villages the diarrheal disease prediction problem focuses on the issue to measure how the construction of a new road or railway in a previously roadless area may affect the epidemiology of infectious diseases in northern coastal ecuador the experimental results show that the proposed adaptive fuzzy interpolation method can overcome the drawbacks of the existing methods

comment on computing the shortest network under a fixed topology a linear programming formulation was given for the problem of computing a shortest network under a fixed topology under the lambda metric we point out a nontrivial error in this paper and give a correct and simpler linear programming formulation we also show that the result can be generalized to any distance function given by a minkowski unit circle that is a centrally symmetric polygon