A Scenario-based Model for Resource Allocation with Price Information

In this paper, we consider the problem of allocating resources among Decision Making Units (DMUs). Regarding the concept of overall (cost) efficiency, we consider three different scenarios and formulate three Resource Allocation (RA) models correspondingly. In the first scenario, we assume that overall efficiency of each unit remains unchanged. The second scenario is related to the case where none of overall efficiency scores is deteriorated. We improve the overall efficiencies by a pre-determined percentage in the last scenario. We formulate Linear Programming problems to allocate resources in all scenarios. All three scenarios are illustrated through numerical and empirical examples.

A MCDM Based on Goal Programming and GIS-Based Risk Assessment for the Evaluation of Educational Locations in Conflict Areas

Conflict is recognized as a major barrier in socio-economic development. In conflict situations, most sectors such as health, food, shelter and education are adversely affected. The provision of education services to conflict-affected children saves them from becoming a lost generation and contributes to community building. Thus, we conducted this research to investigate the potential of a GIS (Geographic Information Systems) approach and risk assessment based multi-criteria decision making (MCDM) for the allocation of displaced dropped-out children to the most appropriate educational centres, taking into account multiple goals related to cost, distance, risk, etc. A two-stage approach was adopted, utilizing a risk assessment approach, and a location-allocation approach. The risk assessment approach was carried out using GIS and F-AHP (Fuzzy Analytic Hierarchy Process) to determine the risk value of each candidate educational centre in the conflict area. In the location-allocation stage, a mathematical model was developed to allocate all demands to the chosen centres. All presented methods were computationally conducted on real case data provided by direct beneficiaries and stakeholders in the 26 sub-districts in the Idleb governorate, Syria. The computational results demonstrate that the proposed approaches ensure practical and theoretical impacts.

Near Approximations in Modules

Rough set theory is a mathematical approach to imperfect knowledge. The near set approach leads to partitions of ensembles of sample objects with measurable information content and an approach to feature selection. In this paper, we apply the previous results of Bagirmaz [Appl. Algebra Engrg. Comm. Comput., 30(4) (2019) 285-29] and [Davvaz et al., Near approximations in rings. AAECC (2020). https://doi.org/10.1007/s00200-020-00421-3] to module theory. We introduce the notion of near approximations in a module over a ring, which is an extended notion of a rough approximations in a module presented in [B. Davvaz and M. Mahdavipour, Roughness in modules, Information Sciences, 176 (2006) 3658-3674]. Then we define the lower and upper near submodules and investigate their properties.

The correctness of large scale analysis of genomic data

Implementing a large genomic project is a demanding task, also from the computer science point of view. Besides collecting many genome samples and sequencing them, there is processing of a huge amount of data at every stage of their production and analysis. Efficient transfer and storage of the data is also an important issue. During the execution of such a project, there is a need to maintain work standards and control quality of the results, which can be difficult if a part of the work is carried out externally. Here, we describe our experience with such data quality analysis on a number of levels - from an obvious check of the quality of the results obtained, to examining consistency of the data at various stages of their processing, to verifying, as far as possible, their compatibility with the data describing the sample.

Assessment Methods for Evaluation of Recommender Systems: A Survey

The recommender system (RS) filters out important information from a large pool of dynamically generated information to set some important decisions in terms of some recommendations according to the user’s past behavior, preferences, and interests. A recommender system is the subclass of information filtering systems that can anticipate the needs of the user before the needs are recognized by the user in the near future. But an evaluation of the recommender system is an important factor as it involves the trust of the user in the system. Various incompatible assessment methods are used for the evaluation of recommender systems, but the proper evaluation of a recommender system needs a particular objective set by the recommender system. This paper surveys and organizes the concepts and definitions of various metrics to assess recommender systems. Also, this survey tries to find out the relationship between the assessment methods and their categorization by type.

A Soft Interval Based Decision Making Method and Its Computer Application

In today’s society, decision making is becoming more important and complicated with increasing and complex data. Decision making by using soft set theory, herein, we firstly report the comparison of soft intervals (SI) as the generalization of interval soft sets (ISS). The results showed that SIs are more effective and more general than the ISSs, for solving decision making problems due to allowing the ranking of parameters. Tabular form of SIs were used to construct a mathematical algorithm to make a decision for problems that involves uncertainties. Since these kinds of problems have huge data, constructing new and effective methods solving these problems and transforming them into the machine learning methods is very important. An important advance of our presented method is being a more general method than the Decision-Making methods based on special situations of soft set theory. The presented method in this study can be used for all of them, while the others can only work in special cases. The structures obtained from the results of soft intervals were subjected to test with examples. The designed algorithm was written in recently used functional programing language C# and applied to the problems that have been published in earlier studies. This is a pioneering study, where this type of mathematical algorithm was converted into a code and applied successfully.

Some Generalized Estimating Equations Models Based on Causality Tests for Investigation of The Economic Growth of The Country Groups

In this study, investigation of the economic growth of the Organization for Economic Cooperation and Development (OECD) countries and the countries in different income groups in the World Data Bank is conducted by using causality analyses and Generalized Estimating Equations (GEEs) which is an extension of Generalized Linear Models (GLMs). Eight different macro-economic, energy and environmental variables such as the gross domestic product (GDP) (current US$), CO2 emission (metric tons per capita), electric power consumption (kWh per capita), energy use (kg of oil equivalent per capita), imports of goods and services (% of GDP), exports of goods and services (% of GDP), foreign direct investment (FDI) and population growth rate (annual %) have been used. These countries have been categorized according to their OECD memberships and income groups. The causes of the economic growth of these countries belonging to their OECD memberships and income groups have been determined by using the Toda-Yamamoto causality test. Furthermore, various GEE models have been established for the economic growth of these countries belonging to their OECD membership and income groups in the aspect of the above variables. These various GEE models for the investigation of the economic growth of these countries have been compared to examine the contribution of the causality analyses to the statistical model establishment. As a result of this study, the highlight is found as the use of causally-related variables in the causality-based GEE models is much more appropriate than in the non-causality based GEE models for determining the economic growth profiles of these countries.

Legendre Matrix Method for Legendre Curve in Sasakian 3-Manifold

In this study, unit-speed the Legendre curves are studied in Sasakian 3-manifold. Firstly, differential equations characterizing the Legendre curves are obtained and the method used for the approximate solution is explained. Then, the approximate solution is found for one of the characterizations of the Legendre curve with the Legendre matrix collocation method. In addition, a sample application is made to make the method more understandable. And finally, with the help of these equations and the approximate solution, the geometric properties of this curve type are examined.

An Introduction to the Special Issue on Numerical Techniques Meet with OR - Part II

The special issue: “Numerical Techniques Meet with OR” of the Foundations of Computing and Decision Sciences consists of two parts which are of the main theme of numerical techniques and their applications in multi-disciplinary areas. The first part of this special issue was already collected in the FCDS Vol. 46, issue 1. In this second part of our special issue editorial, a description of the special issue presents numerical methods which can be used as alternative techniques for Scientific Computing and led Operational Research applications in many fields for further investigation.

New Numerical Approach for Solving Abel’s Integral Equations

In this article, we present an efficient method for solving Abel’s integral equations. This important equation is consisting of an integral equation that is modeling many problems in literature. Our proposed method is based on first taking the truncated Taylor expansions of the solution function and fractional derivatives, then substituting their matrix forms into the equation. The main character behind this technique’s approach is that it reduces such problems to solving a system of algebraic equations, thus greatly simplifying the problem. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method. Figures and tables are demonstrated to solutions impress. Also, all numerical examples are solved with the aid of Maple.