an exposition of the ahp in reply to the paper remarks on the analytic hierarchy process it is a fact that people make decisions and have been making decisions for a very long time contrary to what some of us who are interested in decision making may like to believe most people do not take seriously the existence of theories which purport to set their thinking and feeling right they claim to know their own value system and what they want they may wonder how anyone else can know well enough to tell them how best to organize their thinking in order to make better choices yet research has shown that complex decisions are beyond the capacity of the brain to synthesize intuitively and efficiently since decision making is a natural characteristic of people how do we describe what they do so that an ordinary mortal can understand what we are saying we do not wish to legislate the method with which people should make decisions but only to describe it even when it is prescribed by some method in the process we may learn things that can help people make better decisions how the analytic hierarchy process ahp forman et al harker 1986 harker and vargas 1987 saaty 1986 1988a b saaty and vargas 1987 xu 1988 golden et al 1989 saaty and alexander 1989 is a theory of measurement when applied in decision making it assists one to describe the general decision operation by decomposing a complex problem into a multi level hierarchic structure of objectives criteria subcriteria and alternatives the ahp provides a fundamental scale of relative magnitudes expressed in dominance units to represent judgments in the form of paired comparisons a ratio scale of relative magnitudes expressed in priority units is then derived from each set of comparisons an overall rcatio scale of priorities is then synthesized to obtain a ranking of the alternatives from its axioms to its procedures the ahp has turned out to be historically and theoretically a different and independent theory of decision making from utility theory much as a dialogue evolved in mathematics around the consistency of different geometries and around absolute and relative space and time in physics both to dispel absolute notions those who believe that only utility theory can tell us the absolute truth about man s decision making might take a close look at the ahp it has found varied and serious applications it also has a particular way of generating ratio scales and dealing with inconsistency in judgment that have contributed to its effectiveness in resource allocation and in the setting of priorities by a group of decision makers utility theory is a normative process the ahp as a descriptive theory encompasses procedures leading to outcomes as would be ranked by a normative theory but it must go beyond to deal with outcomes not accounted for by the demanding assumptions of a normative theory we must briefly describe the ahp to enable the reader to see that a practicable theory based on ratio scales need not dilute itself to satisfy expectations of people who derive their understanding from a theory based on interval scales this is particularly true if the rival theory in aspiring for generality also makes unrealistic assumptions for example about the transitivity and consistency of preferences and the difficult use of lotteries

logic based fuzzy networks a study in system modeling with triangular norms and uninorms the ultimate challenges of system modeling concern designing accurate yet highly transparent and user centric models we have witnessed a plethora of neurofuzzy architectures which are aimed at addressing these two highly conflicting requirements this study is concerned with the design and the development of transparent logic networks realized with the aid of fuzzy neurons and fuzzy unineurons the construction of networks of this form requires a formation of efficient interfaces that constitute a conceptually appealing bridge between the model and the real world experimental environment in which the model is to be used in general the interfaces are constructed by invoking some form of granulation of information and binary boolean discretization in particular we introduce a new discretization environment that is realized by means of particle swarm optimization pso and data clustering implemented by the k means algorithm the underlying structure of the network is optimized by invoking a combination of the pso and the mechanisms of conventional gradient based learning we discuss various optimization strategies by considering boolean as well as fuzzy data coming as the result of discretization of original experimental data and then involving several learning strategies we elaborate on the interpretation aspects of the network and show how those could be strengthened through efficient pruning we also show how the interpreted network leads to a simpler and more accurate logic description of the experimental data a number of experimental studies are included

fuzzy logic based algorithms for maximum covering location problems this paper concerns a class of maximum covering location problems in networks in uncertain environments it is assumed that a relative weights of demand nodes are either deterministic or imprecise described by linguistic expressions and b potential facility site locations are limited to network nodes the concept of coverage is extended to include a degree of node coverage which means that the borders between the subset of covered demand nodes and the subset of uncovered demand nodes are inexact the acceptable service distance travelling times from a facility site to demand nodes are modelled by fuzzy sets three new algorithms for choosing the best facility locations are developed which assume that 1 demands at all nodes are equally important 2 relative weights of demand at nodes are deterministic and 3 weights of demand at nodes are imprecise and described by linguistic terms respectively the algorithms are based on searching among potential facility nodes by applying comparison operations on discrete fuzzy sets it is shown how to extend the proposed algorithms from one site to multi site covering problems illustrative examples of selecting locations for logistics centres in a distribution company are given

a clarification of remarks on the analytic hierarchy process the replies by saaty 1990 and by harker and vargas 1990 to my remarks on the analytic hierarchy process dyer 1990 are useful in focusing attention on areas of disagreement regarding the ahp and provide readers with sufficient information to form their own opinions the purpose of this response is not to extend the debate but to clarify the two methods proposed in my paper to resolve the problem of rank reversal in the ahp harker and vargas 1989 misinterpreted my first proposed method method 1 in their reply the key observation they missed is that both the weights on the criteria and the scores of the alternatives on the criteria must be normalized with respect to the same range of alternative values in method 1 the decision maker must specify the ranges over which he assumed the alternatives might vary on each criterion when he determined the weights an example may be useful in clarifying the key ideas suppose each alternative in the harker and vargas 1990 example represents the choice of a decision maker among sums of money deposited in two different bank accounts and each criterion is simply the amount of money deposited in a single bank account obviously the decision maker would use the sum of the accounts as the basis for ranking the alternatives and would select b from the three alternatives a b and c let us see how the appropriate use of method 1 would lead to this result without recourse to the supermatrix technique or to the concept of dependence of the criteria on the alternatives the decision maker would consider the deposits in each bank account to be equally important if he assumed that the ranges of the possible deposits were equal for example suppose the decision maker assumes that the values for each bank account criterion vary over the range 1 80 he responds that changes from 1 to 80 on each criterion are equally important so the normalized eigenvector for the ahp criterion weights is 1 2 1 2 using method 1 since the range of values on criterion c1 is 75 80 and the decision maker assumed a range of 1 80 in determining the equal criterion weights we must introduce a dummy alternative with the value of 1 on criterion c1 this dummy alternative does not need to be explicitly introduced with values on the other criteria but it could be and would not affect the results as long as its assumed values on the other criteria are in the range 1 80 similarly a dummy alternative with a value of 80 must be introduced for criterion c2 the normalized eigenvector for criterion c1 would become 80 235 79 235 75 235 1 235 for example where the last component 1 235 is the score for the dummy alternative we normalize each resulting eigenvector by subtracting its smallest component and then dividing by the largest component the appropriate scores for the three alternatives are

exponential stability of the solutions of the initial value problem for systems with impulse effect abstract in the present paper conditions have been found under which the exponential stability of a given solution of a system with impulse effect follows from the exponential stability of the respective system in variations

an application of fuzzy goal programming to a multiobjective project network problem abstract this paper presents a practical application of fuzzy goal programming fgp in a real life project network problem with two objectives as minimum completion time and crashing costs wanted to be optimized simultaneously fuzziness in the problem stems from the imprecise aspiration levels attained by the decision maker dm to both objectives these imprecise aspiration levels are quantified through the use of piecewise linear and continuous membership functions the objective function of the fgp is to maximize the membership value of both objectives intersection which form the fuzzy decision the problem is solved by using lindo computer package and the best compromised solution is found comparisons between solutions of fgp fuzzy linear programming flp lexicographic maximization method lmm and linear programming lp are also presented

asymptotic equivalence of two systems of differential equations with impulse effect abstract in this paper we prove an analogue of levinson s theorem for asymptotic equivalence of linear differential systems with impulse effect

stability with respect to part of the variables in systems with impulse effect abstract effective sufficient conditions are found for stability with respect to part of the variables in systems of ordinary differential equations with impulse effect the approach presented is based on the specially introduced piecewise continuous ljapunov functions

normal boundary intersection a new method for generating the pareto surface in nonlinear multicriteria optimization problems this paper proposes an alternate method for finding several pareto optimal points for a general nonlinear multicriteria optimization problem such points collectively capture the trade off among the various conflicting objectives it is proved that this method is independent of the relative scales of the functions and is successful in producing an evenly distributed set of points in the pareto set given an evenly distributed set of parameters a property which the popular method of minimizing weighted combinations of objective functions lacks further this method can handle more than two objectives while retaining the computational efficiency of continuation type algorithms this is an improvement over continuation techniques for tracing the trade off curve since continuation strategies cannot easily be extended to handle more than two objectives

approximating pareto frontier using a hybrid line search approach the aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach but it is well known that this technique sometimes fail in different aspects for determining the pareto frontier this paper proposes a new approach for multicriteria optimization which aggregates the objective functions and uses a line search method in order to locate an approximate efficient point once the first pareto solution is obtained a simplified version of the former one is used in the context of pareto dominance to obtain a set of efficient points which will assure a thorough distribution of solutions on the pareto frontier in the current form the proposed technique is well suitable for problems having multiple objectives it is not limited to bi objective problems and require the functions to be continuous twice differentiable in order to assess the effectiveness of this approach some experiments were performed and compared with two recent well known population based metaheuristics namely parego and nsga ii when compared to parego and nsga ii the proposed approach not only assures a better convergence to the pareto frontier but also illustrates a good distribution of solutions from a computational point of view both stages of the line search converge within a short time average about 150ms for the first stage and about 20ms for the second stage apart from this the proposed technique is very simple easy to implement and use to solve multiobjective problems

on the estimation of pareto fronts from the point of view of copula theory a probabilistic framework is applied to pareto front estimation a link between pareto front and level lines of a multivariate distribution is given parametric approximations of pareto front are provided for archimedean copulas consequences and limits of the archimedean hypothesis are discussed the full estimation methodology is analyzed on several examples given a first set of observations from a design of experiments sampled randomly in the design space the corresponding set of non dominated points usually does not give a good approximation of the pareto front we propose here to study this problem from the point of view of multivariate analysis introducing a probabilistic framework with the use of copulas this approach enables the expression of level lines in the objective space giving an estimation of the position of the pareto front when the level tends to zero in particular when it is possible to use archimedean copulas analytical expressions for pareto front estimators are available several case studies illustrate the interest of the approach which can be used at the beginning of the optimization when sampling randomly in the design space

measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming one way of solving multiple objective mathematical programming problems is finding discrete representations of the efficient set a modified goal of finding good discrete representations of the efficient set would contribute to the practicality of vector maximization algorithms we define coverage uniformity and cardinality as the three attributes of quality of discrete representations and introduce a framework that includes these attributes in which discrete representations can be evaluated compared to each other and judged satisfactory or unsatisfactory by a decision maker we provide simple mathematical programming formulations that can be used to compute the coverage error of a given discrete representation our formulations are practically implementable when the problem under study is a multiobjective linear programming problem we believe that the interactive algorithms along with the vector maximization methods can make use of our framework and its tools

arbitrage factor structure and mean variance analysis on large asset markets we examine the implications of arbitrage in a market with many assets the absence of arbitrage opportunities implies that the linear functionals that give the mean and cost of a portfolio are continuous hence there exist unique portfolios that represent these functionals these portfolios span the mean variance efficient set we resolve the question of when a market with many assets permits so much diversification that risk free investment opportunities are available ross 12 14 showed that if there is a factor structure then the mean returns are approximately linear functions of factor loadings we define an approximate factor structure and show that this weaker restriction is sufficient for ross result if the covariance matrix of the asset returns has only k unbounded eigenvalues then there is an approximate factor structure and it is unique the corresponding k eigenvectors converge and play the role of factor loadings hence only a principal component analysis is needed in empirical work

interactive decision making for multiobjective nonlinear programming problems with fuzzy parameters this paper presents interactive decision making methods for multiobjective linear linear fractional and nonlinear programming problems with fuzzy parameters on the basis of the level sets of the fuzzy numbers the concept of multiobjective programming and local m pareto optimality is introduced through the interaction with the decision maker dm the fuzzy goals of the dm for each of the objective functions in multiobjective programming are quantified by eliciting the corresponding membership functions after determining the membership functions in order to generate a candidate for the local satisficing solution which is also local m pareto optimal if the dm specifies the degree of the level sets and the reference membership values the augmented minimax problem is solved and the dm is supplied with the corresponding local m pareto optimal solution together with the trade off rates among the values of the membership functions and the degree then by considering the current values of the membership functions and as well as the trade off rates the dm responds by updating his her reference membership values and or the degree in this way the local satisficing solution for the dm can be derived efficiently from among an m pareto optimal solution set based on the proposed methods for multiobjective linear linear fractional and nonlinear programming problems with fuzzy parameters interactive computer programs are developed and an illustrative numerical example for nonlinear case is demonstrated

a test of the efficiency of a given portfolio a test for the ex ante efficiency of a given portfolio of assets is analyzed the relevant statistic has a tractable small sample distribution its power function is derived and used to study the sensitivity of the test to the portfolio choice and to the number of assets used to determine the ex post mean variance efficient frontier several intuitive interpretations of the test are provided including a simple mean standard deviation geometric explanation a univariate test equivalent to our multivariate based method is derived and it suggests some useful diagnostic tools which may explain why the null hypothesis is rejected empirical examples suggest that the multivariate approach can lead to more appropriate conclusions than those based on traditional inference which relies on a set of dependent univariate statistics

multi objective particle swarm optimization with time variant inertia and acceleration coefficients in this article we describe a novel particle swarm optimization pso approach to multi objective optimization moo called time variant multi objective particle swarm optimization tv mopso tv mopso is made adaptive in nature by allowing its vital parameters viz inertia weight and acceleration coefficients to change with iterations this adaptiveness helps the algorithm to explore the search space more efficiently a new diversity parameter has been used to ensure sufficient diversity amongst the solutions of the non dominated fronts while retaining at the same time the convergence to the pareto optimal front tv mopso has been compared with some recently developed multi objective pso techniques and evolutionary algorithms for 11 function optimization problems using different performance measures

determining the number of factors in approximate factor models in this paper we develop some econometric theory for factor models of large dimensions the focus is the determination of the number of factors r which is an unresolved issue in the rapidly growing literature on multifactor models we first establish the convergence rate for the factor estimates that will allow for consistent estimation of r we then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria the theory is developed under the framework of large cross sections n and large time dimensions t no restriction is imposed on the relation between n and t simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice

stability under persistent disturbances for systems with impulse effect abstract problems concerning the stability of the solution of systems of ordinary differential equations with impulse effect under persistent disturbances are investigated for the first time definitions for stability and unstability of the system considered are introduced the main results are formulated in two theorems in the proofs of the theorems a new analogue of the gronwall belmann inequality for piecewise continuous functions is applied

new family of triangular norms for decreasing generators in the form of a logarithm of a linear fractional function abstract the purpose of this paper is to establish restrictions on the parameters under which a function in the form of a natural logarithm of a linear fractional function is a decreasing generator in addition to the general case all special cases of generators of this type are considered a triangular norm is constructed for each generator in fact a new parametric class of decreasing generators that generalizes and systematizes known generators is proposed such generators generate triangular norms represented by rational functions the results of this paper can be used to construct aggregation operations

ranking fuzzy multicriteria alternatives with respect to a decision maker s fuzzy goal abstract a two stage method for ranking fuzzy multicriteria alternatives with respect to a decision maker s fuzzy goal is presented in the first stage the joint membership function of each fuzzy alternative and the membership function of the fuzzy goal are projected orthogonally from the multicriteria space to the one dimensional preference subspace of the decision maker in the second stage a ranking index is used to rank the fuzzy projections in the decision maker s preference subspace a numerical example demonstrates the method

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

remarks on the analytic hierarchy process the analytic hierarchy process ahp is flawed as a procedure for ranking alternatives in that the rankings produced by this procedure are arbitrary this paper provides a brief review of several areas of operational difficulty with the ahp and then focuses on the arbitrary rankings that occur when the principle of hierarchic composition is assumed this principle requires that the weights on the higher levels of a hierarchy can be determined independently of the weights on the lower levels virtually all of the published examples of the use of the ahp to evaluate alternatives relative to a set of criteria have assumed this principle the key to correcting this flaw is the synthesis of the ahp with the concepts of multiattribute utility theory

generalized medians distance aggregation operators are introduced in the case of singleton based distance a well known class of k medians is recovered for interval based distance characterization of p r distance aggregation operators is given in general as well as for idempotent operators based on the triangle of median factors medians are introduced owa operators are shown to be a linear convex combination of special j medians

a note on continuity in scalarization for multicriteria optimization problems we establish sufficient conditions for solutions of scalarization replacements of multicriteria optimization problems to exhibit continuous dependence on scaling factors and other parameters

testing the apt with the maximum sharpe ratio of extracted factors this paper develops a test of the asymptotic arbitrage pricing theory apt via the maximum squared sharpe ratio of the factors extracted from individual stocks using the connor korajczyk method the test treats the beta pricing relation as approximate without predetermining the systematic factors unlike the existing tests that take the relationship as exact and systematic factors as given this paper also examines the magnitude of pricing errors bounded partly by the maximum squared sharpe ratio for most 60 month subperiods of the sample the hypothesis that the maximum squared sharpe ratio for monthly returns is greater than 0 25 can be rejected simulation indicates that the average pricing error in monthly returns is less than 0 001 these results support the asymptotic apt

designing and learning of adjustable quasi triangular norms with applications to neuro fuzzy systems we introduce a new class of operators called quasi triangular norms they are denoted by h and parameterized by a parameter spl nu h a sub 1 a sub 2 a sub n spl nu from the construction of function h it follows that it becomes a t norm for spl nu 0 and a dual t conorm for spl nu 1 for spl nu close to 0 function h resembles a t norm and for spl nu close to 1 it resembles a t conorm in the paper we also propose adjustable quasi implications and a new class of neuro fuzzy systems most neuro fuzzy systems proposed in the past decade employ engineering implications defined by a t norm as the minimum or product in our proposition a quasi implication i a b spl nu varies from an engineering implication t a b to corresponding s implication as spl nu goes from 0 to 1 consequently the structure of neuro fuzzy systems presented in this work is determined in the process of learning learning procedures are derived and simulation examples are presented

on the asymptotic properties of the solutions of systems of differential equations with impulse effect abstract in the present paper sufficient conditions have been obtained under which the solutions of the initial value problem for a nonlinear system with impulse effect tend to a constant as t

normal constraint method with guarantee of even representation of complete pareto frontier multiobjective optimization is rapidly becoming an invaluable tool in engineering design a particular class of solutions to the multiobjective optimization problem is said to belong to the pareto frontier a pareto solution the set of which comprises the pareto frontier is optimal in the sense that any improvement in one design objective can only occur with the worsening of at least one other accordingly the pareto frontier plays an important role in engineering design it characterizes the tradeoffs between conflicting design objectives some optimization methods can be used to automatically generate a set of pareto solutions from which a final design is subjectively chosen by the designer for this approach to be successful the generated pareto set must be truly representative of the complete optimal design space pareto frontier in other words the set must not overrepresent one region of the design space or neglect others some commonly used methods comply with this requirement whereas others do not this paper offers a new phase in the development of the normal constraint method which is a simple approach for generating pareto solutions that are evenly distributed in the design space of an arbitrary number of objectives the even distribution of the generated pareto solutions can facilitate the process of developing an analytical expression for the pareto frontier in n dimension an even distribution of pareto solutions also facilitates the task of choosing the most desirable final design from among the set of pareto solutions the normal constraint method bears some similarities to the normal boundary intersection and constraint methods importantly the developments presented in this paper define its critical distinction namely the ability to generate a set of evenly distributed pareto solutions over the complete pareto frontier examples are provided that show the normal constraint method to perform favorably under the new developments when compared with the normal boundary intersection method as well as with the original normal constraint method

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

increasing selective pressure towards the best compromise in evolutionary multiobjective optimization the extended nosga method most current approaches in the evolutionary multiobjective optimization literature concentrate on adapting an evolutionary algorithm to generate an approximation of the pareto frontier however finding this set does not solve the problem the decision maker still has to choose the best compromise solution out of that set here we introduce a new characterization of the best compromise solution of a multiobjective optimization problem by using a relational system of preferences based on a multicriteria decision aid way of thinking and an outranked based dominance generalization we derive some necessary and sufficient conditions which describe satisfactory approximations to the best compromise such conditions define a lexicographic minimum of a bi objective optimization problem which is a map of the original one the nosga ii method is a nsga ii inspired efficient way of solving the resulting mapped problem

logic based fuzzy neurocomputing with unineurons in this paper we introduce a new category of logic neurons unineurons that are based on the concept of uninorms as uninorms form a certain generalization of the generic categories of fuzzy set operators such as t norms and t conorms the proposed unineurons inherit their logic processing capabilities which make them flexible and logically appealing we discuss several fundamental categories of uninorms such as uni or uni and and alike in particular we focus on the interpretability of networks composed of unineurons leading to several categories of rules to be exploited in rule based systems the learning aspects of the unineurons are presented along with detailed optimization schemes experimental results tackle two categories of problems such as a a logic approximation of fuzzy sets and b a design of associations between information granules where the ensuing development schemes directly relate to the fundamentals of granular fuzzy modeling

continuous generated associative aggregation operators continuous generated associative aggregation operators are discussed the only asymmetric solutions are the trivial operators of the projection to the first or the last coordinate respectively the only nontrivial convenient aggregation operators are necessarily symmetric and they are either continuous archimedean t norms and t conorms or generated nullnorms the latter may combine any nilpotent t conorm and any t norm with any prescribed annihilator k 0 1

fuzzy integral in multicriteria decision making abstract this paper presents a synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making definitions essential properties are given and compared to those of usual aggregation operators a quick survey on applications is given

stability of linear impulsive differential equations abstract in the present paper the notion of stability of linear impulsive differential equations at fixed moments is made more precise

a bayesian approach to testing the arbitrage pricing theory abstract we consider new methods of testing the restrictions imposed on asset returns implied by an equilibrium version of the arbitrage pricing theory in the competitive equilibrium version of the apt see for example connor and korajczyk 1988 excess returns on a collection of portfolios or individual assets are related to measured factors in a multivariate regression model without intercepts the traditional significance testing approach uses estimates of these intercept terms and a likelihood ratio procedure for statistical testing in our approach we quantify differences between the restricted and unrestricted models by computing posterior model probabilities these posterior model probabilities are combined to form posterior odds ratios which represent the weight of prior and sample evidence for or against the pricing restrictions a dramatic simplification of the odds ratio calculation is achieved by using the savage density ratio method the special structure of the apt model with factors extracted by principal components is exploited to produce a simple prior the sensitivity of the odds ratio to different prior specifications is explored we apply these new methodologies to tests of the apt with a collection of ten size based portfolios the factors are extracted by a principal components technique developed by connor and korajczyk using all listed amex nyse firms over the period 1964 1983 the odds ratios show that the sample evidence is weak and does not favor the apt pricing restrictions we are able to gauge the strength of the evidence in the data by examining the sensitivity of the odds ratio to the prior

criteria importances in median like aggregation an axiomatization of criteria importances appearing in a given aggregation operator is proposed some distinguished examples are recalled for the class of k medians an integral based approach for inclusion of criteria importances is introduced several examples are given the case of ordinal scales is also discussed

extensions of a theorem of wintner on systems with asymptotically constant solutions a theorem of wintner concerning sufficient conditions for a system y a t y to have linear asymptotic equilibrium is extended to a system x a t x f t x the integrability conditions imposed on permit conditional convergence of some of the improper integrals that occur the results improve on wintner s even if 0

triangular norm based iterative compensatory operators abstract aggregation operators based on a fixed t norm and on suitable transformations of processed data are introduced a special attention is paid to the class of iterative compensatory operators containing also the classical arithmetic geometric and harmonic means several properties of introduced operators are studied e g the symmetry the associativity the idempotency the anihilation etc several examples are given including continuous idempotent bisymmetric iterative compensatory operators with zero anihilator

evolutionary constrained optimization using an addition of ranking method and a percentage based tolerance value adjustment scheme one of the most important issues in developing an evolutionary optimization algorithm is the proper handling of any constraints on the problem one must balance the objective function against the degree of constraint violation in such a way that neither is dominant common approaches to strike this balance include implementing a penalty function and the more recent stochastic ranking method but these methods require an extra tuning parameter which must be chosen by the user the present paper demonstrates that a proper balance can be achieved using an addition of ranking method through the ranking of the individuals with respect to the objective function and constraint violation independently we convert these two properties into numerical values of the same order of magnitude this removes the requirement of a user specified penalty coefficient or any other tuning parameters direct addition of the ranking terms is then performed to integrate all information into a single decision variable this approach is incorporated into a m l evolution strategy and tested on thirteen benchmark problems one engineering design problem and five difficult problems with a high dimensionality or many constraints the performance of the proposed strategy is similar to that of the stochastic ranking method when dealing with inequality constraints but it has a much simpler ranking procedure and does not require any tuning parameters a percentage based tolerance value adjustment scheme is also proposed to enable feasible search when dealing with equality constraints

strange an interactive method for multi objective linear programming under uncertainty abstract in the field of investment planning within a time horizon problems typically involve multiple objectives and basic data are uncertain in a large number of cases these decision problems can be written as linear programming problems in which time dependent uncertainties affect the coefficients and the right hand side of constraints given the possibility of defining plausible scenarios on basic data discrete sets of such coefficients are given each with its subjective probability of occurrence the corresponding structure is then characteristic for multi objective stochastic linear programming moslp in the paper an interactive procedure is described to obtain a best compromise for such a moslp problem this algorithm called strange extends the stem method to take the random aspects into account it involves in particular the concepts of stochastic programming with recourse in its interactive steps the efficiency projection techniques are used to provide the decision maker with detailed graphical information on efficient solution families as an illustration of the successive steps a didactic example is solved in some detail and the results of a case study in energy planning are given

on the asymptotic equivalence of systems with impulse effect abstract in the present paper sufficient conditions for asymptotic equivalence and restricted asymptotic equivalence of a linear system of differential equations with impulse effect and its respective perturbed non linear system are found

fuzzy linear programming problems with fuzzy numbers abstract linear programming problems with fuzzy parameters are formulated by fuzzy functions the ambiguity considered here is not randomness but fuzziness which is associated with the lack of a sharp transition from membership to nonmembership parameters on constraint and objective functions are given by fuzzy numbers in this paper our object is the formulation of a fuzzy linear programming problem to obtain a reasonable solution under consideration of the ambiguity of parameters this fuzzy linear programming problem with fuzzy numbers can be regarded as a model of decision problems where human estimation is influential

mathematical and pragmatic perspectives of physical programming physical programming pp is an emerging multiobjective and design optimization method that has been applied successfully in diverse areas of engineering and operations research the application of pp calls for the designer to express preferences by defining ranges of differing degrees of desirability for each design metric although this approach works well in practice it has never been shown that the resulting optimal solution is not unduly sensitive to these numerical range definitions pp is shown to be numerically well conditioned and its sensitivity to designer input with respect to optimal solution is compared with that of other popular methods the important proof is provided that all solutions obtained through pp are pareto optimal and the notion of pareto optimality is extended to one of pragmatic implication the important notion of p dominance that extends the concept of pareto optimality beyond the cases minimize and maximize is introduced p dominance is shown to lead to the important concept of generalized pareto optimality numerical results are provided that illustrate the favorable numerical properties of physical programming