inference based sensitivity analysis for mixed integer linear programming a new method of sensitivity analysis for mixed integer linear programming milp is derived from the idea of inference duality the inference dual of an optimization problem asks how the optimal value can be deduced from the constraints in milp a deduction based on the resolution method oftheorem proving can be obtained from the branch and cut tree that solves the primal problem one can then investigate which perturbations ofthe problem leave this proof intact on this basis it is shown that in a minimization problem any perturbation that satisfies a certain system of linear inequalities will reduce the optimal value no more than a prespecified amount one can also give an upper bound on the increase in the optimal value that results from a given perturbation the method is illustrated on two realistic problems

a convergence theorem for arrays of l r fuzzy numbers the purpose of this paper is to provide a general law of large numbers for arrays of l r fuzzy numbers

allocation and scheduling of conditional task graphs we propose an original complete and efficient approach to the allocation and scheduling of conditional task graphs ctgs in ctgs nodes represent activities some of them are branches and are labeled with a condition arcs rooted in branch nodes are labeled with condition outcomes and a corresponding probability a task is executed at run time if the condition outcomes that label the arcs in the path to the task hold at schedule execution time this can be captured off line by adopting a stochastic model tasks need for their execution either unary or cumulative resources and some tasks can be executed on alternative resources the solution to the problem is a single assignment of a resource and of a start time to each task so that the allocation and schedule is feasible in each scenario and the expected value of a given objective function is optimized for this problem we need to extend traditional constraint based scheduling techniques in two directions i compute the probability of sets of scenarios in polynomial time in order to get the expected value of the objective function ii define conditional constraints that ensure feasibility in all scenarios we show the application of this framework on problems with objective functions depending either on the allocation of resources to tasks or on the scheduling part also we present the conditional extension to the timetable global constraint experimental results show the effectiveness of the approach on a set of benchmarks taken from the field of embedded system design comparing our solver with a scenario based solver proposed in the literature we show the advantages of our approach both in terms of execution time and solution quality

a convergence of geometric mean for t related fuzzy numbers we study a convergence of geometric mean for t related fuzzy numbers where t is an archimedian t norm in particular we show that the class of archimedian t norms can be characterized by the validity of a general convergence of geometric mean for sequences of l r fuzzy numbers

an lpcc approach to nonconvex quadratic programs filling a gap in nonconvex quadratic programming this paper shows that the global resolution of a feasible quadratic program qp which is not known a priori to be bounded or unbounded below can be accomplished in finite time by solving two linear programs with linear complementarity constraints i e lpccs specifically this task can be divided into two lpccs the first confirms whether the qp is bounded below on the feasible set and if not computes a feasible ray on which the qp is unbounded the second lpcc computes a globally optimal solution if it exists by identifying a stationary point that yields the best quadratic objective value in turn the global resolution of these lpccs can be accomplished by a parameter free mixed integer programming based finitely terminating algorithm developed recently by the authors which can be enhanced in this context by a new kind of valid cut derived from the second order conditions of the qp and by exploiting the special structure of the lpccs throughout our treatment makes no boundedness assumption of the qp this is a significant departure from much of the existing literature which consistently employs the boundedness of the feasible set as a blanket assumption the general theory is illustrated by 3 classes of indefinite problems qps with simple upper and lower bounds existence of optimal solutions is guaranteed same qps with an additional inequality constraint extending the case of simple bound constraints and nonnegatively constrained copositive qps no guarantee of the existence of an optimal solution we also present numerical results to support the special cuts obtained due to the qp connection

renewal reward processes with fuzzy rewards and their applications to t age replacement policies the application of fuzzy set theory to renewal reward processes is proposed in this paper the reward is modeled as a fuzzy random variable a theorem which presents the long run average fuzzy reward per unit time is stated a procedure to obtain the best t age replacement policy with fuzzy cost structure is developed the original problem is transformed into a nonlinear program in order to evaluate the membership of the long run average fuzzy cost per unit time

integer programming duality price functions and sensitivity analysis recently a duality theory for integer programming has been developed here we examine some of the economic implications of this theory in particular the necessity of using price functions in place of prices and the possibility of carrying out sensitivity analysis of optimal solutions in addition we consider the form of price functions that are generated by known algorithms for integer programming

law of large numbers for the possibilistic mean value abstract a law of large numbers for the possibilistic mean value of a variable in a possibility space is presented an example shows that the convergence in distribution under a definition involving the possibilistic mean value of the sample average to a variable with a certain distribution cannot be replaced in general by convergence either almost surely or in necessity even so the usual presentation of the law of large numbers as a statement that holds in necessity follows from this result

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

a branch and check algorithm for minimizing the weighted number of late jobs on a single machine with release dates in this paper we consider the scheduling problem of minimizing the weighted number of late jobs on a single machine 1 rj wjuj a branch and check algorithm is proposed where a relaxed integer programming formulation is solved by branch and bound and infeasible solutions are cut off using infeasibility cuts we suggest two ways to generate cuts first tightened no good cuts are derived using a modification of the algorithm by carlier 1982 ejor v 11 42 47 which was developed for the problem of minimizing maximum lateness on a single machine secondly we show how to create cuts by using constraint propagation the proposed algorithm is implemented in the mosel modelling and optimization language computational experiments on instances with up to 140 jobs are reported a comparison is presented with the exact approach of peridy at al 2003 ejor v 148 591 603

sensitivity theorems in integer linear programming we consider integer linear programming problems with a fixed coefficient matrix and varying objective function and right hand side vector among our results we show that for any optimal solution to a linear program max wx ax b the distance to the nearest optimal solution to the corresponding integer program is at most the dimension of the problem multiplied by the largest subdeterminant of the integral matrixa using this we strengthen several integer programming proximity results of blair and jeroslow graver and wolsey we also show that the chvatal rank of a polyhedron x ax b can be bounded above by a function of the matrixa independent of the vectorb a result which as blair observed is equivalent to blair and jeroslow s theorem that each integer programming value function is a gomory function

steepest descent method for solving fuzzy nonlinear equations in this paper we propose the numerical solution for a fuzzy nonlinear equation by steepest descent method the fuzzy quantities are presented in parametric form some numerical illustrations are given to show the efficiency of steepest descent method

single facility scheduling with multiple job classes abstract this paper considers a static single facility scheduling problem where jobs are divided into several mutually exclusive classes the jobs in a given class need not be processed together in addition to a known processing time for each job there is a switching time involved which depends on the class of the job immediately preceding a job a heuristic algorithm is proposed to find a minimum mean flow time schedule the effectiveness of the proposed heuristic algorithm is empirically evaluated and found to indicate that the solutions obtained from this heuristic algorithm are often close to optimal

some properties of fuzzy random renewal processes fuzzy random variable is a measure function from a probability space to a collection of fuzzy variables based on the fuzzy random theory this paper addresses some properties of fuzzy random renewal processes generated by a sequence of independent and identically distributed iid fuzzy random interarrival times the relationship between the expected value of the fuzzy random renewal variable and the distribution functions of the alpha pessimistic values and alpha optimistic values of the interarrival times is discussed furthermore the fuzzy random style of renewal equation is provided finally fuzzy random blackwell s renewal theorem and smith s key renewal theorem are also given

sensitivity analysis for branch and bound integer programming after an integer program is solved we may be interested in the effect of small changes in the right hand side or objective function coefficients without modifying the underlying branch and bound or cutting plane algorithm we show what additional data to collect during the solution of the original integer program to give useful bounds on the solution of the modified problem

the benders decomposition algorithm a literature review the benders decomposition algorithm has been successfully applied to a wide range of difficult optimization problems this paper presents a state of the art survey of this algorithm emphasizing its use in combinatorial optimization we discuss the classical algorithm the impact of the problem formulation on its convergence and the relationship to other decomposition methods we introduce a taxonomy of algorithmic enhancements and acceleration strategies based on the main components of the algorithm the taxonomy provides the framework to synthesize the literature and to identify shortcomings trends and potential research directions we also discuss the use of the benders decomposition to develop efficient meta heuristics describe the limitations of the classical algorithm and present extensions enabling its application to a broader range of problems

a note to the sum of fuzzy variables abstract we generalize the results of rao and rashed 1981 285 292 and the results of nahmias 1978 97 110 for the membership function of a finite sum of mutually unrelated fuzzy variables the main result is to give a necessary and sufficient condition to the following problem if x1 x2 xn are mutually unrelated fuzzy variables with common membership function and 1 2 n are real numbers satisfying i 0 for every i and i 1n i when does z ni 1 ixi have the same membership function

the law of large numbers for fuzzy variables under a general triangular norm extension principle this paper presents a law of large numbers for t noninteractive weakly noninteractive fuzzy variables when using a general t norm extension principle the result is that convergence to a crisp set is obtained for all archimediean t norm intersection operators this generalises a previous result of badard the result is proved by deriving it from a similar result for the law of large numbers for dependency bounds of sums of random variables dependency bounds are used when nothing is known of the joint distribution of two random variables apart from their marginals the bridge used to connect dependency bounds with fuzzy number operations is used to give a probabilistic interpretation of fuzzy number operations some numerical examples are presented and a new method of numerically calculating the sup t convolutions of fuzzy numbers is presented this new method generalises the well known result for the calculation of sup min convolutions in terms of the level sets of membership functions

an elementary survey of general duality theory in mathematical programming we survey some recent developments in duality theory with the idea of explaining and unifying certain basic duality results in both nonlinear and integer programming the idea of replacing dual variables prices by price functions suggested by everett and developed by gould is coupled with an appropriate dual problem with the consequence that many of the results resemble those used in linear programming the dual problem adopted has a traditional economic interpretation and dual feasibility then provides a simple alternative to concepts such as conjugate functions or subdifferentials used in the study of optimality in addition we attempt to make precise the relationship between primal dual and saddlepoint results in both the traditional lagrangean and the more general duality theories and to see the implications of passing from prices to price functions finally and perhaps surprisingly it appears that all the standard algorithms terminate by constructing primal and dual feasible solutions of equal value i e by satisfying generalised optimality conditions

convex subclass of harmonic starlike functions complex valued harmonic functions that are univalent and sense preserving in the unit disk u can be written in the form f h g where h and g are analytic in u we define and investigate a convex subclass of harmonic starlike functions of order a 0 a 1 we obtain coefficient conditions extreme points distortion bounds convolution conditions and convex combination for the above class of harmonic functions

global constraints for round robin tournament scheduling abstract in the presence of side constraints and optimization criteria round robin tournament problems are hard combinatorial problems commonly tackled with tree search and branch and bound optimization recent results indicate that constraint based tree search has crucial advantages over integer programming based tree search for this problem domain by exploiting global constraint propagation algorithms during search in this paper we analyze arc consistent propagation algorithms for the global constraints all different and one factor in the domain of round robin tournaments the best propagation algorithms allow us to compute all feasible perfectly mirrored pattern sets with minimal breaks for intermural tournaments of realistic size and to improve known lower bounds for intramural tournaments balanced with respect to carry over effects

on fuzzily measurable random variables abstract a fuzzy random variable is given as a measurable function transforming the sets of elementary events into the real line where is a fuzzy algebra and is a soft fuzzy algebra defined by means of the fuzzy relation less or equal 8 the main properties of a fuzzy random variable are proved the connections between a fuzzy random variable its distribution and its cumulative distribution are investigated too

the law of large numbers for fuzzy processes and the estimation problem abstract we study how the law of large numbers can be extended to the case of fuzzy numbers we work with l fuzzy sets where l is a cl commutative monoid with an operation we define the independence of fuzzy numbers we find when is the operation of the lattice that the arithmetical mean of independent fuzzy numbers does not converge we think that this case could be a limit one we show for particular cases of the operation that generally convergence holds we build estimators for fuzzy models we particularly consider the minimum fuzziness estimator we study the convergence of these estimators and compare them by way of the fuzzy subsets they induce we lastly study the case where we have dependent fuzzy numbers and particularly the case of linearly filtered autoindependent fuzzy processes

a simulated annealing and hill climbing algorithm for the traveling tournament problem abstract the traveling tournament problem ttp e easton g nemhauser m trick the traveling tournament problem description and benchmarks in proceedings of the 7th international conference on principles and practice of constraint programming cp 2001 2001 pp 580 584 m trick challenge traveling tournament problems 2004 schedules a double round robin tournament to minimize the total distance traveled by competing teams it involves issues of feasibility and optimality and is a challenge to constraint and integer programming in this work we divide the search space and use simulated annealing sa to search a timetable space and hill climbing to explore a team assignment space the sa component mutates timetables using conditional local jumps to find timetables which lead to better schedules while hill climbing is enhanced by pre computation and dynamic cost updating to provide fast and efficient search computational experiments using this hybrid approach on benchmark sets give results comparable to or better than current best known solutions

joint optimization of product family configuration and scaling design by stackelberg game abstract product family design is generally characterized by two types of approaches module based and scale based while the former aims to enable product variety based on module configuration the latter is to variegate product design by scaling up or down certain design parameters the prevailing practice is to treat module configuration and scaling design as separate decisions or aggregate two design problems as a single level all in one optimization problem in practice optimization of scaling variables is always enacted within a specific modular platform and meanwhile an optimal module configuration depends on how design parameters are to be scaled the key challenge is how to deal with explicitly the coupling of these two design optimization problems this paper formulates a stackelberg game theoretic model for joint optimization of product family configuration and scaling design in which a bilevel decision structure reveals coupled decision making between module configuration and parameter scaling a bilevel mixed 0 1 non linear programming model is developed and solved comprising an upper level optimization problem and a lower level optimization problem the upper level seeks for an optimal configuration of modules and module attributes by maximizing the shared surplus of an entire product family the lower level entails parametric optimization of attribute values for optimal technical performance of each individual module a case study of electric motors demonstrates that the bilevel joint optimization model excels in leveraging optimal scaling in conjunction with optimal module configuration which is advantageous over the existing paradigm of product family scaling design that cannot change the product family configuration

a theorem of renewal process for fuzzy random variables and its application the fuzzy set was introduced by zadeh 1965 and the concept of fuzzy random variables was provided by kwakernaak 1981 sequences of independent and identical distributed fuzzy random variables were considered by kruse 1982 he also showed the strong law of large numbers for fuzzy random variables in this paper we consider the stochastic process for fuzzy random variables and prove a theorem for fuzzy rate of a fuzzy renewal process

equivalent conditions for laws of large numbers for t related l r fuzzy numbers in this paper we give some necessary and sufficient conditions for laws of large numbers for sequence of mutually t related l r fuzzy numbers when t is an continuous archimedean t norm and diameter of support of the fuzzy numbers is not uniformly bounded we also consider some necessary and sufficient conditions for laws of large numbers for l r fuzzy random numbers and generalize earlier results of fuller fuzzy sets and systems 45 1992 299 303 triesch fuzzy sets and systems 58 1993 339 342 and hong and lee fuzzy sets and systems 121 2001 537 543

renewal process with t related fuzzy inter arrival times and fuzzy rewards in this paper we consider a renewal process in which the inter arrival times and rewards are characterized as fuzzy variables under t norm based fuzzy operations a t related fuzzy renewal theorem and a fuzzy renewal reward theorem are proved using a law of large numbers for fuzzy variables

harmonic functions starlike in the unit disk complex valued harmonic functions that are univalent and sense preserving in the unit disk can be written in the form f h where h and g are analytic in we give univalence criteria and sufficient coefficient conditions for normalized harmonic functions that are starlike of order 0 1 these coefficient conditions are also shown to be necessary when h has negative and g has positive coefficients these lead to extreme points and distortion bounds

logic based benders decomposition benders decomposition uses a strategy of learning from one s mistakes the aim of this paper is to extend this strategy to a much larger class of problems the key is to generalize the linear programming dual used in the classical method to an inference dual solution of the inference dual takes the form of a logical deduction that yields benders cuts the dual is therefore very different from other generalized duals that have been proposed the approach is illustrated by working out the details for propositional satisfiability and 0 1 programming problems computational tests are carried out for the latter but the most promising contribution of logic based benders may be to provide a framework for combining optimization and constraint programming methods

neighborhoods of a new class of harmonic multivalent functions abstract we introduce and investigate a new subclass of harmonic multivalent functions defined by using a differential operator we obtain coefficient conditions distortion bounds extreme points convex combination for the above class of harmonic multivalent functions we also derive inclusion relationships involving the neighborhoods of harmonic multivalent functions

minimal inequalities and subadditive duality in this note we use a duality theorem for mixed integer programs first explicitly stated by johnson 1973 for the one row group problem to characterize minimal inequalities this characterization extends earlier results which assumed either a rational or a bounded constraint set blair 1978 jeroslow 1979 johnson 1976 by relaxing these assumptions either entirely or almost so it also extends results given first by gomory and johnson 1969 for the group problem

fuzzy linear systems a general fuzzy linear system is investigated using the embedding approach conditions for the existence of a unique fuzzy solution to n n linear system are derived and a numerical procedure for calculating the solution is designed the applicability of the proposed model is illustrated with examples

injectivity of sections of univalent harmonic mappings abstract if s denotes the class of functions h z z n 2 a n z n which are analytic and univalent in the unit disk z 1 then the classical result of szego shows that every section s n h z k 1 n a k z k of h is univalent in z 1 4 exact largest radius of univalence r n of s n h remains an open problem although the corresponding results for sections of various geometric subclasses of s have been obtained which include those h s for which re h z 0 holds in the unit disk however no attempt has been made to derive harmonic analog of these results the central object in this case is the class s h 0 of sense preserving harmonic univalent mappings f h g defined on the unit disk normalized so that h 0 g 0 h 0 1 g 0 0 our primary objective in this paper is to solve the univalency of every section of a harmonic function in the class p h 0 where p h 0 denotes the class of normalized univalent harmonic mapping f h g in the unit disk z 1 satisfying the condition re h z g z for z 1 where g 0 0 and 0 1 in this paper we first present sharp bounds for the moduli of the coefficients a n b n of f p h 0 and then determine the value of r so that the partial sums of f p h 0 are close to convex in z r

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

scheduling double round robin tournaments with divisional play using constraint programming abstract we study a tournament format that extends a traditional double round robin format with divisional single round robin tournaments elitserien the top swedish handball league uses such a format for its league schedule we present a constraint programming model that characterizes the general double round robin plus divisional single round robin format this integrated model allows scheduling to be performed in a single step as opposed to common multistep approaches that decompose scheduling into smaller problems and possibly miss optimal solutions in addition to general constraints we introduce elitserien specific requirements for its tournament these general and league specific constraints allow us to identify implicit and symmetry breaking properties that reduce the time to solution from hours to seconds a scalability study of the number of teams shows that our approach is reasonably fast for even larger league sizes the experimental evaluation of the integrated approach takes considerably less computational effort to schedule elitserien than does the previous decomposed approach

harmonic univalent functions with negative coefficients we give sufficient coefficient conditions for normalized harmonic functions to map onto either starlike or convex regions these conditions are also shown to be necessary when the coefficients are negative this leads to distortion bounds and extreme points

fuzzy data analysis by possibilistic linear models abstract since fuzzy data can be regarded as distribution of possibility fuzzy data analysis by possibilistic linear models is proposed in this paper possibilistic linear systems are defined by the extension principle fuzzy parameter estimations are discussed in possibilistic linear systems and possibilistic linear models are employed for fuzzy data analysis with non fuzzy inputs and fuzzy outputs defined by fuzzy numbers the estimated possibilistic linear system can be obtained by solving a linear programming problem this approach can be regarded as fuzzy interval analysis

a multi round generalization of the traveling tournament problem and its application to japanese baseball abstract in a double round robin tournament involving n teams every team plays 2 n 1 games with one home game and one away game against each of the other n 1 teams given a symmetric n by n matrix representing the distances between each pair of home cities the traveling tournament problem ttp seeks to construct an optimal schedule that minimizes the sum total of distances traveled by the n teams as they move from city to city subject to several natural constraints to ensure balance and fairness in the ttp the number of rounds is set at r 2 in this paper we generalize the ttp to multiple rounds r 2 k for any k 1 and present an algorithm that converts the problem to finding the shortest path in a directed graph enabling us to apply dijkstra s algorithm to generate the optimal multi round schedule we apply our shortest path algorithm to optimize the league schedules for nippon professional baseball npb in japan where two leagues of n 6 teams play 40 sets of three intra league games over r 8 rounds our optimal schedules for the pacific and central leagues achieve a 25 reduction in total traveling distance compared to the 2010 npb schedule implying the potential for considerable savings in terms of time money and greenhouse gas emissions

characterisation of archimedian t norms and a law of large numbers abstract we study a law of large numbers for mutually t related fuzzy numbers where t is an archimedian t norm and extend earlier results of fuller in this area in particular we show that the class of archimedian t norms can be characterised by the validity of a very general law of large numbers for sequences of l r fuzzy numbers

a law of large numbers for fuzzy numbers abstract we study the problem if 1 2 are fuzzy numbers with modal values m1 m2 then what is the strongest t norm for which where mn m1 mn n the arithmetic mean 1 n n i is defined via sup t norm convolution and nes denotes necessity

a benders approach for the constrained minimum break problem this paper presents a hybrid ip cp algorithm for designing a double round robin schedule with a minimal number of breaks both mirrored and non mirrored schedules with and without place constraints are considered the algorithm uses benders cuts to obtain feasible home away pattern sets in few iterations and this approach leads to significant reductions in computation time for hard instances furthermore the algorithm is capable of solving a number of previously unsolved benchmark problems for the traveling tournament problem with constant distances

concepts of probabilistic sets abstract in the field of pattern recognition or decision making theory the important subjects are as follows 1 ambiguity of property of objects 2 variety of character of objects 3 subjectivity of observers 4 evolution of knowledge of observers i e learning considering these points the concept of probabilistic set is proposed it is based on both probability theory and fuzzy concepts a probabilistic set on a total space is defined by a point wise measurable function from a parameter space which is a probability space to a characteristic space which is a measurable space it is shown that the family of all probabilistic sets constitutes a complete pseudo boolean algebra moment analysis is possible by using a probability measure of the parameter space other useful concepts are also mentioned such as probabilistic mappings and expected cardinal numbers

combinatorial benders cuts for mixed integer linear programming mixed integer programs mips involving logical implications modeled through big m coefficients are notoriously among the hardest to solve in this paper we propose and analyze computationally an automatic problem reformulation of quite general applicability aimed at removing the model dependency on the big m coefficients our solution scheme defines a master integer linear problem ilp with no continuous variables which contains combinatorial information on the feasible integer variable combinations that can be distilled from the original mip model the master solutions are sent to a slave linear program lp which validates them and possibly returns combinatorial inequalities to be added to the current master ilp the inequalities are associated to minimal or irreducible infeasible subsystems of a certain linear system and can be separated efficiently in case the master solution is integer the overall solution mechanism closely resembles the benders one but the cuts we produce are purely co

the value function of an integer program we consider integer programs in which the objective function and constraint matrix are fixed while the right hand side varies the value function gives for each feasible right hand side the criterion value of the optimal solution we provide a precise characterization of the closed form expression for any value function

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

on the law of large numbers for mutually t related l r fuzzy numbers abstract we study a law of large numbers for sequences of mutually t related l r fuzzy numbers where t is an archimedean t norm and the diameter of the support of the fuzzy numbers is not uniformly bounded earlier results of fuller 1992 and triesch 1993 in this area are extended some conditions concerning the shapes of f r and f l and spreads of l r fuzzy numbers are given where f is the additive generator of the archimedean t norm t several examples are given to illustrate the results

connections between various subclasses of planar harmonic mappings involving hypergeometric functions the main purpose of this paper is to establish connections between various subclasses of harmonic mappings in the plane by applying certain convolution operators involving hypergeometric functions to be more precise we investigate such connections with harmonic k uniformly starlike and harmonic k uniformly convex mappings in the plane

combinatorial benders cuts for the strip packing problem we study the strip packing problem in which a set of two dimensional rectangular items has to be packed in a rectangular strip of fixed width and infinite height with the aim of minimizing the height used the problem is important because it models a large number of real world applications including cutting operations where stocks of materials such as paper or wood come in large rolls and have to be cut with minimum waste scheduling problems in which tasks require a contiguous subset of identical resources and container loading problems arising in the transportation of items that cannot be stacked one over the other the strip packing problem has been attacked in the literature with several heuristic and exact algorithms nevertheless benchmark instances of small size remain unsolved to proven optimality in this paper we propose a new exact method that solves a large number of the open benchmark instances within a limited computational effort our method is based on a benders decomposition in whi

a branching scheme for finding cost minimal round robin tournaments abstract single round robin tournaments are a well known class of sports leagues schedules we consider leagues with a set t of n teams where n is even costs are associated to each possible match the goal is to find the minimum cost tournament among those having the minimum number of breaks we pick up structural properties of home away pattern sets having the minimum number of breaks a branching idea using these properties is developed in order to guide branching steps on the first levels of a branch and bound tree in order to avoid nodes corresponding to infeasible subproblems

planning and scheduling by logic based benders decomposition we combine mixed integer linear programming milp and constraint programming cp to solve an important class of planning and scheduling problems tasks are allocated to facilities using milp and scheduled using cp and the two are linked via logic based benders decomposition tasks assigned to a facility may run in parallel subject to resource constraints cumulative scheduling we solve problems in which the objective is to minimize cost makespan or total tardiness we obtain significant computational speedups of several orders of magnitude for the first two objectives relative to the state of the art in both milp and cp we also obtain better solutions and bounds for problems than cannot be solved to optimality

the law of large numbers and renewal process for t related weighted fuzzy numbers on rp this paper considers the law of large numbers for t related weighted fuzzy variables whose underlying spaces are r p we provide new sufficient conditions that do not depend on the shape of fuzzy numbers and the additive generator of a t norm t for the law of large numbers for t related weighted fuzzy variables the results provide a far reaching generalization of previous findings on the law of large numbers for t related fuzzy numbers in addition we prove t related fuzzy renewal theorems in which the inter arrival time is characterized as weighted fuzzy numbers under t norm based fuzzy operations on r p by using the law of large numbers for weighted fuzzy variables on r p we also investigate the law of large numbers and the renewal process for t related fuzzy numbers on r p with respect to the credibility measure the chance measure and the expected value

needed an empirical science of algorithms deductive algorithmic science has reached a high level of sophistication but its worst case and average case results seldom tell us how well an algorithm is actually going to work in practice i argue that an empirical science of algorithms is a viable alternative i respond to misgivings about an empirical approach including the prevalent notion that only a deductive treatment can be theoretical or sophisticated np completeness theory for instance is interesting partly because it has significant if unacknowledged empirical content an empirical approach requires not only rigorous experimental design and analysis but also the invention of empirically based explanatory theories i give some examples of recent work that partially achieves this aim

parameter estimations of mutually t related fuzzy variables abstract cai fuzzy sets and systems 55 1993 179 185 discussed parameter estimation methods for normal fuzzy variables in nahmias sense in this paper we investigate more the parameter estimations of general t related not necessarily normal fuzzy variables

the strong law of large numbers for fuzzy random variables abstract sequences of independent and identically distributed fuzzy random variables are considered it is shown that the strong law of large numbers holds also for fuzzy random variables this result is used to give a consistent estimator for the expectation of a fuzzy random variable

blackwell s theorem for t related fuzzy variables in this paper we consider blackwell s theorem in which inter arrival times are characterized as fuzzy variables under t norm based fuzzy operations we first prove that blackwell s theorem for t related fuzzy variables with respect to necessity measure holds true where t is an archimedean t norm subsequently we provide a counter example under which blackwell s theorem does not hold when t min finally we evaluate the expected value of fuzzy variable with respect to credibility measure and derive fuzzy blackwell s theorem based on the expected value of fuzzy variables

the law of large numbers for fuzzy numbers with unbounded supports we study laws of large numbers for mutually t related fuzzy numbers with unbounded supports where t is an archimedean t norm and generalize earlier result of badard

a new branch and price algorithm for the traveling tournament problem abstract the traveling tournament problem ttp consists of finding a distance minimal double round robin tournament where the number of consecutive breaks is bounded for solving the problem exactly we propose a new branch and price approach the starting point is a new compact formulation for the ttp the corresponding extensive formulation resulting from a dantzig wolfe decomposition is identical to one given by easton k nemhauser g trick m 2003 solving the traveling tournament problem a combined interger programming and constraint programming approach in burke e de causmaecker p eds practice and theory of automated timetabling iv volume 2740 of lecture notes in computer science springer verlag berlin heidelberg pp 100 109 who suggest to solve the tour generation subproblem by constraint programming in contrast to their approach our method explicitly utilizes the network structure of the compact formulation first the column generation subproblem is a shortest path problem with additional resource and task elementarity constraints we show that this problem can be reformulated as an ordinary shortest path problem over an expanded network and thus be solved much faster an exact variable elimination procedure then allows the reduction of the expanded networks while still guaranteeing optimality second the compact formulation gives rise to supplemental branching rules which are needed since existing rules do not ensure integrality in all cases third non repeater constraints are added dynamically to the master problem only when violated the result is a fast exact algorithm which improves many lower bounds of knowingly hard ttp instances from the literature for some instances solutions are proven optimal for the first time

complexity of the traveling tournament problem we consider the complexity of the traveling tournament problem which is a well known benchmark problem in tournament timetabling the problem was supposed to be computationally hard ever since its proposal in 2001 recently the first np completeness proof has been given for the variant of the problem were no constraints on the number of consecutive home games or away games of a team are considered the complexity of the original traveling tournament problem including these constraints however is still open in this paper we show that this variant of the problem is strongly np complete when the upper bound on the maximal number of consecutive away games is set to 3

algebraic metric and probabilistic properties of convex combinations based on the t normed extension principle the strong law of large numbers consider the strong law of large numbers for t normed averages of fuzzy random variables in the uniform metric d that probabilistic property is known to hold when the t norm is the minimum and to fail when the t norm is the product we prove that it is characterized by an algebraic property of the t norm that of being eventually idempotent and by a metric property of the space of fuzzy sets that it becomes a convex combination space we show that the equivalence holds not only for euclidean or banach spaces but in the more general setting of convex combination spaces

generalized benders decomposition for one class of minlps with vector conic constraint in this paper we mainly study one class of mixed integer nonlinear programming problems minlps with vector conic constraint in banach spaces duality theory of convex vector optimization problems applied to this class of minlps is deeply investigated with the help of duality we use the generalized benders decomposition method to establish an algorithm for solving this minlp several convergence theorems on the algorithm are also presented the convergence theorems generalize and extend the existing results on minlps in finite dimensional spaces

general fuzzy linear systems we study the general mxn fuzzy linear system using the embedding method the solution and therefore the weak fuzzy solution to the fuzzy system are expressed by using the generalized inverses of the coefficient matrix the existence of the strong fuzzy solution to the fuzzy system is also discussed some examples are presented to illustrate the theory