odd cycles embedding on folded hypercubes with conditional faulty edges let ff e be the set of ff e 4 and n is even under this assumption we show that every fault free edge of fq n lies on a fault free cycle of every odd length from n 1 to 2 n 1 in terms of the number of tolerant faulty edges and embedding odd cycles in fq n our result improves not only the result in xu and ma 2006 where ff e 0 but also the previous best result gotten by xu et al 2006 where ff e

fault tolerant cycles embedding in hypercubes with faulty edges let q n be an n dimensional hypercube with f e 5 in this paper we consider the faulty hypercube under the following two additional conditions 1 each vertex is incident to at least two fault free edges and 2 every 4 cycle does not have any pair of non adjacent vertices whose degrees are both two after removing the faulty edges we prove that there exists a fault free cycle of every even length from 4 to 2 n in q n our result improves the result by liu and wang 2014 in terms of the lengths of embedding cycles where under the same conditions a fault free hamiltonian cycle was constructed

robust fuzzy structural safety assessment using mathematical programming approach this paper presents a robust safety assessment for engineering structures involving fuzzy uncertainties uncertain applied loads and yielding capacities of structural elements are modelled as fuzzy variables with associated membership functions representing possibility distributions a new computation orientated methodology namely the level collapse assessment level ca approach is developed to provide structural safety profile by constructing membership function of the structural collapse load limit accommodating fuzzy uncertainties the proposed method firstly utilizes the level strategy to transform the fuzzy limit analysis into a series of interval limit analyses by implementing the concept of robust and optimistic optimizations a mathematical programming mp scheme is proposed to explicitly capture the upper and lower bounds of the collapse load limit at each sublevel subsequently the membership function of the collapse load limit is established by using the upper and lower bounds obtained from the series of sublevel calculations the proposed level mathematical programming scheme preserves the quality of sharpness of the bounds of collapse load limit at each sublevel which consequently provides a rigorous evaluation on the fuzzy profile of the safety of engineering structures against structural collapse numbers of numerical examples motivated by real world engineering applications have been investigated to illustrate the accuracy efficiency and applicability of the proposed method

two node disjoint paths in balanced hypercubes the balanced hypercube bhn proposed by wu and huang is a variation of the hypercube it has been proved that the balanced hypercube is a node transitive and bipartite graph assume that the nodes are divided into two bipartite node sets x and y u and x are two different nodes in x and v and y are two different nodes in y in this paper we prove that there exist two node disjoint paths p x y and r u v in bhn and v p x y v r u v v bhn where n 1 the hamiltonian laceability of bhn which was proved by xu et al is also obtained from the corollary of our result

probabilistic safety analysis of structures under hybrid uncertainty the probabilistic and the possibilistic methods of safety evaluation of structure under uncertain parameters have been developed independently when the structural system is defined with some of the input parameters as possibilistic and others are sufficient enough to model as probabilistic available literatures normally start with either probabilistic or possibilistic description of all the variables this may pose restriction on necessary flexibility to the designer at early stage of modelling of the structural system the primary objective of the present work is to critically examine various emerging methods of transformation of the possibilistic variables to equivalent probabilistic variables so that probabilistic safety evaluation approach becomes compatible with the nature and quality of the input data relying on the fundamental concept of equivalent transformations i e the entropy based transformation and the scaling of fuzzy membership function the reliability analysis is proposed in the framework of second moment format in doing so the bounds on the reliability indices based on the evidence theory are also obtained encompassing the first order reliability analysis for consistent comparison among alternative transformations finally the reliability computation under hybrid uncertainty is elucidated numerically with examples for comparative study on the suitability of the transformation alternatives

fuzzy based robust structural optimization robust optimization is conventionally defined as the collection of the possible problem solutions that can ensure acceptable performances and sufficient immunity against the effects of uncertain parameter variability methods proposed until now use a probabilistic way to model uncertainty and to quantify the final sensitivity in this work a fuzzy uncertainty modellization is adopted for structural engineering in particular to define solution performance scattering the fuzzy entropy is used as a global measure of variable dispersion the final formulation of the problem deals with two antithetical objective functions the fuzzy expected value of structural performance and its fuzzy entropy this fuzzy based approach in robust design is able to give a set of pareto optimal solutions in terms of structural efficiency and sensitivities regarding uncertainty and represents a suitable tool in supporting the decision maker finally different applications have been developed to demonstrate the applicability of the proposed method

direction specific gradient scaling for interactive multicriterion optimization using an abstract mass concept in the method of abstract forces for the direction finding or tradeoff cut subproblems of interactive multicriterion optimization it is necessary to scale criterion gradients previously an ad hoc analyst assisted but nevertheless effective scaling method was used this paper introduces a concept of abstract mass it is shown that the previous ad hoc scaling method may be considered an approximation to the present direction specific approach also the abstract mass approach provides a strengthening of the original newton s second law of motion analogy motivation for the method of abstract forces a method for automatic and direction specific scaling is proposed which depends on the solution of a continuous piecewise polynomial system of equations the method is illustrated on an example with three criterion functions in this example newton s method for solving simultaneous nonlinear systems converges to a solution more generally restart homotopy methods may be required

bipanconnectivity of balanced hypercubes the balanced hypercube proposed by wu and huang is a variant of the hypercube network in this paper paths of various lengths are embedded into balanced hypercubes a bipartite graph g is bipanconnected if for two arbitrary nodes x and y of g with distance d x y there exists a path of length l between x and y for every integer l with d x y l v g 1 and l d x y 0 mod 2 we prove that the n dimensional balanced hypercube bh n is bipanconnected for all n 1 this result is stronger than that obtained by xu et al which shows that the balanced hypercube is edge bipancyclic and hamiltonian laceable

a random fuzzy analysis of existing structures abstract two approaches are proposed to estimate the reliability of existing structures by considering both the randomness in some of the design parameters and the fuzzy imprecision in some other parameters representing the in place condition of the aged structures in the first approach the fuzzy imprecision is transformed into random uncertainty using the entropy concept and the reliability of existing structures is estimated using well established theories of probability in the second approach a hybrid approach in the random fuzzy domain is used to evaluate the reliability using an level concept the multiple fuzzy variables case is also considered both discrete and continuous fuzzy variables are considered the results obtained from the proposed approaches are compared with other techniques available in the literature whenever possible both methods are applied to civil structural engineering problems in this paper the results obtained are very encouraging and demonstrate the applicability and robustness of the algorithms

vertex pancyclicity of augmented cubes with maximal faulty edges abstract the n dimensional augmented cube denoted as aqn a variation of the hypercube possesses some properties superior to those of the hypercube in this paper we show that every vertex in aqn lies on a fault free cycle of every length from 4 to 2n even if there are up to 2n 3 link faults we also show that this result is optimal

fault free hamiltonian cycles in crossed cubes with conditional link faults the crossed cube which is a variation of the hypercube possesses some properties superior to the hypercube in this paper assuming that each node is incident with at least two fault free links we show that an n dimensional crossed cube contains a fault free hamiltonian cycle even if there are up to 2n 5 link faults the result is optimal with respect to the number of link faults tolerated we also verify that the assumption is practically meaningful by evaluating its occurrence probability which is very close to 1

conditional edge fault tolerant hamiltonicity of dual cubes the dual cube is an interconnection network for linking a large number of nodes with a low node degree it uses low dimensional hypercubes as building blocks and keeps the main desired properties of the hypercube a dual cube dc n has n 1 links per node where n is the degree of a cluster n cube and one more link is used for connecting to a node in another cluster in this paper assuming each node is incident with at least two fault free links we show a dual cube dc n contains a fault free hamiltonian cycle even if it has up to 2n 3 link faults the result is optimal with respect to the number of tolerant edge faults

a new approach to fuzzy finite element analysis in this paper a new finite element analysis method for fuzzy structure is proposed by using the information entropy concept according to this method the fuzzy variables can be transferred into random variables so that the fuzzy structure can be treated as random structure when the random variables transferred from fuzzy structure are small the perturbation finite element method can be used to obtain the mean values and the variances of the structural responses

pancyclicity and bipancyclicity of conditional faulty folded hypercubes a graph is said to be pancyclic if it contains cycles of every length from its girth to its order inclusive and a bipartite graph is said to be bipancyclic if it contains cycles of every even length from its girth to its order the pancyclicity or the bipancyclicity of a given network is an important factor in determining whether the network s topology can simulate rings of various lengths an n dimensional folded hypercube fq n is an attractive variant of an n dimensional hypercube q n that is obtained by establishing some extra edges between the vertices of q n fq n for any odd n is known to be bipartite in this paper we explore the pancyclicity and bipancyclicity of fq n for any fq n n 2 with at most 2n 3 faulty edges where each vertex is incident to at least two fault free edges we prove that there exists a fault free cycle of every even length from 4 to 2 n and when n 2 is even we prove there also exists a fault free cycle of every odd length from n 1 to 2 n 1 the result is optimal with respect to the number of faulty edges tolerated

fault tolerant path embedding in folded hypercubes with both node and edge faults the folded hypercube fq n is a well known variation of the hypercube structure fq n is superior to q n in many measurements such as diameter fault diameter connectivity and so on let email protected fq n resp email protected fq n denote the set of faulty nodes resp faulty edges in fq n in the case that all nodes in fq n are fault free it has been shown that fq n contains a fault free path of length 2 n 1 resp 2 n 2 between any two nodes of odd resp even distance if email protected fq n n 1 where n 1 is odd and fq n contains a fault free path of length 2 n 1 between any two nodes if email protected fq n n 2 where n 2 is even in this paper we extend the above result to obtain two further properties which consider both node and edge faults as follows 1 fq n contains a fault free path of length at least 2 n 2 email protected fq n 1 resp 2 n 2 email protected fq n 2 between any two fault free nodes of odd resp even distance if email protected fq n email protected fq n n 1 where n 1 is odd 2 fq n contains a fault free path of length at least 2 n 2 email protected fq n 1 between any two fault free nodes if email protected fq n email protected fq n n 2 where n 2 is even

dea based dimensionality reduction for classification problems satisfying strict non satiety assumption abstract this study shows how data envelopment analysis dea can be used to reduce vertical dimensionality of certain data mining databases the study illustrates basic concepts using a real world graduate admissions decision task it is well known that cost sensitive mixed integer programming mip problems are np complete this study shows that heuristic solutions for cost sensitive classification problems can be obtained by solving a simple goal programming problem by that reduces the vertical dimension of the original learning dataset using simulated datasets and a misclassification cost performance metric the performance of proposed goal programming heuristic is compared with the extended dea discriminant analysis mip approach the holdout sample results of our experiments shows that the proposed heuristic approach outperforms the extended dea discriminant analysis mip approach

fuzzy sets based interpretation of the safety factor abstract safety factor is a universally utilized concept in several branches of engineering on one hand most engineers as it were neglect uncertainty but on the other hand the allowable stress level was introduced long time ago as a ratio of the yield stress to the so called safety factor to provide the region for the safe utilization of the structure thus the uncertainty is introduced into practice by the back door this observation led to a considerable literature dedicated to the probabilistic interpretation of the safety factor the present paper deals with the novel aspect of elucidation of the concept of safety factor through the theory of fuzzy sets apparently for the first time in the literature the aim of the paper is to present the safety factor that is uniformly employed by engineers but in the new light the safety factor in the fuzzy setting is introduced the ideas are illustrated on two strength of material problems simple examples are chosen so as to allow for clearer illustration of ideas

the spanning laceability on the faulty bipartite hypercube like networks a w container c u v of a graph g is a set of w disjoint paths joining u to v a w container of g is a w container if it contains all the nodes of v g a bipartite graph g is w laceable if there exists a w container between any two nodes from different parts of g let n and k be any two positive integers with n 2 and k

matching preclusion for balanced hypercubes matching preclusion is a measure of robustness in the event of edge failure in interconnection networks the matching preclusion number of a graph g is the minimum number of edges whose deletion leaves the resulting graph without a perfect matching or an almost perfect matching and the conditional matching preclusion number of g is the minimum number of edges whose deletion leaves the resulting graph with no isolated vertices and without a perfect matching or an almost perfect matching in this paper we consider balanced hypercubes we obtain that an n dimension balanced hypercube bh n has the matching preclusion number 2n and mainly prove that for the balanced hypercube bh n each matching preclusion set of cardinality 2n is trivial and the conditional matching preclusion number of balanced hypercube is 4n 2 whenever n 2

various cycles embedding in faulty balanced hypercubes consider the balanced hypercube bh n with f e 2 n 3 faulty edges prove that every edge of bh n f e lies on fault free cycles of even lengths from 6 to 22n prove that the lower limit of the length 6 is sharp quite a lot of interconnection networks are served as the underlying topologies of large scale multiprocessor systems the hypercube is one of the most popular interconnection networks in this paper we consider the balanced hypercube which is a variant of the hypercube huang and wu showed that the balanced hypercube has better properties than hypercube with the same number of links and processors let f e be the set of faulty edges in an n dimensional balanced hypercube bh n where n 2 in this paper we consider bh n with f e 2 n 3 faulty edges and prove that every fault free edge lies on a fault free cycle of every even length from 6 to 2 2 n in bh n f e furthermore we prove that the lower limit of the length 6 is sharp by giving a counter example

a convergent interactive cutting plane algorithm for multiobjective optimization this paper presents an interactive cutting plane algorithm for determining a best compromise solution to a multiobjective optimization problem in situations with an implicitly defined utility function we derive cutting planes that are based on suitable pairwise trade offs between the objective functions as prescribed by the decision maker at each iterate generated by the algorithm the proposed algorithm requires no line searches and generates iterates that are all contained in the efficient frontier this feature facilitates the preference judgment of the decision maker and permits an analyst to terminate short of optimality with an efficient near optimal solution a convergence analysis establishes that any accumulation point generated by the algorithm is a best compromise solution we also conduct an error analysis to point out the effect of inconsistencies in trade off information provided by the decision maker the algorithm may be extended to situations involving nonconvex feasible regions as well as nonconcave for a max problem objective functions we offer remarks for such cases and describe an application to an urban runoff control design problem

fault tolerant hamiltonian connectivity of the wk recursive networks abstract many research on the wk recursive network has been published during the past several years due to its favorite properties in this paper we consider the fault tolerant hamiltonian connectivity of the wk recursive network we use k d t to denote the wk recursive network of level t each of which basic modules is a d vertex complete graph where d 1 and t 1 the fault tolerant hamiltonian connectivity h f g is defined to be the maximum integer k such that g is k fault tolerant hamiltonian connected if g is hamiltonian connected and is undefined otherwise in this paper we prove that h f k d t d 4 if d 4