multiple objective programming problems with possibilistic coefficients abstract we consider the problem of incorporating possibilistic data into a multiple objective linear programming framework a solution concept that is attractive from the standpoints of feasibility and efficiency is specified a necessary and sufficient condition for such a solution is established and ways to single out some satisfying alternative in this context are described a numerical example is also included for the sake of illustration throughout the paper we indicate topics for further research

branch and price algorithm for fuzzy integer programming problems with block angular structure this paper deals with fuzzy integer linear programming problems with block angular structure in which the fuzzy constraints are simplified by using possibility and necessity relations this main fuzzy problem is efficiently decomposed and is solved by a branch and price algorithm in the nodes of the branch and price tree the linear relaxation of the problem is solved by applying a column generation method also the relationship between the optimal solutions of this problem under possibility and necessity relations is derived to show the validation of the proposed algorithm some results are proved in addition the application of this algorithm is illustrated on fuzzy multicommodity flow problem for this case a new branching scheme is proposed to preserve the network structure of the subproblems which are produced in the column generation method some examples are solved and their results are compared with the previous works also the results of the proposed algorithm are reported on some large scale benchmark instances

satisficing solutions and duality in interval and fuzzy linear programming in this paper we introduce a class of fuzzy linear programming problems and define the concepts of feasible and satisficing solutions the necessary tools for dealing with such problems in this way we show that the class of crisp classical lp problems can be embedded into the class of flp ones moreover for flp problems we define the concept of duality and prove the weak and strong duality theorems further we define a class of interval linear programming problems as a special subclass of flp problems and apply the previous results to this special case

new exact traveling wave solutions for the modified form of degasperis procesi equation abstract with the aid of symbolic computation a generalized auxiliary equation method is proposed to construct more general exact solutions to some types of nlpdes in this letter using the auxiliary equation method some new solitary and traveling wave solutions of such nonlinear mdp equations given by u t u xxt 4 u 2 u x 3 u x u xx uu xxx are obtained in a very general form several interesting special cases of these general solutions are also discussed

on a special type of solutions of arbitrary higher spin dirac operators in this paper an explicit expression is determined for the elliptic higher spin dirac operator acting on functions f x taking values in an arbitrary irreducible finite dimensional module for the group spin m characterized by a half integer highest weight also a special class of solutions of these operators is constructed and the connection between these solutions and transvector algebras is explained

linear programming with a possibilistic objective function abstract this paper proposes some ways for dealing with a linear program when the coefficients of the objective function are subject to possibilistic imprecision i e they are characterized by fuzzy restrictions emphasis is placed upon a passive approach that yields a satisfying solution via an appropriate semi infinite program and an active one that allows to reach a solution with a high possibility level of optimality extensions to the possibilistic constraints case and to the case of multiple objective programming problems with possibilistic coefficients are also hinted we end up with some concluding remarks and indicate axes for further developments

multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system compared with most of the existing tanh methods the jacobi elliptic function method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters the solutions obtained in this paper include a kink shaped and bell shaped soliton solutions b rational solutions c triangular periodic solutions and d jacobi and weierstrass doubly periodic wave solutions among them the jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition the efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper kdv mkdv ito s fifth mkdv hirota nizhnik novikov veselov broer kaup generalized coupled hirota satsuma coupled schrodinger kdv 2 1 dimensional dispersive long wave 2 1 dimensional davey stewartson equations in addition as an illustrative sample the properties of the soliton solutions and jacobi doubly periodic solutions for the hirota equation are shown by some figures the links among our proposed method the tanh method extended tanh method and the jacobi elliptic function method are clarified generally

new solitary wave solutions to the modified forms of degasperis procesi and camassa holm equations abstract in this work we establish new solitary wave solutions to the modified forms of degasperis procesi and camassa holm equations unlike the standard degasperis procesi and camassa holm equations where multi peakon solutions arise the modified forms cause a change in the characteristic of these solutions and change it to bell shaped solitons periodic and complex solutions the extended tanh method the rational hyperbolic functions method and the rational exponential functions method are employed to reveal these new solutions

new exact solutions for mch and mdp equations by auxiliary equation method abstract with the aid of symbolic computation auxiliary equation method is introduced to investigate modified forms of camassa holm and degasperis procesi equations a series of new exact traveling wave solutions including smooth solitary wave solution peakons singular solution periodic wave solution jacobi elliptic solution are obtained in general form these new exact solutions will enrich previous results and help us further understand the physical structures of these two nonlinear equations

construction of conformally invariant higher spin operators using transvector algebras this paper deals with a systematic construction of higher spin operators defined as conformally invariant differential operators acting on functions on flat space rm with values in an arbitrary half integer irreducible representation for the spin group to be more precise the higher spin version of the dirac operator and associated twistor operators will be constructed as generators of a transvector algebra hereby generalising the well known fact that the classical dirac operator on rm and its symbol generate the orthosymplectic lie superalgebra osp 1 2 to do so we will use the extremal projection operator and its relation to transvector algebras in the second part of the article the conformal invariance of the constructed higher spin operators will be proven explicitly

relationships between modality constrained programming problems and various fuzzy mathematical programming problems abstract in this paper we focus on the relationships between modality constrained programming problems and various fuzzy mathematical programming problems i e flexible programming problem fuzzy goal programming problem and fuzzy mathematical programming problems proposed by orlovski tanaka et al inuiguchi et al dubois and sakawa et al fuzzy mathematical programming problems discussed in this paper can be interpreted in the framework of modality constrained programming problems thus modality constrained programming problems can be regarded as a base model for unifying various fuzzy mathematical programming problems

a dual approach to solve the fuzzy linear programming problem abstract a concept of fuzzy objective based on the fuzzification principle is presented in accordance with this concept the fuzzy linear mathematical programming problem is easily solved a relationship of duality among fuzzy constraints and fuzzy objectives is given the dual problem of a fuzzy linear programming problem is also defined

duality in fuzzy linear programming with possibility and necessity relations a class of fuzzy linear programming flp problems with fuzzy coefficients based on fuzzy relations is introduced the concepts of feasible and a b maximal and minimal solutions are defined the class of crisp classical lp problems can be embedded into the class of flp ones moreover for flp problems a new concept of duality is introduced and the weak and strong duality theorems are derived the introduced concepts and results are illustrated and discussed on a simple numerical example

remarks on classical invariant theory a uniform formulation applying to all classical groups simultaneously of the first fundamental theory of classical invariant theory is given in terms of the weyl algebra the formulation also allows skew symmetric as well as symmetric variables examples illustrate the scope of this formulation

the higher spin laplace operator in several vector variables in this paper an explicit expression is obtained for the conformally invariant higher spin laplace operator which acts on functions taking values in an arbitrary finite dimensional irreducible representation for the orthogonal group with integer valued highest weight once an explicit expression is obtained a special kind of polynomial solutions of this operator is determined

ranking function based solutions of fully fuzzified minimal cost flow problem the aim of minimal cost flow problem mcfp is to find the least transportation cost of a single commodity through a capacitated network this paper presents a model to deal with one particular group of such problems in which the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers for easier reference hereafter we refer to this group of problems as fully fuzzified mcfp to represent our model hukuhara s difference and approximated multiplication are used thereafter we sort fuzzy numbers by an order using a ranking function and show that it is a total order i e a reflexive anti symmetric transitive and complete binary relation utilizing the proposed ranking function we transform the fully fuzzified mcfp into three crisp problems solvable in polynomial time from this standpoint combinatorial algorithms are provided to solve the above mentioned problem and find the fuzzy optimal flow furthermore the proposed order is related to the importance weights of the center the left spread and the right spread of each fuzzy number thus this method is capable of handling the decision maker s risk taking by comparing some previous ranking function based works with our method the efficiency of the latter is revealed finally an application of our proposed method to petroleum industry is presented

stability of vector optimization problems with fuzzy weights in the objective functions and fuzzy matrix parameters in the constraints the aim of this paper is to investigate the stability of multiobjective nonlinear programming problems with fuzzy weights in the objective functions and fuzzy matrix parameters in the constraints and represent in addition the related dual problems for which the set of feasible parameters and the solvability set are studied these fuzzy weights and fuzzy matrix parameters are characterized by fuzzy numbers the existing results concerning the basic notions parametric space in convex programs are redefined and analyzed qualitatively under the concept of a pareto optimality an illustrative example is given to clarify the obtained results

bector chandra type duality in fuzzy linear programming with exponential membership functions in this paper we study a pair of fuzzy primal dual linear programming problems and calculate duality results using an aspiration level approach we use an exponential membership function which is in contrast to the earlier works that relied on a linear membership function as the fuzzy environment causes a duality gap we investigate how choosing the exponential membership function impacts this gap this issue is particularly important for fuzzy linear programming where in general the primal and dual objective values may not be bounded

on casimir s ghost we define on the universal enveloping superalgebra of a nonstandard adjoint action endowing it with a module structure this allows in particular to construct a bosonic operator which anticommutes with all the fermionic generators and which appears to be the square root of a certain casimir operator

a note on exact travelling wave solutions for the modified camassa holm and degasperis procesi equations abstract exact solutions for the modified camassa holm and degasperis procesi equations by liu et al 2010 y f liu x y zhu j x he factorization technique and new exact solutions for the modified camassa holm and degasperis procesi equations appl math comput 217 2010 1658 1665 are investigated liu et al has used the factorization technique to reduce the modified camassa holm and degasperis procesi equations to first order ordinary differential equations and then derived some exact travelling wave solutions by direct integral method in this note we will explain that the implementation of the so called factorization technique is completely unnecessary moreover based on the method of complete discrimination system for polynomial we shall demonstrate that the general explicit exact solution and its classification for the above two types of equations can be obtained directly and many exact solutions by liu et al are our special cases besides some known results in previously relevant literatures are extended and some simple remarks are also made

fuzzy optimization an appraisal abstract this paper takes a general look at core ideas that make up the burgeoning body of fuzzy mathematical programming emphasizing the methodological view although fuzzy mathematical programming has enjoyed a rapidly increasing acceptance within the scientific community some technical hurdles exist to hinder a unanimity reasons for this as well as possible ways for improvement are also discussed

optimal solutions in optimization problem with objective function depending on fuzzy parameters in this paper we first introduce a broad class of fuzzy optimization problems with an objective function depending on fuzzy parameters fo problems and introduce the concept a maximal solutions of fo problems with respect to some fuzzy relation we derive a simple and natural sufficient condition for a feasible solution to be an a maximal solutions of fo problem later on we define possibly and necessarily a maximal solutions of fo problems and prove that any possibly or necessarily a maximal solution of fo problem is an a maximal solution with respect to the possibilistic fuzzy relation or necessity fuzzy relation respectively the introduced concepts and results are illustrated and discussed on two numerical examples

on starshaped fuzzy sets in this paper we firstly define some new types of fuzzy starshapedness discuss the relationships among the different types of fuzzy starshapedness and then present some basic properties of them finally we develop several important results on the shadows of starshaped fuzzy sets

the stability of solutions of vakhnenko s equation vakhnenko s equation has two families of travelling wave solutions the method of rowlands and infeld 1990 is used to investigate whether these solutions are stable to long wavelength perturbations of small amplitude the method predicts stability for both families of solutions some comments on the validity of the method are given

application of fuzzy minimum cost flow problems to network design under uncertainty this paper deals with fuzzy quantities and relations in multi objective minimum cost flow problem when t norms and t conorms are available the goal programming is applied to minimize the deviation among the multiple costs of fuzzy flows and the given targets when the fuzzy supplies and demands are satisfied to obtain the most optimistic and the most pessimistic satisficing solutions of this problem two polynomial time algorithms are introduced applying some network transformations to demonstrate the performance of this approach in actual substances network design under fuzziness is considered and an efficient scheme is proposed including genetic algorithm together with fuzzy minimum cost flow problem this scheme is applied on a pilot network for more description

on the fundamental solution for higher spin dirac operators abstract in this paper we will determine the fundamental solution for the higher spin dirac operator q which is a generalisation of the classical rarita schwinger operator to more complicated irreducible half integer representations for the spin group in m dimensions this will allow us to generalise the stokes theorem the cauchy pompeiu theorem and the cauchy integral formula which lie at the very heart of the function theory behind arbitrary elliptic higher spin operators

decomposition of the polynomial kernel of arbitrary higher spin dirac operators in a series of recent papers we have introduced higher spin dirac operators which are generalisations of the classical dirac operator whereas the latter acts on spinor valued functions the former acts on functions taking values in arbitrary irreducible half integer highest weight representations for the spin group in this paper we describe how the polynomial kernel spaces of such operators decompose in irreducible representations of the spin group we will hereby make use of results from representation theory

stable branching rules for classical symmetric pairs we approach the problem of obtaining branching rules from the point of view of dual reductive pairs specifically we obtain a stable branching rule for each of 10 classical families of symmetric pairs in each case the branching multiplicities are expressed in terms of littlewood richardson coefficients some of the formulas are classical and include for example littlewood s restriction rule as a special case

the solution and duality of imprecise network problems duality properties have been investigated by many researchers in the recent literature they are introduced in this paper for a fully fuzzified version of the minimal cost flow problem which is a basic model in network flow theory this model illustrates the least cost of the shipment of a commodity through a capacitated network in terms of the imprecisely known available supplies at certain nodes which should be transmitted to fulfil uncertain demands at other nodes first we review on the most valuable results on fuzzy duality concepts to facilitate the discussion of this paper by applying hukuhara s difference approximated and exact multiplication and wu s scalar production we exhibit the flow in network models then we use combinatorial algorithms on a reduced problem which is derived from fully fuzzified mcfp to acquire fuzzy optimal flows to give duality theorems we utilize a total order on fuzzy numbers due to the level of risk and realize optimality conditions for providing some efficient combinatorial algorithms finally we compare our results with the previous worthwhile works to demonstrate the efficiency and power of our scheme and the reasonability of our solutions in actual decision making problems

soft robust solutions to possibilistic optimization problems abstract this paper discusses a class of uncertain optimization problems in which unknown parameters are modeled by fuzzy intervals the membership functions of the fuzzy intervals are interpreted as possibility distributions for the values of the uncertain parameters it is shown how the known concepts of robustness and light robustness for the traditional interval uncertainty representation of the parameters can be generalized to choose solutions that optimize against plausible parameter realizations under the assumed model of uncertainty in the possibilistic setting furthermore these solutions can be computed efficiently for a wide class of problems in particular for linear programming problems with fuzzy parameters in constraints and objective function thus the problems under consideration are not much computationally harder than their deterministic counterparts in this paper a theoretical framework is presented and results of some computational tests are shown

traveling wave solutions of the degasperis procesi equation we classify all weak traveling wave solutions of the degasperis procesi equation in addition to smooth and peaked solutions the equation is shown to admit more exotic traveling waves such as cuspons stumpons and composite waves

higher symmetries of the laplacian we identify the symmetry algebra of the laplacian on euclidean space as an explicit quotient of the universal enveloping algebra of the lie algebra of conformal motions we construct analogues of these symmetries on a general conformal manifold

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

possible and necessary optimality tests in possibilistic linear programming problems in this paper two kinds of optimality concepts are introduced into fuzzy linear programming problems in order to discuss the rationality of an obtained solution one is possible optimality evaluating the possibility degree to which the solution is optimal the other the dual concept is necessary optimality evaluating the necessity degree to which the solution is optimal when possibility distributions are defined by closed intervals degrees of possible and necessary optimalities become binary necessary and sufficient conditions for possible and necessary optimalities are induced in this case extending the results methods of calculating the degrees of possible and necessary optimalities are proposed some numerical examples are given to demonstrate the proposed methods

fuzzy capital rationing model in this paper we study the fuzzification of weingartner s pure capital rationing model and its analysis we develop a primal dual pair based on t norm t conorm relation for the constraints and objective function for a fully fuzzified pure capital rationing problem except project selection variables we define the a interval under which the weak duality is proved we perform sensitivity analysis for a change in a budget level or in a cash flow level of a non basic as well as a basic variable we analyze the problem based on duality and complementary slackness results we illustrate the proposed model by computational analysis and interpret the results

new exact complex traveling wave solutions for 2 1 dimensional bkp equation by using some exact solutions of the auxiliary ordinary differential equation a direct algebraic method is obtained to construct the exact complex solutions for non linear partial differential equations the method is implemented for the 2 1 dimensional bkp equation new exact complex solutions are obtained

solutions for fuzzy matrix games in this paper we deal with two person zero sum games with fuzzy payoffs and fuzzy goals we have presented two models for studying two person zero sum matrix games with fuzzy payoffs and fuzzy goals we assume that each player has a fuzzy goal for each of the payoffs we obtained that the fuzzy relation approach and the max min solution are equivalent

some properties of extended fuzzy preference relations using modalities abstract a fuzzy preference relation is extended to six kinds of relations between fuzzy sets the properties of the six extended relations are investigated especially a sufficient condition for reducing the extended relations to four kinds is discussed when fuzzy sets are bounded and normal and some examples are given to illustrate it further a sufficient condition for the extended negative relations to coincide with the extended inverse relations is described