a deletion contraction algorithm for the characteristic polynomial of a multigraph expression du polynome caracteristique d un multigraphe fini g en termes de polynomes caracteristiques des modifications locales de g application de la formule obtenue a l etude des plus grandes valeurs propres de certains graphes theta

how to make a decision the analytic hierarchy process abstract this paper serves as an introduction to the analytic hierarchy process a multicriteria decision making approach in which factors are arranged in a hierarchic structure the principles and the philosophy of the theory are summarized giving general background information of the type of measurement utilized its properties and applications

pictorial representations of fuzzy connectives part ii cases of compensatory operators and self dual operators abstract as the continuation of part i in which pictorial representations of t norms t conorms and averaging operators were made with the aid of a computer this paper discusses compensatory operators and proposes generalized compensatory operators which can be obtained from averaging operators self dual operators are discussed which can be defined by using t norms t conorms and averaging operators finally symmetric sums are reviewed which are also self dual operators the pictorial representations of these operators are also made

fuzzy potential solutions in multi criteria and multi constraint level linear programming problems abstract given a multi criteria and multi constraint level mc 2 linear programming problem we can use an mc 2 simplex method to find a set of potential solutions each potential solution optimizes the mc 2 problem under a certain range of decision parameters namely the criteria weight vector and the constraint level weight vector in this paper we extend the potential solution to a fuzzy potential solution for a given fuzzy mc 2 problem with a certain range of the decision parameters a membership function of the mc 2 problem is first constructed then for such a parameter range a fuzzy potential solution is determined in terms of the membership function and a primal potential basis based on the theoretical analysis we propose a heuristic algorithm to systematically and effectively locate all fuzzy potential solutions for all possible changes of the decision parameters a numerical example is used to illustrate the algorithm

an oriented hypergraphic approach to algebraic graph theory abstract an oriented hypergraph is a hypergraph where each vertex edge incidence is given a label of 1 or 1 we define the adjacency incidence and laplacian matrices of an oriented hypergraph and study each of them we extend several matrix results known for graphs and signed graphs to oriented hypergraphs new matrix results that are not direct generalizations are also presented finally we study a new family of matrices that contains walk information

fuzzy sets and decision analysis abstract this survey points out recent advances in multiple attribute decision making methods dealing with fuzzy or ill defined information fuzzy maut as well as fuzzy outranking methods are reviewed aggregation procedures choice problems and treatment of interactive attributes are covered trends in research and open problems are indicated

a characterization of oriented hypergraphic balance via signed weak walks abstract an oriented hypergraph is a hypergraph where each vertex edge incidence is given a label of 1 or 1 and each adjacency is signed the negative of the product of the incidences an oriented hypergraph is balanced if the product of the adjacencies in each circle is positive we provide a combinatorial interpretation for entries of k th power of the oriented hypergraphic laplacian via the number of signed weak walks of length k using closed weak walks we prove a new characterization of balance for oriented hypergraphs and matrices that generalizes harary s theorem for signed graphs

joins of hypergraphs and their spectra abstract here we represent a general hypergraph by a matrix and study its spectrum we extend the definition of equitable partition and joining operation for hypergraphs and use those to compute eigenvalues of different hypergraphs we derive the characteristics polynomial of a complete m uniform m partite hypergraph k n 1 n 2 n m m studying edge corona of hypergraphs we find the complete spectrum of s loose cycles c l s n m for m 2 s 1 and the characteristics polynomial of s loose paths p l s n m some of the eigenvalues of p l s n m are also derived moreover using vertex corona we show how to generate infinitely many pairs of non isomorphic co spectral hypergraphs

a connection between hadamard matrices oriented hypergraphs and signed graphs abstract matrices associated to oriented hypergraphs produce a connection between signed graphs and hadamard matrices the existence of a family of signed graphs that are switching equivalent to k n and whose adjacency matrices sum to the zero matrix is shown to be equivalent to the existence of a hadamard matrix this equivalent problem is used to make explicit signed graph constructions which specialize to known hadamard constructions

fuzzy multiple objective programming and compromise programming with pareto optimum abstract a fuzzy multiple objective decision making approach is proposed based on the desirable features of compromise programming and the fuzzy set theory the proposed two phase approach guarantees both nondominated and balanced solutions for solving both the crisp and the fuzzy multiple objective decision making problems furthermore it is shown that the original compromise programming does not guarantee nondominated solutions if the distance parameter is assumed to be infinite and the resulting programming problem s solution is not unique

balance 0 1 matrices bicoloring and total dual integrality a 0 1 matrixa is balanced if in every submatrix with two nonzero entries per row and column the sum of the entries is a multiple of four this definition was introduced by truemper 1978 and generalizes the notion of a balanced 0 1 matrix introduced by berge 1970 in this paper we extend a bicoloring theorem of berge 1970 and total dual integrality results of fulkerson hoffman and oppenheim 1974 to balanced 0 1 matrices

spectra of uniform hypergraphs abstract we present a spectral theory of uniform hypergraphs that closely parallels spectral graph theory a number of recent developments building upon classical work has led to a rich understanding of symmetric hyperdeterminants of hypermatrices a k a multidimensional arrays symmetric hyperdeterminants share many properties with determinants but the context of multilinear algebra is substantially more complicated than the linear algebra required to address spectral graph theory i e ordinary matrices nonetheless it is possible to define eigenvalues of a hypermatrix via its characteristic polynomial as well as variationally we apply this notion to the adjacency hypermatrix of a uniform hypergraph and prove a number of natural analogs of basic results in spectral graph theory open problems abound and we present a number of directions for further study

degenerate nonlinear parabolic boundary value problems for t 0 and x e q c r here q is a smooth bounded domain and the boundary condition could be either linear e g dirichlet neumann robin or periodic or nonlinear robin type i e on k2 j j e j u also the diffusion coefficient 4 is allowed to degenerate on the boundary i e 4 0 possibly on x2 we solve 1 using semigroup theory the idea is rather simple 1 can be written as an ordinary differential equation du dt au in a suitable banach space x which we take to be c a 11 ii the b oundary conditions are absorbed in the domain of definition of the operator a we show that a is m dissipative or essentially m dissipative which means the closure a of a is m dissipative and then apply the crandall liggett theorem 61 this theorem says that in this case a generates a contraction semigroup t t and iffe d a i e fis in the closure of the domain of a then t t fis the unique solution to the initial value problem

on the laplacian coefficients of signed graphs abstract let g be a signed graph where g is its underlying graph and its sign function defined on edges of g a signed graph the subgraph of is its signed tu subgraph if the signed graph induced by the vertices of consists of trees and or unbalanced unicyclic signed graphs let l d g a be the laplacian of in this paper we express the coefficient of the laplacian characteristic polynomial of based on the signed tu subgraphs of and establish the relation between the laplacian characteristic polynomial of a signed graph with adjacency characteristic polynomials of its signed line graph and signed subdivision graph as an application we identify the signed unicyclic graphs having extremal coefficients of the laplacian characteristic polynomial

a characterization of oriented hypergraphic laplacian and adjacency matrix coefficients abstract an oriented hypergraph is an oriented incidence structure that generalizes and unifies graph and hypergraph theoretic results by examining its locally signed graphic substructure in this paper we obtain a combinatorial characterization of the coefficients of the characteristic polynomials of oriented hypergraphic laplacian and adjacency matrices via a signed hypergraphic generalization of basic figures of graphs additionally we provide bounds on the determinant and permanent of the laplacian matrix characterize the oriented hypergraphs in which the upper bound is sharp and demonstrate that the lower bound is never achieved

an interactive fuzzy satisficing method for generalized multiobjective linear programming problems with fuzzy parameters abstract a new interactive fuzzy satisficing method for multiobjective linear programming problems with fuzzy parameters is proposed in general two types of fuzziness of human judgements should be incorporated in multiobjective programming problems one is the experts ambiguous understanding of the nature of the parameters in the problem formulation process and the other is the fuzzy goals of the decision maker for each of the objective functions in order to cope with both types of fuzziness multiobjective linear programming problems with fuzzy parameters which reflect the experts ambiguous understanding in the problem formulation are formulated and the concept of generalized multiobjective linear programming and m pareto optimality is introduced in our interactive fuzzy satisficing method the satisficing solution of the decision maker is derived efficiently from among m pareto optimal solutions on the basis of the proposed method an interactive computer program is written to implement man machine interactive procedures finally an illustrative numerical example for multiobjective linear programming problems with fuzzy parameters is demonstrated along with the corresponding computer outputs

fuzzy approaches to multicriteria de novo programs abstract multicriteria de novo programming is a promising tool for optimal system design however there exist no algorithms for solving a general multicriteria de novo program only special cases have been discussed this paper proposes a two step fuzzy approach based on the ideal and negative ideal solutions it is shown that this approach is very efficient and is applicable to the general multicriteria de novo programming the fuzzy version of this problem is also formulated and analyzed numerical examples are given to illustrate the approaches

spectral properties of complex unit gain graphs abstract a complex unit gain graph is a graph where each orientation of an edge is given a complex unit which is the inverse of the complex unit assigned to the opposite orientation we extend some fundamental concepts from spectral graph theory to complex unit gain graphs we define the adjacency incidence and laplacian matrices and study each of them the main results of the paper are eigenvalue bounds for the adjacency and laplacian matrices

singular nonlinear parabolic boundary value problems in one space dimension global existence and uniqueness are established for the mixed initial boundary problem for the nonlinear parabolic equation u t x u x 2u x2 0 x 1 t 0 where x 0 x 0 for 0 x 1 and 01 0 x 1 dx the boundary conditions can be either linear e g dirichlet neumann or periodic or nonlinear in which case they take the form 1 j u j t j ux j t for j 0 1 where j is a maximal monotone graph in r r containing the origin

using analytic hierarchy process and fuzzy set theory to rate and rank the disability abstract any discrimination against qualified disabled people in all employment practices is violating the americans with disabilities act ada and it must be prohibited assigning qualified disabled people to a proper job or making reasonable accommodations for disabled employees is not only ethical but also necessary for reducing the social economic burden therefore in order to place qualified disabled people in appropriate job positions a multidimensional assessment method should be developed for measuring and interpreting the disabled people s residual capabilities with respect to their strengths weaknesses and their compatibility to job requirements and work environments thus the primary purpose of this study is to discuss how to structure a hierarchy related to the problem of deriving an overall disability index odi for measuring the individual s disability the analytic hierarchy process along with the entropy theory and fuzzy set theory is applied for eliciting the weights among the attributes and aggregating the multiple attributes into a single measurement we believe that the resultant odi is meaningful and useful for both the evaluator who supervises a rehabilitation program and the human resource director who engages in a hiring process

signed k uniform hypergraphs and tensors abstract a signed k graph is a k graph with an incidence function on each vertex and its incident edge in this paper we extend some concepts of the adjacency and laplacian tensor from k graphs to signed k graphs based on the spectral properties of the real symmetric tensor we investigate the h spectrum of adjacency and laplacian tensors for signed k graphs finally the inverse perron value of any vertex is present some bounds for the inverse perron value are established in terms of some invariants including the number of vertices edges the degree sequence

combinatorial approach for computing the characteristic polynomial of a matrix the study of the spectrum of weighted di graphs has attracted recently much attention in the literature here we use the coates digraph as a main tool to extend in a combinatorial way some well known results from the spectral graph theory on computing the characteristic polynomial of graphs new results are related to weighted di graph and thus to any square matrix

spectra of cycle and path families of oriented hypergraphs abstract an oriented hypergraph is a hypergraph where each vertex edge incidence is given a label of either 1 or 1 this generalizes signed graphs to a hypergraph setting and simultaneously provides a natural definition for a signed adjacency which is used to define the adjacency and laplacian matrices many properties of these matrices are known but there are no nontrivial families of oriented hypergraphs with their spectrum determined in this paper we define and study hypergraph families that are analogous to cycles and paths in graphs and signed graphs the adjacency and laplacian eigenvalues for some of these families is determined