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As a key research area in data mining technologies, outlier detection can expose data inconsistent with the majority in the dataset and therefore is applicable in extensive areas. The addition of entropy weighting to the spatial local outlier measure (SLOM) and local distance-based outlier factor (LDOF) algorithms in outlier data mining, i.e., the adoption of entropy in the calculation of weighted distance is taken into consideration, leads to enhanced accuracy of outlier detection and produces more expense of time. The algorithm of entropy-weighted LDOF is more optimised than that of entropy-weighted SLOM in terms of detection accuracy. The superiority of the entropy-weighted algorithm is verified through experimental results.

Aimed at solving difficulties of managing test routing and matching resource ,this paper brings out an instrument resource matching algorithm based on minimum weighted distance .The algorithm adopts weighted distance to describe similarity between signals , while weight value is determined by experts' experience with consideration of actual condition ,which can describe similarity more reasonable .At the same time the strategy and algorithm of resource matching are given ,serial and parallel testing are optimized with simpler and rapider criterion. Application example tests the method possess better routing management capability ,strengthens system reliability and improves resource matching and routing management efficiency on the basis of testing demand models and instrument resource models.

Positioning scheme is one of the fundamental issue in wireless sensor network (WSN), especially for the situation needing the accurate position of sensed information. Many approaches have been performed to identify the inaccurate node localization. DV-Hop (Distance Vector-hop) is a well-known localization algorithm [1,2]. In wireless sensor network with conventional algorithm for DV-Hop localization, ordinary nodes use average hop distance value estimated by the nearest beacon node to locate themselves. However, hop distance value estimated by only one beacon node may not reflect the true situation accurately. For the purpose of further improving the position accuracy, in view of the analysis of DV-HOP algorithm, this paper presents a strengthen method of weighted distance: ordinary nodes reference estimated average hop distance node and operate on weighted numbers of hop from multiple beacon nodes to make network average hop distance estimate more accurate and improve positioning accuracy. Results from simulation show that the proposed WDV-Hop algorithm has been greatly improved by 10%–15% in terms of the accuracy of positioning compared to the conventional DV-Hop.

Traditional PSO(Particle Swarm Optimization) algorithm has the problems of particle cross-border and premature convergence while solving the normalized constrained optimization problem. Our paper uses the attractor and spatial zoom method, and presented the normalized PSO algorithm. Secondly, each attribute is treated equally in the traditional classification algorithm, without considering the differences in attribute measure and contribution, which cause the problem of low classification accuracy. Our paper introduce the use of the normalized PSO algorithm to solve the optimal attribute normalized weighted distance. For example, in KNN classifier, leave-one-out experimental results with multiple UCI data sets show that the classification accuracy using normalization PSO algorithm to calculate normalized weighted distance is higher than using PSO algorithm and traditional none-attribute weighted classifiers.

© 2016 IEEE. The aim of the paper is to develop new aggregation operators using Bonferroni means, ordered weighted averaging (OWA) operators and some distance measures. We introduce the Bonferroni-Hamming weighted distance, Bonferroni OWA distance, and Bonferroni distances with OWA operators and weighted averages. The main advantages of using these operators are that they allow considering different aggregations contexts, multiple-comparison between each argument and distance measures in the same formulation.

The paper undertakes the estimation of two alternative indicators of integration—potential trade and trade distance—by estimating the Global Gravity Model, consisting a panel data of nearly 100 largest trading partners of the world and 12–years period during 2002–13. Empirical results show that South Asia utilizes only 14 per cent of its intra-regional trade potential. Considering the global experience, this would indicate that implied average distance between South Asian trading pairs is 3,240 km, significantly higher than the actual geographical weighted distance of 1,872 km. Two pairs—India-Pakistan and India-Bangladesh—are found to be majorly responsible for low integration in South Asia.

A novel clustering method for bivariate functional data is proposed to group streams based on their water-air temperature relationship. A distance measure is developed for bivariate curves by using a time-varying coefficient model and a weighting scheme. This distance is also adjusted by spatial correlation of streams via the variogram. Therefore, the proposed distance not only measures the difference among the streams with respect to their water-air temperature relationship but also accounts for spatial correlation among the streams. The proposed clustering method is applied to 62 streams in Southeast US that have paired air-water temperature measured over a ten-month period. The results show that streams in the same cluster reflect common characteristics such as solar radiation, percent forest and elevation. Copyright (C) 2015 John Wiley & Sons, Ltd USFS Southern Research StationUnited States Department of Agriculture (USDA)United States Forest Service [JV 2010 11330140-137] We thank Joe Cline for data collection and management, and the USFS Southern Research Station for support under JV 2010 11330140-137. Helpful comments from Hongxiao Zhu on the manuscript were appreciated. Public domain – authored by a U.S. government employee

The aim of this paper is to develop the continuous intuitionistic fuzzy ordered weighted distance (C-IFOWD) measure by using the continuous intuitionistic fuzzy ordered weighted averaging (C-IFOWA) operator in the interval distance. We investigate some desirable properties and different families of the C-IFOWD measure. We also generalize the C-IFOWD measure. The prominent characteristics of the C-IFOWD measure are that it is not only a generalization of some widely used distance measure, but also it can deal with interval deviations in aggregation on interval-valued intuitionistic fuzzy values (IVIFVs) by using a controlled parameter, which can decrease the uncertainty of argument and improve the accuracy of decision. The desirable characteristics make the C-IFOWD measure suitable to wide range situations, such as decision making, engineering and investment, etc. In the end, we introduce a new approach to group decision making with IVIFVs in human resource management. First published online:18 Sep 2015

The WeDiBaDis package provides a user friendly environment to perform discriminant analysis (supervised classification). WeDiBaDis is an easy to use package addressed to the biological and medical communities, and in general, to researchers interested in applied studies. It can be suitable when the user is interested in the problem of constructing a discriminant rule on the basis of distances between a relatively small number of instances or units of known unbalanced-class membership measured on many (possibly thousands) features of any type. This is a current situation when analyzing genetic biomedical data. This discriminant rule can then be used both, as a means of explaining differences among classes, but also in the important task of assigning the class membership for new unlabeled units. Our package implements two discriminant analysis procedures in an R environment: the well-known distance-based discriminant analysis (DB-discriminant) and a weighteddistance- based discriminant (WDB-discriminant), a novel classifier rule that we introduce. This new procedure is based on an improvement of the DB rule taking into account the statistical depth of the units. This article presents both classifying procedures and describes the implementation of each in detail. We illustrate the use of the package using an ecological and a genetic experimental example. Finally, we illustrate the effectiveness of the new proposed procedure (WDB), as compared with DB. This comparison is carried out using thirty-eight, high-dimensional, class-unbalanced, cancer data sets, three of which include clinical features.

The interval 2-tuple linguistic representation method (Zhang 2012) is a useful computational model for computing with words, which has the capability of expressing different types of decision makers’ assessment information and has been widely used in many real-world engineering and management problems. Moreover, via this method, decision makers can express their preferences by the use of linguistic term sets with different granularity of uncertainty.

The webgraph link structure of an E-supermarket website is different from static websites. E-commerce companies want to make the browsing experience of their customers hassle free. This can be done by frequently rearranging the link structure of the website according to changing browsing patterns of the users. Only few methods have been developed to optimally design the link structure of an E-supermarket website. In this paper, an ant colony system (ACS) is used to optimize the link structure of E-supermarket website. It has been observed that the ant colony-based method improves the link structure by decreasing the overall weighted distance between webpages. The performance issues of ACS-based method for E-supermarket link structure optimization are also presented.

Automatic image annotation is a challenging problem due to the label-image-matching, label-imbalance and label-missing problems. Some research tried to address part of these problems but didn't integrate them. In this paper, an adaptive weighted distance method which incorporates the CNN convolutional neural network feature and multiple handcrafted features is proposed to handle the label-image-matching and label-imbalance issues, while the K nearest neighbors framework is improved by using the neighborhood with all labels which can reduce the effects of the label-missing problem. Finally, experiments on three benchmark datasets Corel-5k, ESP-Game and IAPRTC-12 for image annotation are performed, and the results show that our approach is competitive to the state-of-the-art methods.

Selects 58 tourist attraction in Lanzhou,based on GIS, analyses its Spatial structure by means of Nearest Neighbor Index,Geographic Concentration Index and Gini Coefficient index;calculates the spatial accessibility of tourist attraction using cost weighted distance method.Analysis showed:the whole,the Nearest Neighbor Index of Lanzhou tourist attractions is 0.77,exhibit an aggregated and uneven distribution.the internal differences of Spatial structure is evident,the Nearest Neighbor Index of Chengguan is 0.56,the lowest,the highest is Gaolan county,about 1.23.To provide a reference through this research for the sustainable development of tourism in Lanzhou.

In this paper we introduce the weighted distances on the Khalimsky grid. There are two types of natural neighborhood relations and one semi-neighborhood is also defined. Based on them two types of weighted distances are defined. We give formulae for computing the weighted distance of any point-pair on the Khalimsky grid in both cases.

We consider the p-median problem which is to find the location of p-facilities so as to minimize the average weighted distance or time between demand points and service centers. Many heuristic algorithms have been proposed for this problem. In this paper we present a simple new heuristic which is effective for moderately size problem. The heuristic uses a reduction and an exchange procedure. Our methodology is tested on 400 randomly generated problems with 10 to 50 customer locations as well as 6 well known literature test problems. We also compare our method with the Branch and Bound method in terms of quality and computational time using a larger problem size of 150 customer locations. For the random problems the generated solutions were on average within 0.61 % of the optimum. A similar result was achieved for the literature test problems. A comparative analysis with literature heuristics supports the superiority of our method. The computational time of our heuristic is 0.75 % of the Branch and Bound Method. We also apply our heuristic to a case study involving the location of emergency vehicles (ambulances) in Perth City (Australia).

A natural methodology for discriminating functional data is based on the distances from the observation or its derivatives to group representative functions (usually the mean) or their derivatives. It is proposed to use a combination of these distances for supervised classification. Simulation studies show that this procedure performs very well, resulting in smaller testing classification errors. Applications to real data show that this technique behaves as well as-and in some cases better than-existing supervised classification methods for functions.

The urban expansion direction and mode of Shizuishan City is addressed based on GIS and improved spatial diffusion model-replacing the spatial straight distance with cost weighted distance. This paper divides its spatial expansion into four cases: zero resistance, resistance, incomplete barrier and isolation. The diffusion model of urban space in terms of the new understanding of the resistance barrier in the spatial diffusion process is discussed. Then, this paper puts forward new trends of spatial development. The results reveal that Dawukou city area and Pingluo city, and Wuhai city and Huinong district form the coordination development tendency.

The ordered weighted distance and is a new decision-making technique, having been proved useful for the treatment of input data in the form of exact numbers. In this paper, we consider the situation with intuitionistic fuzzy information and develop an intuitionistic fuzzy ordered weighted distance (IFOWD) operator. The IFOWD operator is very suitable to deal with the situations where the input data are represented in intuitionistic fuzzy information and includes a wide range of distance measures and aggregation operators. We study some of its main properties and different families of IFOWD operators. Finally, we develop an application of the new approach in a group decision-making under intuitionistic fuzzy environment and illustrate it with a numerical example.

Xu and Chen (J Syst Sci Syst Eng 17:432–445, 2008) introduced a new decision-making technique called the ordered weighted distance (OWD) measure, having been proved useful for the treatment of situation where the available information is represented in exact numerical values. In this paper, we consider the situations with intuitionistic fuzzy and interval-valued intuitionistic information, and develop some intuitionistic fuzzy weighted distance measures such as intuitionistic fuzzy ordered weighted distance (IFOWD) measure, interval-valued intuitionistic fuzzy ordered weighted distance (IVIFOWD) measure, intuitionistic fuzzy hybrid weighted distance (IFHWD) measure and interval-valued intuitionistic fuzzy hybrid weighted distance (IVIFHWD) measure. These developed weighted distance measures are very suitable to deal with the situation where the input data are represented in intuitionistic fuzzy numbers or interval-lvalued intuitionistic fuzzy numbers. Then we present a consensus reaching process for group decision making with intuitionistic fuzzy preference information based on the developed distance measures. Finally, a practical application of he developed approach to the problem of evaluating university faculty for tenure and promotion is given.

In this paper, we propose a variety of distance measures for hesitant fuzzy sets, based on which the corresponding similarity measures can be obtained. We investigate the connections of the aforementioned distance measures and further develop a number of hesitant ordered weighted distance measures and hesitant ordered weighted similarity measures. They can alleviate the influence of unduly large (or small) deviations on the aggregation results by assigning them low (or high) weights. Several numerical examples are provided to illustrate these distance and similarity measures.

This paper calculated spatial accessibility of all counties (city, urban district) in China with cost weighted distance method. Region divisions of county accessibility were conducted, and relation of traffic accessibility and population aggregation was discussed in this paper. The results indicated that county accessibility in China had mainly low values and a distribution structure of circle layer and reverse-to-natural gradient. There was an obvious correlation between county accessibility and population density in China. With these analyses, inner mechanisms of population migration in different traffic conditions and region types were revealed, and can provide useful proposals to regional planning, traffic planning and smart distribution of people in China.

We are interested in locations of multiple facilities in the plane with the aim of minimizing the sum of weighted distance between these facilities and regional customers, where the distance between a facility and a regional customer is evaluated by the farthest distance from this facility to the demand region. By applying the well-known location-allocation heuristic, the main task for solving such a problem turns out to solve a number of constrained Weber problems (CWPs). This paper focuses on the computational contribution in this topic by developing a variant of the classical Barzilai-Borwein (BB) gradient method to solve the reduced CWPs. Consequently, a hybrid Cooper type method is developed to solve the problem under consideration. Preliminary numerical results are reported to verify the evident effectiveness of the new method.

The p-median and flow-refueling models are two of the more popular models for optimal location of alternative-fuel stations. The p-median model, one of the most widely used location models of any kind, locates p facilities and allocates demand nodes to them to minimize total weighted distance traveled. In comparison, the flow-refueling location model (FRLM) is a path-based demand model that locates p stations to maximize the number of trips on their shortest paths that can be refueled. For a path to be considered refuelable, one or more stations must be located on the path in a way that allows the round trip to be completed without running out of fuel, given the vehicle driving range. In this paper, we analyze how well the facilities located by each model perform on the other’s objective function on road networks in Florida. While each objective function degrades somewhat when facilities are located by the other model, the stations located by the flow-refueling model generally do better on the p-median objective than the stations located by the p-median model do on the flow-refueling objective. This difference between the two models is even more pronounced at the state scale than at the metropolitan scale. In addition, the optimal locations for the FRLM tend to be more much more stable as p increases than those located by the p-median model.

The accuracy and efficiency of case retrieval decline with individuality and diversity of customer needs in current product configuration design. To cope with this problem, this paper proposes the method of case retrieval based on NRS and KNN. Firstly, setting neighbor value can effectively avoid errors generated by discretization of continuous attributes in classical RS. Secondly, NRS is used for redundant reduction and weight allocation of attributes, and to calculate distance of each sample points by weighted distance. Thirdly, K similar cases are selected according to Euclidean distance with weight, then the case that meet customer needs best is acquired. Lastly, product configuration of coal mining machine is used to illustrate that accuracy and efficiency of the method are superior to the existing methods of case retrieval.

Considerable interest has been directed in the past to developing approaches for solving the p-median problem with maximum distance constraints. All current solution techniques consider potential facilities to be located only at nodes of the network. This paper deals with the solution of this problem under the condition where facility placement is not restricted to nodes. The examples given show that improvement in weighted distance can be obtained by solving the unrestricted site problem. In addition, feasible solutions can be obtained for smaller numbers of facilities than possible by all nodal facility placement.

The objective of this study was to determine the best probability distributions of annual, seasonal and monthly precipitation in Korea. Data observed at 32 stations in Korea were analyzed using the L-moment ratio diagram and the average weighted distance (AWD) to identify the best probability distributions of each precipitation. The probability distribution was best represented by 3-parameter Weibull distribution (W3) for the annual precipitation, 3-parameter lognormal distribution (LN3) for spring and autumn seasons, and generalized extreme value distribution (GEV) for summer and winter seasons. The best probability distribution models for monthly precipitation were LN3 for January, W3 for February and July, 2-parameter Weibull distribution (W2) for March, generalized Pareto distribution (GPA) for April, September, October and November, GEV for May and June, and log-Pearson type III (LP3) for August and December. However, from the goodness-of-fit test for the best probability distributions of the best fit, GPA for April, September, October and November, and LN3 for January showed considerably high reject rates due to computational errors in estimation of the probability distribution parameters and relatively higher AWD values. Meanwhile, analyses using data from 55 stations including additional 23 stations indicated insignificant differences to those using original data. Further studies using more long-term data are needed to identify more optimal probability distributions for each precipitation.

By terms of extracting quantization values of each index making contributions to classification, this paper defines index classification weight; and also defines class representative points, weighted distance between samples and representative points; provides an iterative algorithm of searching class representative points, establishes a supervised clustering method based on representative points and it is apply into Fault diagnosis of Diesel Engine.

In 2007, Zeng and Li proposed a weighted triangular approximation of a fuzzy number. Unfortunately, this approximation may fail to be a fuzzy number. In this paper, we improve this approximation and propose a generalization by the name of weighted trapezoidal approximation. Their algorithms are also presented. Finally, some examples and relevant properties are discussed.

Nonuniform tubular neighborhoods of curves in R n are studied by using weighted distance functions and generalizing the normal exponential map. Different notions of injectivity radii are introduced to investigate singular but injective exponential maps. A generalization of the thickness formula is obtained for nonuniform thickness. All singularities within almost injectivity radius are classified by the Horizontal Collapsing Property. Examples are provided to show the distinction between the different types of injectivity radii, as well as showing that the standard differentiable injectivity radius fails to be upper semicontinuous on a singular set of weight functions.

Layout of temporary construction facilities (objects) is an important activity during the planning process of construction projects. The construction area layout is a complex problem whose solution requires the use of analytical models. Existing popular models employ genetic algorithms that have proven to be useful tools in generating near optimal site layouts. This paper presents an alternative approach based on mathematical optimization that offers several important features and generates a global optimal solution. The construction area consists of an unavailable area that includes existing facilities (sites) and available area in which the objects can be located. The available area is divided into regions that are formulated using binary variables. The locations of the objects are determined by optimizing an objective function subject to a variety of physical and functional constraints. The objective function minimizes the total weighted distance between the objects and the sites as well as among the o...

This paper considers the problem of locating semi-obnoxious facilities assuming that ''too close'' demand nodes can be expropriated by the developer at a given price. The objective is to maximize the minimum weighted distance from the facility to the non-expropriated demand nodes given a limited budget while taking into account the fact that customers do not want to be too far away from the facility. Two models of this problem on a network are presented. One is to minimize the difference between the maximum and the minimum weighted distances. The other one is to maximize the minimum weighted distance subject to an upper bound constraint on the maximum weighted distance. The dominating sets are determined and efficient algorithms are presented.

Bilateral trade of geographically distant countries is likely to be negatively affected by the distance separating them from their trading partners and positively affected by their remoteness, defined as the average weighted distance between two countries with weights reflecting the absorptive capacity of the partner country. In presence of competitive transport costs, the effect of remoteness and distance is diluted. An augmented gravity model applied to the Pacific islands' bilateral trade from 1980 to 2004 shows that a doubling of the elasticity of distance would decrease their average bilateral trade by 80 per cent. Remoteness positively affects the Pacific islands' bilateral trade, but does not compensate for the negative effect of distance. The opposite is found for the Caribbean islands, where the elasticity of trade with respect to remoteness is six times bigger than that for the Pacific islands. By lowering transport costs, improved infrastructure fosters trade. A cluster analysis for 30 small island developing states shows that the Pacific islands belong to the clusters with the weaker infrastructure stocks, leaving them with a large scope for improvement. Copyright © 2008 John Wiley & Sons, Ltd.

The method of L-moment ratio diagrams and the average weighted distance (AWD) are used to determine the probability distribution type of annual, seasonal and monthly precipitation in Japan. For annual precipitation, the log-Pearson type III (LP3) distribution provides the best fit to the observations with the generalized-extreme value (GEV), three-parameter lognormal (LN3) and Pearson type III (P3) distributions as potential alternatives. For seasonal precipitation, the P3 distribution shows the best fit to the observations of spring precipitation; the LP3 the best fit for summer and winter precipitation; and the LN3 the best fit for autumn precipitation with the LP3 as a potential alternative. For monthly precipitation, the P3 distribution fits the precipitation best for January, February, March, May, July, October and December; the LP3 for June; and the LN3 for April, August, September and November. The identified probability distribution types of annual, seasonal and monthly precipitation are ...

In this paper, we use the weighted distance between fuzzy numbers to investigate the approximation of arbitrary fuzzy numbers by weighted distance. We then discuss properties of the approximation strategy including continuity, translation invariance, scale invariance and identity and give an application to the generation of fuzzy partitions.

A new distance ND1 between fuzzy numbers based on an averaged representative of a fuzzy number (Weighting Average Based on Levels, WABL) is proposed. Based on this distance a new least squares regression model is proposed. The proposed model is studied for a broad class of fuzzy numbers and class of functions the membership of which is formed on the basis of the template mu([.])(x) = max(0.1 - vertical bar x vertical bar(s)).

Grey Wolf Optimizer (GWO) is one of the recently introduced Swarm Intelligence (SI) algorithms, developed by the inspiration from grey wolves prey search characteristics. The GWO algorithm imitate the hierarchical leadership and hunting mechanism of grey wolves in nature. The GWO simulates the major steps of grey wolves like hunting, searching for prey, encircling and attacking. The GWO move the wolves pack toward prey by updating location vector, which is an average of best locations of the pack. This paper addresses the GWO issues and proposes the Weighted distance Grey Wolf Optimizer (wdGWO). In proposed wdGWO algorithm, the location update strategy is modified and weighted sum of best locations is used instead of just a simple average. The proposed algorithm is well tested over set of complex benchmark problems and the performance is comprehensively compared with SI algorithms counterpart. The dimensions of the problems are varied from 10 to 50 for fair comparison among basic state of-the-art. Simulation results supports the superior performance of the proposed algorithm.

Aiming at the feature of signer-independent sign language recognition the training data complexity caused by mass data and noticeable distinctions between different people data, the weighted KNN/HMM model is presented in this paper. This model is made of two blocks, which is part of sign language classification and recognition. In classing part, the KNN (K-Nearest Neighbor, KNN) is used to learn the training samples. Considering the different contributions of sign language features to pattern classification we give different weight to different characteristics. And the category of test sample is decided by the sum of weighted distance. In recognition part, weighted KNN classification result is taken as the state-input of HMM (Hidden Markov models, HMM) to implement sign language recognition, combine with the ability to temporal data modeling and fuzzy inference of HMM model. Experiment results show that weighted KNN/HMM sign language recognition model are efficient on either recognition speed or recognition rate.

This paper aims at a dynamic gesture recognition method based on the improved DTW algorithm. Firstly, the 3D position of human skeletal points is obtained through the analysis of the depth information, which is obtained by SDK of the Kinect sensor. 8 points are selected as the hand movement characteristics, and the mathematical model of the gesture is established by the method of weighted distance. Then the DTW algorithm is improved by distortion threshold and the path constraints, which is used for training templates and dynamic gesture recognition. The results show that this method can realize the dynamic gesture recognition and have a good real-time performance and robustness. At the same time, the improved DTW algorithm has great improvement in speed and accuracy.

In the natural disasters, reserve capacity of the government affects directly the efficiency of disaster relief, especially in the crucial period. Base on current situation and problems of emergency resources reserve in China, a combination of suppliers and state central warehouse reserve method is proposed to improve emergency reserve capability. This article proposed a multi-objective approach for choosing reserve mode and quantity. The objectives are (i) minimizing total operating cost and (ii) minimizing total weighted distance. The model is solved using-constraint methods. The results derived from CPLEX based on a case study are also presented. The results indicate that the model serves as an efficient tool for handling emergency resource reserve problem.

International audience; The performance of nearest-neighbor (NN) classifiers is known to be very sensitive to the distance metric used in classifying a query pattern, especially in scarce-prototype cases. In this paper, a class-conditional weighted (CCW) distance metric related to both the class labels of the prototypes and the query patterns is proposed. Compared with the existing distance metrics, the proposed metric provides more flexibility to design the feature weights so that the local specifics in feature space can be well characterized. Based on the proposed CCW distance metric, a multi-hypothesis nearest-neighbor (MHNN) classifier is developed. The scheme of the proposed MHNN classifier is to classify the query pattern under multiple hypotheses in which the nearest-neighbor sub-classifiers can be implemented based on the CCW distance metric. Then the classification results of multiple sub-classifiers are combined to get the final result. Under this general scheme, a specific realization of the MHNN classifier is developed within the framework of Dempster-Shafer theory due to its good capability of representing and combining uncertain information. Two experiments based on synthetic and real data sets were carried out to show the effectiveness of the proposed technique.

We discuss the 1-median and l-antimedJan problems with probabilistic demand. It is assumed that demand weights of users generated at nodes of the network are independent continuous random variables. In the 1-median problem with probabilistic demand the objective is to find a location of a desirable facility on a network that maximizes the probability that the weighted sum distance does not exceed some pre-detemiined value T. In the l-antimedian problem tbe objective is to locate an undesirable facility and tbus we maximize the probability tbat the total weighted distance is at least T. We discuss how to solve the problems under arbitrary distributions and for small and large networks.

Problems of optimal object location in a plane outside rectangular forbidden gaps are considered. Objects under location are connected with one another and with the objects, located in the same plane. The criteria are the minimization of maximal weighted distance or total cost of the links between objects. A model building procedure of integer linear programming of the problems above for rectangular metric is given. Solution algorithms are briefly described. The outcomes of a numerical experiment are given.

The D. (Degree) E. (Extent) R. (Relevancy) evaluation method is increasingly adopted to assess the repair ranking of existing reinforced concrete(RC) bridges in Taiwan. The present study is the first to distinguish between relevancy (Ra, a = 1.5, 2) and non‐relevancy (Ra, a = 1) for the repair ranking of existing RC bridges to be evaluated. The generalized weighted distance method has been mainly employed to find the optimum repair ranking. Five existing RC bridges, namely Chi‐jou, Lanyang, Dah‐jea, Dah‐duh, and Dah‐an in Taiwan, are chosen as practical examples. The investigation's results show that when all the bridges are judged to be non‐relevant by the system, the repair ranking rated by the D.E.R. evaluation method is correct. However, when there are one or more important bridges, the repair ranking predicted by the D.E.R evaluation method is not accurate. The proposed method may remedy the shortcoming of the D.E.R. evaluation method. The predicted results are compared with the results obta...

Center problems or minimax facility location problems are among the most active research areas in location theory. In this paper, we find the best unique location for a facility in the plane such that the maximum expected weighted distance to all random demand points is minimized.