generalized means as model of compensative connectives abstract empirical investigations have shown that instead of strong logical and and or connectives there is often some degree of compensation in between in this paper the generalized means are proposed as connective operators for fuzzy set theory which easily allow for modelling the degree of compensation in a natural manner including the arithmetic and geometric means as well as the maximum and minimum operators as special cases numerical examples with empirical data form an illustration of this concept some aspects of applications to decision making are discussed

linear invariants of complex manifolds and their plurisubharmonic variations abstract for a bounded domain d and a real number p 0 denote by a p d the linear space of l p integrable holomorphic functions on d equipped with the l p pseudonorm we prove that two bounded hyperconvex domains d 1 c n and d 2 c m are biholomorphic in particular n m if there is a linear isometry between a p d 1 and a p d 2 for some 0 p 2 the same result holds for p 2 p 2 4 provided that the p bergman kernels on d 1 and d 2 are exhaustive with this as a motivation we show that for all p 0 the p bergman kernel on a strongly pseudoconvex domain with c 2 boundary or a simply connected homogeneous regular domain is exhaustive these results show that spaces of pluricanonical sections of complex manifolds equipped with canonical pseudonorms are important linear invariants of complex manifolds the second part of the present work devotes to studying variations of these invariants we show that the direct image sheaf of the twisted relative pluricanonical bundle associated to a holomorphic family of stein manifolds or compact kahler manifolds is positively curved with respect to the canonical singular finsler metric

using fuzzy sets in operational research abstract during the last four decades a large number of mainly mathematical tools have been developed in and for operational research they are primarily devices to find optimal solutions after a problem has been modelled formally hardly any new tools have been developed for proper modelling of problems which are not well structured and which can not easily be cast into classical mathematical models fuzzy set theory as proposed by l zadeh in 1965 promises to bridge part of this gap it is much more adaptable to different problem structures and better suited to model human evaluation and decision making processes than classical mathematics this paper will primarily focus attention on four questions why fuzzy sets in or what are fuzzy sets where can they be used and how are they being used

a tower of coverings of quasi projective varieties abstract the main goal of this article is to relate asymptotic geometric properties on a tower of coverings of a non compact kahler manifold of finite volume with reasonable geometric assumptions to its universal covering examples to which our findings are applicable include moduli spaces of hyperbolic punctured riemann surfaces and hermitian locally symmetric spaces of finite volume

a labeling algorithm for the fuzzy assignment problem abstract this paper concentrates on the assignment problem where costs are not deterministic numbers but imprecise ones here the elements of the cost matrix of the assignment problem are subnormal fuzzy intervals with increasing linear membership functions whereas the membership function of the total cost is a fuzzy interval with decreasing linear membership function by the max min criterion suggested by bellman and zadeh the fuzzy assignment problem can be treated as a mixed integer nonlinear programming problem we show that this problem can usually be simplified into either a linear fractional programming problem or a bottleneck assignment problem here we propose an efficient algorithm based on the labeling method for solving the linear fractional programming case the algorithm begins with primal feasibility and proceeds to obtain dual feasibility while maintaining complementary slackness until the primal optimal solution is found the computational results show that the proposed labeling algorithm offers an effective and efficient way for handling the fuzzy assignment problem

a simplex based algorithm for the lexicographically extended linear maxmin problem abstract let f x cx c where c is a real m n matrix c a constant m vector and x a variable n vector g x denotes the vector with components f i x in order of ascending magnitude the problem is to maximize g x over x in the lexicographic sense where x is the set of all points such that ax b x 0 a a real r n matrix it is known that this problem can be reduced to a sequence of m maximum problems where the maxmin problems can be solved by the well known simplex method of linear optimization a prerequisite such a procedure is the knowledge of at least one common index per stage it is shown that these common indices can readily be obtained from the respective optimal simplex tableaux some simple tests help to obtain more than just one common index per stage

the behavior of the free boundary for reaction diffusion equations with convection in an exterior domain with neumann or dirichlet boundary condition let l a r d2dr2 b r ddr be a second order elliptic operator and consider the reaction diffusion equation with neumann boundary condition lu upforr r u r h u r h u 0is minimal where p 0 1 p 0 1 r 0r 0 h 0h 0 and r 0 r 0 this equation is the radially symmetric case of an equation of the form lu upinrd d u n hon d u 0is minimal where l i j 1dai j 2 xi xj i 1dbi xi is a second order elliptic operator and where d 2d 2 h 0h 0 is continuous d rdd rd is bounded and n is the unit inward normal to the domain rd d consider also the same equations with the neumann boundary condition replaced by the dirichlet boundary condition namely u r hu r h in the radial case and u hu h on d in the general case the solutions to the above equations may possess a free boundary in the radially symmetric case if r h inf r r u r 0 r u r 0 we call this the radius of the free boundary otherwise there is no free boundary we normalize the diffusion coefficient a to be on unit order consider the convection vector field b to be on order rmrm m rm r pointing either inward or outward and consider the reaction coefficient to be on order r jr j j rj r for both the neumann boundary case and the dirichlet boundary case we show for which choices of m and j a free boundary exists and when it exists we obtain its growth rate in h as a function of m and j these results are then used to study the free boundary in the non radially symmetric case

interactive multiple objective programming subject to flexible constraints abstract an interactive decision support system is introduced which aids in solving multiple objective programming problems subject to strict and flexible constraints integral part is an extension of a well known fuzzy sets approach evaluating possible solutions by their degrees of membership to objectives and constraints this approach is linked to classical multiple objective programming models if the decision maker cannot determine membership functions a priori the system suggests functions dependent on the given information and interactive modifications are allowed

towards the ideal solution in a learning problem with different t norm operators abstract the ideal solution of a learning problem is discussed our learning problem is that of finding p in p q with a given data sequence of q written as q i i 1 2 n based on the concept of zadeh s relative sigma count we formulate the problem as a multi objective optimization with sufficiency and necessity criteria we give explicit formulae of the ideal evidence sequence p 1 and we analyze how the ideal sequence depends on different t norm operations and the parameters specified in the criteria using schweizer and sklar s one parameter family of t norms

a local version of karamardian s theorem on lower semicontinuous strictly quasiconvex functions abstract it is known that lower semicontinuous strictly quasiconvex functions are quasiconvex it is shown that semilocally strictly quasiconvex functions are semilocally quasiconvex on a locally star shaped domain if some condition of semilocal lower semicontinuity is satisfied these things are analyzed in some detail the functions involved have a connected quasiorder as their range as a motivation it is shown that a multiobjective function is a quasiconvex and strictly quasiconvex with respect to the lexminmax order if its components have the same properties there is a discussion of some applications to multiobjective decision particularly with lexminmax as the underlying decision criterion

pareto optimal solutions in fuzzy multi objective linear programming the problem of solving multi objective linear programming problems by assuming that the decision maker has fuzzy goals for each of the objective functions is addressed several methods have been proposed in the literature in order to obtain fuzzy efficient solutions to fuzzy multi objective programming problems in this paper we show that in the case that one of our goals is fully achieved a fuzzy efficient solution may not be pareto optimal and therefore we propose a general procedure to obtain a non dominated solution which is also fuzzy efficient two numerical examples illustrate our procedure

the use of a fuzzy decision making method in a large scale computer system choice problem abstract we recently proposed a fuzzy decision making method for multiple objectives problems in an uncertain and ill defined environment this paper presents a real and large scale application of the method the problem is to decide what sort of computer system for research and education should be renewed in the department of computer engineering one member of a renewal committee appears as a decision maker after describing the outline of the fuzzy decision making method the decision analysis process objective hierarchy identification of decision maker s preference structure rating and ranking of alternatives and sensitivity analysis is presented

optimization of logistic systems using fuzzy weighted aggregation logistic scheduling problems are often multi criteria optimization problems with many contradictory objectives and constraints which cannot be properly described by conventional cost functions the use of fuzzy decision making may improve the performance of this type of systems since it allows an easier and suitable description of the confluence of the different criteria of the scheduling process this paper introduces the application of fuzzy weighted aggregation to formulate the logistic system optimization problem further this paper also extends the application of this framework to different types of optimization methodologies dispatching rules if it is used as a performance index or meta heuristics such as genetic algorithms ga or ant colony optimization aco if it is used as an objective function simulation results show that the fuzzy combination of criteria improves the scheduling results whatever optimization methodology is used

the modularity condition for semi t operators and semi uninorms abstract the aim of this paper is mainly to solve the functional equations given by the modularity condition several years ago the modularity equations for t norms t conorms uninorms and t operators which are commutative and associative have been studied our investigations are motivated by modularity condition for generalizations of these operators by removing associativity or commutativity in this work the following main conclusions are proved 1 a continuous t norm with respect to a continuous semicopula is modular if and only if they are equal the case for a semicopula with respect to a strict t norm is also the same a semicopula with respect to a co semicopula is modular if and only if the semicopula is min and the co semicopula is max the modularity condition does not hold for a co semicopula with respect to a semicopula 2 necessary and sufficient conditions are given for a semi t operator with respect to a semi uninorm a pseudo uninorm with respect to a semi t operator to satisfy the modularity condition equation new solutions to the modularity condition equations of the case 1 are characterized

the dead core for reaction diffusion equations with convection and its connection with the first exit time of the related markov diffusion process on considere un probleme de reaction diffusion avec convection dans une region bornee d r n on demontre l existence d une solution

compactification of complete kahler manifolds of negative ricci curvature soit m une variete de kahler complete de dimension m et soit la forme de kahler on suppose 1 ric 0 2 m est tres fortement m 2 pseudoconcave 3 le recouvrement universel de m est de stein alors m est biholomorphe a une variete quasiprojective

a fuzzy decision making method and its application to a company choice problem abstract we propose a fuzzy decision making method for multiobjective decision problems its main features are the use of fuzzy connectives to represent the decision maker s preference structure and fuzzy probability to express imprecise and uncertain outcomes the preference structure is extracted through interaction between the decision maker and a computer the fuzzy connectives adopted here are zimmermann s operation and its two extensions the extended operations describe the preference structure better than the operation the proposed method consists of the following five steps 1 1 identification of the problem 2 2 a questionnaire process 3 3 parameter identification 4 4 evaluations of alternatives 5 5 aggregated rating and ranking of alternatives finally an application of this method to a company choice problem is presented

aggregation of fuzzy opinions an axiomatic approach abstract the importance of fuzzy valuations in diagnostics is mentioned the problem of aggregation of fuzzy opinions obtained from a group of experts in answer to the question has an object the property labeled a and no property labeled 1a is formulated the set of fung and fu s 10 aggregation axioms is shortly described the idea of weighting expert s opinions is formalized then a new set of aggregation axioms is presented and an aggregating operator is introduced a posteriori weighting of opinions in aggregation is examined

an extended rule based inference for general decision making problems complex decision making problems are usually modeled in terms of a number of decisive variables that are related hierarchically pieces of evidence are aggregated in a bottom up way to determine the final decision goal for dealing with such problems ishizuka et al 5 6 developed a rule based inference procedure by using fuzzy sets to represent imprecise data and employed the dempster shafer theory to aggregate evidence for structural damage assessment this paper highlights the necessity of applying the rules with all possible consequent clauses in the procedure with the considerations of information quality and quantity when applying the procedure to more general decision making problems the use of such rules can provide high quality information which contains much less ignorance in the resultant information also it can afford more information due to the decrease in total ignorance a simple example with two cases is used to compare the results based on the two different presentations of rules in the inference procedure for illustrating the importance of considering the rules proposed in this paper

a fuzzy decision theory of optimal social discount rate collective choice theoretic abstract in this essay we present a fuzzy decision theory of the optimal social discount rate by combining methods of fuzzy logic consensus combination of expert judgments and fuzzy aggregation algorithms are developed for computing optimal social discount rates from individual and collective time preferences the results are examined against the computation of social discount rate on individual preferences as measured by utilities an example is provided to illustrate the applicational mechanism of the theory the essay is concluded with an appendix which is devoted to examining the properties of the required time set for the construction of the social discount

short rational generating functions for solving some families of fuzzy integer programming problems in this paper we present new complexity results for solving single and multiobjective fuzzy integer programs with soft constraints and fuzzy objective function coefficients our method is based on the use of barvinok s short rational generating functions of convenient transformations of the fuzzy problems to crisp ones this analysis allows us to provide new insights on the structure of these families of fuzzy programs

the modularity condition for uninorms and t operators in this work we study the functional equation given by the modularity condition f x g y z g f x y z for all z x where the unknown functions f g are uninorms and or t operators we characterize all the solutions in the four possible cases i when f g are t operators ii when f is a t operator and g a uninorm iii when f is a uninorm and g a t operator and finally iv when f g are uninorms

fuzzy rule generation methods for high level computer vision abstract in many decision making systems involving multiple sources the decisions made may be considered as the result of a rule based system in which the decision rules are usually enumerated by experts or generated by a learning process in this paper we discuss the various issues involved in the generation of fuzzy rules automatically from training data for high level computer vision features are treated as linguistic variables that appear in the antecedent clauses of the rules we present methods to generate the corresponding linguistic labels values and their membership functions rules are generated by constructing a minimal approximate fuzzy aggregation network and then training the network using gradient descent methods several examples are given

optimal encoding of graph homomorphism energy using fuzzy information aggregation operators abstract the attributed relational graph matching arg strategy is a well known approach to object pattern recognition in the past for the parallel solution of arg matching problem an overall objective function was constructed using linearly weighted information aggregation function and one set of parameter values was chosen for all models by trial and error for the parameters in the function in this paper the compatibility between every pair of model and scene attributes is interpreted as a fuzzy value and subsequently the nonlinear fuzzy information aggregation operators are used to fuse the information captured in the chosen attributes to learn the parameters in the fuzzy information aggregation operators the learning from samples strategy is used the learning of weight parameters is formulated as an optimisation problem and solved using the gradient projection algorithm based learning procedure the learning procedure implicitly evaluates ambiguity robustness and discriminatory power of the relational attributes chosen for graph matching and assigns weights appropriately to the chosen attributes the learning procedure also enables us to compute a distinct set of optimal parameters for every model to reflect the characteristics of the model so that the homomorphic arg matching problem can be optimally encoded in the energy function for the model experimental results are presented to illustrate effectiveness and necessity of the parameter estimation and learning procedures

the modularity condition for semi t operators abstract the aim of this paper is mainly to solve the functional equations given by the modularity condition several years ago the modularity equations were discussed in families of certain commutative operations such as t norms t conorms uninorms 2 uninorms and t operators in this study we continue the investigation of this same topic by focusing on semi t operators which are generalization of t operators by omitting commutativity our results are not only the full characterization of this modularity condition for semi t operators with continuous underlying operators but also generalize the case for t operators under certain conditions

properties of the aggregation operators related with fuzzy relations abstract the problem of information generalization in multicriteria decision making is considered in this paper the information is unified by fuzzy relations and the generalization is realized with the help of aggregation operators some of the most oftenly used operators are presented and their properties depending on the properties of the fuzzy relations which they aggregate are proved the sensitivity of the operators with respect to variations in their arguments is investigated the numerical example deciding the problem of alternatives ranking is given as well

an interactive fuzzy programming system abstract an interactive system is introduced which supports a decision maker in solving programming models with crisp or fuzzy constraints and crisp or fuzzy goals one part of the system is the determination of membership functions representing goals to this purpose fuzzy extreme solutions are computed and are presented to the decision maker these and each of the proposed compromise solutions are fuzzy efficient

geometry of domains with the uniform squeezing property abstract we introduce the notion of domains with uniform squeezing property study various analytic and geometric properties of such domains and show that they cover many interesting examples including teichmuller spaces and hermitian symmetric spaces of non compact type the properties supported by such manifolds include pseudoconvexity hyperconvexity kahler hyperbolicity vanishing of cohomology groups and quasi isometry of various invariant metrics it also leads to nice geometric properties for manifolds covered by bounded domains and a simple criterion to provide positive examples to a problem of serre about stein properties of holomorphic fiber bundles

basic concepts for a theory of evaluation hierarchical aggregation via autodistributive connectives in fuzzy set theory abstract the aggregative operator introduced by combi 1982 in his analysis of basic concepts for a theory of evaluation in this journal is based on the axioms of associativity continuity and monotonicity in this paper an alternative approach is given where associativity is replaced by another axiom viz autodistributivity implying a kind of hierarchical aggregation instead of the former horizontal one the new set of properties yields a general class of operators for connecting fuzzy sets which are formally similar to the aggregative operators but are purely compensative in a strong sense moreover this modified approach generalizes a recent approach based on generalized means as compensative connectives it appears to be similar to expected utility approaches in decision making under uncertainty and seems to be a very promising tool to handle representation problems as they grow from other fields of human decision making e g of multicriteria analysis and of welfare theory

comparison of empirical and computed values of fuzzy conjunction abstract the necessity for further experiments such as in 4 for the foundation of fuzzy sets theory is shown generality of the experimental results on fuzzy conjunction in the paper by thole zimmermann and zisno 1979 4 for the other objects and language is verified for other conditions usually the minimum the product and the restricted sum operators are used as an intersection conjunction of fuzzy sets in fuzzy optimization f optimization on the basis of experiments it is shown that these operators are correct for f optimization their correctness is founded on the stability of the extremal point a decision in bellman zadeh s scheme under a positive linear mapping it is shown that these mappings exist between empirical conjunction and considered operators as a statistical result of linear regression analysis

logit choice models for interactive attributes abstract in multi attribute decision making madm the choice of a decision maker dm is often the result of an interplay between the dm s unique attitude the utilities specific to the dm for the attributes and the degree of positive or negative interaction among the attributes based on this conglomeration of information we introduce a few choice models to give the probabilities for different possible choices of a dm more specifically the conventional multinomial logit mnl model is extended to consider the interaction among the attributes and also the dm s unique attitudinal character the usefulness of the proposed models is illustrated in a real world application

duality in linear programming with fuzzy parameters and matrix games with fuzzy pay offs abstract a dual for linear programming problems with fuzzy parameters is introduced and it is shown that a two person zero sum matrix game with fuzzy pay offs is equivalent to a primal dual pair of such fuzzy linear programming problems further certain difficulties with similar studies reported in the literature are discussed

canonical metrics on the moduli space of riemann surfaces i in this paper we continue our study of the canonical metrics on the moduli space of curves we first prove the bounded geometry of the ricci and perturbed ricci metrics by carefully choosing the pertubation constant and by studying the asymptotics we show that the ricci and holomorphic sectional curvatures of the perturbed ricci metric are bounded from above and below by negative constants based on our understanding of the kahler einstein metric we show that the logarithmic cotangent bundle over the deligne mumford moduli space is stable with respect to the canonical polarization finally in the last section we prove the strongly bounded geometry of the kahler einstein metric by using the kahler ricci flow and a priori estimates of the complex monge ampere equation

a vanishing theorem on generalized cartan hartogs domain of the second type abstract in this paper we consider the vanishing theorem of square integrable harmonic forms with respect to the bergman metric on the second type of generalized cartan hartogs domain by using three main tools the properties of bergman kernel function holomorphic invariant and holomorphic automorphism group

estimate of the squeezing function for a class of bounded domains we construct a class of bounded domains on which the squeezing function is not uniformly bounded from below near a smooth and pseudoconvex boundary point

structural and functional quantization of vagueness abstract this paper proposes two methods of quantizing vague categories in terms of quantities whose identities have been either widely recognized in the fuzzy set theory literature or established by bayesian decision theory the methods are called structural quantization and functional quantization respectively the idea behind structural quantization is that for a comparative vague category like good scores there exists a preference ordering among the possible scores and how good a particular score is depends on how large the portion of examinees whose scores are lower than that score is functional quantization adopts the conclusion of bayesian decision theory that a rational agent s belief can be represented by a probability to quantize the term good score the method first assesses the two probabilities that respectively represent a rational agent s beliefs about john s score before and after learning that john has got a good score it then derives a membership function by comparing those two probabilities the equivalence of the two quantization methods is hypothesized the logic connectives not and and or are discussed in the setting of structural quantization while aggregation of information is addressed in the setting of functional quantization

properties of squeezing functions and global transformations of bounded domains the central purpose of the present paper is to study boundary behavior of squeezing functions on bounded domains we prove that the squeezing function of a strongly pseudoconvex domain tends to 1 near the boundary in fact such an estimate is proved for the squeezing function on any domain near its globally strongly convex boundary points we also study the stability of squeezing functions on a sequence of bounded domains and give comparisons of intrinsic measures and metrics on bounded domains in terms of squeezing functions as applications we give new and simple proofs of several well known results about geometry of strongly pseudoconvex do mains and prove that all cartan hartogs domains are homogenous regular finally some related problems that ask for further study are proposed

on some solutions of the distributivity equation abstract the aim of this paper is to present some interesting results on the distributivity equation for which several pairs of binary operations on 0 1 are considered moreover different methods to solve distributivity equations are used in this work

compensatory fuzzy multiple level decision making abstract fuzzy set theory has been shown to be an effective tool to overcome the computational difficulties encountered in solving large multiple level programming problems shih et al 1996 in this paper compensatory operators are introduced for adjusting the decision making process between the different levels and also between the decision makers of the same level after a brief consideration of the bi level and three level systems the large decentralized organizations with both equal and unequal goals are investigated various numerical examples are given to compare the influences of compensation and to illustrate the approaches

fuzzy optimal control the problem of fuzzy optimal control of nonlinear systems is formulated and solved on the basis of fuzzy mathematical programming the fuzzy optimal control problem is extended to the case of multicriteria optimal control a particular case of fuzzy optimal control with fuzzy objective function and crisp transversality conditions is also considered

characterizing strong pseudoconvexity obstructions to biholomorphisms and lyapunov exponents in this paper we consider the following question for bounded domains with smooth boundary can strong pseudoconvexity be characterized in terms of the intrinsic complex geometry of the domain our approach to answering this question is based on understanding the dynamical behavior of real geodesics in the kobayashi metric and allows us to prove a number of results for domains with low regularity for instance we show that for convex domains with c 2 epsilon boundary strong pseudoconvexity can be characterized in terms of the behavior of the squeezing function near the boundary the behavior of the holomorphic sectional curvature of the bergman metric near the boundary or any other reasonable measure of the complex geometry near the boundary the first characterization gives a partial answer to a question of fornaess and wold as an application of these characterizations we show that a convex domain with c 2 epsilon boundary which is biholomorphic to a strongly pseudoconvex domain is also strongly pseudoconvex

multi objective fuzzy inventory model with three constraints a geometric programming approach a multi item multi objective inventory model with shortages and demand dependent unit cost has been formulated along with storage space number of orders and production cost restrictions in most of the real world situations the cost parameters the objective functions and constraints of the decision makers are imprecise in nature hence the cost parameters the objective functions and constraints are imposed here in fuzzy environment this model has been solved by geometric programming method the results for the model without shortages are obtained as a particular case the sensitivity analysis has been discussed for the change of the cost parameters the models are illustrated with numerical examples

the squeezing function on doubly connected domains via the loewner differential equation for any bounded domains varomega in mathbb c n deng guan and zhang introduced the squeezing function s varomega z which is a biholomorphic invariant of bounded domains we show that for n 1 the squeezing function on an annulus a r lbrace z in mathbb c r z 1 rbrace is given by s a r z max left z frac r z right for all 0 r 1 this disproves the conjectured formula for the squeezing function proposed by deng guan and zhang and establishes up to biholomorphisms the squeezing function for all doubly connected domains in mathbb c other than the punctured plane it provides the first non trivial formula for the squeezing function for a wide class of plane domains and answers a question of wold our main tools used to prove this result are the schottky klein prime function following the work of crowdy and a version of the loewner differential equation on annuli due to komatu we also show that these results can be used to obtain lower bounds on the squeezing function for certain product domains in mathbb c n

additive hybrid networks for fuzzy logic abstract evidence aggregation networks based on multiplicative fuzzy hybrid operators were introduced by krishnapuram and lee they have been used for image segmentation pattern recognition and general multicriteria decision making one of the drawbacks of these networks is that the training is complex and quite time consuming we have recently modified these aggregation networks to implement additive fuzzy hybrid connectives these new networks have similar excellent properties for decision making under uncertainty as do their multiplicative precursors and have the advantage that training is easier since the additive operators are not as complex in form in earlier work trainable neural networks have been used to perform inference in a fuzzy logic system fixed architecture networks of fuzzy operators and standard neural networks have been utilized the additive hybrid operators are extremely flexible and so are excellent candidates for nodes in a network structure for fuzzy logic inference the purpose of this paper is to demonstrate the capability of networks of additive hybrid nodes to learn appropriate functional relationships for fuzzy logic an added advantage of these networks is that they are transparent i e after training the individual nodes can be analyzed as a collection of mini rules

two phase approach for solving the fuzzy linear programming problems we propose a two phase approach to solve the fuzzy linear programming problem although several methods in the literature have been proposed to treat this problem the two phase approach has the merit stated as if the decision maker is seeking an efficient solution which can improve the max min operators solution so that each membership degree should be improved then the two phase method automatically attains this desire if there is room to improve an interpretation of this result is that the two phase method not just pursue the highest membership degree in the objective but also pursue a better utilization of each constrained resource

applications of fuzzy set theory to mathematical programming mathematical programming is one of the areas to which fuzzy set theory has been applied extensively primarily based on bellman and zadeh s model of decision in fuzzy environments models have been suggested which allow flexibility in constraints and fuzziness in the objective function in traditional linear and nonlinear programming in integer and fractional programming and in dynamic programming these models in turn have been used to offer computationally efficient approaches for solving vector maximum problems this paper surveys major models and theories in this area and offers some indication on future developments which can be expected

multi criteria decision making in german automotive industry using fuzzy logic abstract in recent years fuzzy logic technologies have been widely applied to control applications in engineering where they are now considered an enabling technology for intelligent control systems fuzzy logic expedites the design of complex systems by allowing heuristic control strategies to be formulated by natural language rules rather than mathematical models hence the essence of fuzzy logic is its ability to put engineering expertise right into an algorithm the domain of such a technology is not limited to control engineering it can also be applied to incorporate complex decision making and the analysis of numerical data into non control systems this paper covers such an application realized at mercedes benz in germany for the optimization of the design process of truck components such as gear boxes the maturity of a current component development needs to be evaluated the objective is to reduce the amount of existing data of the development project to a single parameter describing the overall maturity of the design

an interactive satisfying method based on alternative tolerance for multiple objective optimization with fuzzy parameters an interactive satisfying method based on alternative tolerance is presented for the multiple objective optimization problem with fuzzy parameters using the alpha level sets of the fuzzy numbers all the objectives are modeled as the fuzzy goals and the tolerances of the objectives are iteratively changed according to a decision maker for a satisfying solution via a specific attainable point programming model the membership functions can be modified and then a lexicographic two phase programming procedure is constructed correspondingly to find the final solution in a special case the objective constraint is added instead of changing the membership functions therefore the dissatisfying objectives for the decision maker can be improved step by step the presented method not only acquires the alpha pareto optimal or weak alpha pareto optimal solution of the fuzzy multiple objective optimization but also satisfies the progressive preference of the decision maker a numerical example shows its power

introduction to a new weighting method hierarchy consistency analysis abstract this paper proposes a new methodology hierarchy consistency analysis hca the approach to this methodology was developed owing to the fact that in the analysis of large scale problems a different viewpoint or specific points emphasis will result in different hierarchy structures on the basis of different structures being created the methodology is designed to combine these different structures and estimate their compromised criterion weights so that all different hierarchy structures will have the same aggregated index the hca methodology will thus provide us with a comprehensive framework for solving hierarchy evaluation problems its merits include amongst others providing a simpler method for calculating the weight of criteria providing a consistency index for monitoring dm judgment consistency and delivering more types of hierarchy structure schemata to aid the decision maker in understanding and auditing the performance status of systems

interactive fuzzy linear programming abstract in this study an interactive fuzzy linear programming approach is investigated to improve the flexibility and robustness of linear programming lp technique this paper provides a practical modelling method which is a symmetric integration of zimmermann s werners s vergegay s and chanas s fuzzy lp approaches and additionally provides a decision support system for solving a specific domain of practical lp problems the interactive concept provides a learning process about the system whereby the decision maker can learn to recognize good solutions relative importance of factors in the system and then design a high productivity system instead of optimizing a given system this interactive fuzzy lp system provides integration oriented adaptation and learning features by considering all the possibilities of a specific domain of lp problems which are integrated in logical order using an if then rule

the euler characteristic of the moduli space of curves let fg 1 g 1 be the mapping class group consisting of all isotopy classes of base point and orientation preserving homeomorphisms of a closed oriented surface f of genus g let 1 be its euler characteristic in the sense of wall that is z f i fgl f l z e f where f is any torsion free subgroup of finite index in f 1 and e is a contractible space on which f acts freely and properly discontinuously an example of such a space is the teichmiiller space 1 and g f can be interpreted as the orbifold euler characteristic of f i join the moduli space of curves of genus g with base point the purpose of this paper is to prove the following formula for f i

decisions and evaluations by hierarchical aggregation of information usually in preparing a decision a hierarchy of criteria for evaluating alternatives can he agreed upon by the decision makers the problem addressed in this paper is the appropriate modelling of such evaluations and their aggregation in order to arrive at a proper overall evaluation function by which the decision alternatives can be ordered easily representing the criteria subjective categories by fuzzy sets it is possible to use aggregation operators as models for the amalgamation of those criteria in the framework of an empirical research project a hierarchy of criteria was developed for the evaluation of credit worthiness of customers 50 credit applications were evaluated by a number of credit managers of banks and their judgement could be appropriately modelled by a four level hierarchy of criteria

fuzzy connective based hierarchical aggregation networks for decision making abstract decision making is usually based on the aggregation of several criteria although the aggregation can be performed at one level in simple cases in more complex situations it becomes necessary that it be performed in a hierarchical manner in a multilevel framework this is particularly true in many engineering applications in this paper we investigate the use of fuzzy connectives in multilayer networks to arrive at appropriate overall aggregation functions the characteristics of suitable fuzzy connectives are studied and an iterative algorithm to determine the type of aggregation function and its parameters at each node in the network is proposed we believe that our aggregation scheme is powerful and flexible since we use several types of aggregation connectives and since the parameters of the network can be determined using a simple algorithm the behavior of the network can also be modified depending on the desired attitude conditions for unique convergence of the algorithm in simple cases are discussed and examples of applications of the method are also presented

fuzzy chance constrained linear programming model for optimizing the scrap charge in steel production optimizing the charge in secondary steel production is challenging because the chemical composition of the scrap is highly uncertain the uncertainty can cause a considerable risk of the scrap mix failing to satisfy the composition requirements for the final product in this paper we represent the uncertainty based on fuzzy set theory and constrain the failure risk based on a possibility measure consequently the scrap charge optimization problem is modeled as a fuzzy chance constrained linear programming problem since the constraints of the model mainly address the specification of the product the crisp equivalent of the fuzzy constraints should be less relaxed than that purely based on the concept of soft constraints based on the application context we adopt a strengthened version of soft constraints to interpret fuzzy constraints and form a crisp model with consistent and compact constraints for solution simulation results based on realistic data show that the failure risk can be managed by proper combination of aspiration levels and confidence factors for defining fuzzy numbers there is a tradeoff between failure risk and material cost the presented approach applies also for other scrap based production processes

a spectrum of compromise aggregation operators for multi attribute decision making in many decision making problems a number of independent attributes or criteria are often used to individually rate an alternative from an agent s local perspective and then these individual ratings are combined to produce an overall assessment now in cases where these individual ratings are not in complete agreement the overall rating should be somewhere in between the extremes that have been suggested however there are many possibilities for the aggregated value given this this paper systematically explores the space of possible compromise operators for such multi attribute decision making problems specifically we axiomatically identify the complete spectrum of such operators in terms of the properties they should satisfy and show the main ones that are widely used namely averaging operators uninorms and nullnorms represent only three of the nine types we identify for each type we then go onto analyse their properties and discuss how specific instances can actually be developed finally to illustrate the richness of our framework we show how a wide range of operators are needed to model the various attitudes that a user may have for aggregation in a given scenario bidding in multi attribute auctions

compactifying complete kahler einstein manifolds of finite topological type and bounded curvature siu yau 16 studied the compactification of complete kaihler manifolds of finite volume and of riemannian sectional curvature pinched between two negative constants in 12 the first author of the present article started a systematic study of the more general problem of compactifying complete kwhler manifolds of finite volume and of bounded curvature a number of conjectures were formulated which can all be regarded as conjectural generalizations of the compactification of arithmetic varieties i e quotients of bounded symmetric domains q by torsion free arithmetic subgroups of aut q in a differentialgeometric setting here and henceforth all discrete groups of automorphisms will be assumed torsion free in the same article we treated the case of kaihler surfaces and proved