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Considers a conceptual model that leads to the notions of a “distance function” g(t) and that of a “controlled‐disturbance function” δ(t)=h(g(t)). Using these notions we begin a mathematical theory of a system that is self‐organizing to achieve a given state of affairs in a given environment. Obtains, in terms of the functions δ(t) and g(t), a condition under which the system always progresses towards the goal. We also establish the form of expression for the distance function g(t). This comes as a major tool in the proofs of the so‐called goal‐state‐description theorems. These theorems have results that facilitate the determination of the “working functions” of the self‐organizing system (SOS). When they exist, the “working functions” specify a goal‐path for the SOS to learn to adopt.

The set of fuzzy threshold functions is defined to be a fuzzy set over the set of functions. All threshold functions have full memberships in this fuzzy set. Defines and investigates a distance measure between a non‐linearly separable function and the set of all threshold functions. Defines an explicit expression for the membership function of a fuzzy threshold function through the use of this distance measure and finds three upper bounds for this measure. Presents a general method to compute the distance, an algorithm to generate the representation automatically, and a procedure to determine the proper weights and thresholds automatically. Presents the relationships among threshold gate networks, artificial neural networks and fuzzy neural networks. The results may have useful applications in logic design, pattern recognition, fuzzy logic, multi‐objective fuzzy optimization and related areas.

This paper proposes the use of a gauge function as a measure of technical efficiency. The measure of technical inefficiency from a gauge function is desirable as the estimation of a gauge function is not subject to the endogeneity problem under the behavioral assumption of profit maximization in the competitive market.

The authors address three important properties of a gauge function, i.e. linear homogeneity, monotonicity and convexity in inputs and outputs, and show how such properties are utilized in its estimation. Then, the authors apply the estimation of a gauge function to US Blacksmiths in 1850 and 1880 to show that a failure to satisfy such properties may lead to an incorrect inference on the technical efficiency.

The authors find that the Blacksmiths in the 1850s were technically more efficient than the ones in the 1880s, indicating technical regress in Blacksmithing when the properties are satisfied.

This paper introduces a measure of technical inefficiency from a gauge function and shows how to estimate the gauge function parametrically for the measure. The authors show McFadden's gauge function and its properties, which differ from the properties of other distance functions. The authors emphasize linear homogeneity as well as monotonicity and convexity in inputs and outputs, which must be satisfied in the estimation of a gauge function.

This paper discusses a knowledge based information retrieval model with hierarchical thesaurus. The model computes the conceptual distance between a query and an object and both are indexed with weighted terms from a hierarchical thesaurus. The hierarchical thesaurus is represented by a hierarchical‐concept graph (HCG) in which nodes represent concepts and directed edges represent generalisation relationships. Rada et al. have developed a similar model. However, their model considered only a binary indexing scheme and revealed some counter‐intuitive results. Our proposed model extends theirs by allowing the index term and the edge of the HCG to be weighted. A new concept mapping method is devised to overcome Rada's counter‐intuitive results. In addition, a scheme for allowing Boolean operators in user queries is provided with a formula for computing conceptual distance from negated index terms. Experimental results have shown that our model simulates human performance more closely than Rada's model.

The COVID-19 pandemic has forced countries to consider how to reach vulnerable communities with extended outreach services to improve vaccination uptake. The authors created an optimization model to align with decision-makers' objective to maximize immunization coverage within constrained budgets and deploy resources considering empirical data and endogenous demand.

A mixed integer program (MIP) determines the location of outreach sites and the resource deployment across health centers and outreach sites. The authors validated the model and evaluated the approach in consultation with UNICEF using a case study from The Gambia.

Results in The Gambia showed that by opening new outreach sites and optimizing resource allocation and scheduling, the Ministry of Health could increase immunization coverage from 91.0 to 97.1% under the same budget. Case study solutions informed managerial insights to drive gains in vaccine coverage even without the application of sophisticated tools.

The research extended resource constrained LMIC vaccine distribution modeling literature in two ways: first, endogenous calculation of demand as a function of distance to health facility location enabled the effective design of the vaccine network around convenience to the community and second, the model's resource bundle concept more accurately and flexibly represented complex requirements and costs for specific resources, which facilitated buy-in from stakeholders responsible for managing health budgets. The paper also demonstrated how to leverage empirical research and spatial analysis of publicly available demographic and geographic data to effectively represent important contextual factors.

Focuses on the effect of both proximity and size of shopping centres on surrounding residential property values, using hedonic modelling. States that the data bank consists of a subset of some 4,000 single‐detached, owner‐occupied housing units transacted all over the Quebec Urban Community territory between January 1990 and December 1991. Tests several functional forms and uses up to 60 descriptors. Reveals that in line with previous studies, findings indicate that shopping‐centre size exerts a positive contributory effect on values; they also tend to confirm the non‐monotonicity of the price‐distance function. Concludes that, in that respect, resorting to the gamma function for distance variables yields most interesting results and provides consistent estimates of optimal distances for various shopping‐centre size categories.

There have been several document ranking methods to calculate the conceptual distance or closeness between a Boolean query and a document. Though they provide good retrieval effectiveness in many cases, they do not support effective weighting schemes for queries and documents and also have several problems resulting from inappropriate evaluation of Boolean operators. We propose a new method called Knowledge‐Based Extended Boolean Model (kb‐ebm) in which Salton's extended Boolean model is incorporated. kb‐ebm evaluates weighted queries and documents effectively, and avoids the problems of the previous methods. kb‐ebm provides high quality document rankings by using term dependence information from is‐a hierarchies The performance experiments show that the proposed method closely simulates human behaviour.

Traditionally, economic production models consider pollution as bads that may be modeled as either outputs or inputs in economic models. The purpose of this paper is to examine the implications of these modeling choices on the measurements of productive efficiency and private costs of pollution control.

The authors apply the hyperbolic distance functions to measure trucking efficiency and the private costs of pollution control.

The results show: (i) regardless of the choice of modeling, when only one bad was incorporated in hyperbolic distance functions, the efficiency loss and private abatement cost measures derived from the two models were equivalent, but potential pollution reduction and good output expansion differed; (ii) when more than one bad were introduced, the equivalence of efficiency loss measure in (i) did not hold; and (iii) the potential amounts of pollution reduction and good output expansion were larger when bads were modeled as inputs. With multiple bads, private abatement costs varied considerably under the two modeling treatments.

From a policy standpoint, the results suggest that one should consider the modeling options with caution when multiple economic bads are involved, because the resulting measures of economic burden of pollution control differ.

The paper shows that the traditional conceptual framework for modeling pollution in hyperbolic distance functions could yield inconsistent results.

The purpose of this paper is to present the obtained analytic solutions of maximal and minimal inter-satellite distances for flying-around satellite formation.

The relative motion equation is used to express the inter-satellite distance as the function of the orbital elements of two participating satellites for the flying-around satellite formation. Then by taking the derivative of the distance function with respect to the true anomaly, some possible extreme value points are obtained. According to the detailed analysis, the maximal and minimal distance solutions are found. By a reverse process, the expected initial differential orbital elements that generate the required extreme inter-satellite distances are also obtained.

The maximal and minimal distances of the flying-around formation can be analytically written as the functions of three initial orbital elements differences, i.e. the differential orbital inclination, the differential eccentricity and the differential right ascension. For the given maximal and minimal distances, there are lots of solutions of the initial differential orbital elements, which can produce the expected relative motions.

The solutions of the maximal and minimal inter-satellite distances are only accurate for the circular or near circular reference orbit. For the elliptic reference orbit, there is a need to develop new methods to find the analytic solutions.

The results here can be applied to design the factual flying-around formation with dimension requirements in mission analysis stage.

By using the solutions presented in this paper, the engineers can design the expected flying-around formation with required maximal and minimal inter-satellite distances in a very easy way.

Inverse distance weighted (IDW) functions are utilized to make models of heterogenous materials such as functionally graded materials (FGM) in computer aided design (CAD). However, the use of IDW function based FGM for stress concentration reduction is scarcely available in the literature. The present work aims to analyze and reduce the stress concentration around a circular hole in IDW function-based finite FGM panel under biaxial loading.

Extended finite element method (XFEM) model was prepared using MATLAB to investigate the effect of geometrical and material parameters on the stress concentration factor (SCF). The obtained results of IDW FGM are compared with homogeneous material as well as two different FGMs based on the power-law function.

It was observed that the IDW function based FGM is simple in material modeling, conformal with all domain boundaries and shows lower stress concentration in comparison with the homogeneous material case. While comparing IDW FGM with power-law based FGMs, it was observed that the IDW FGM has least values of stress concentration for low d/W (diameter of the hole to panel width ratio) and is comparable with power-law based FGMs for high d/W.

It can be stated that IDW FGM is highly suitable for stress concentration reduction in finite panels with d/W = 0.5, which can further be intended for obtaining optimum hole and panel designs.