The role of multiplier bounds in fuzzy data envelopment analysis

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The non-Archimedean epsilon ε is commonly considered as a lower bound for the dual input weights and output weights in multiplier data envelopment analysis (DEA) models. The amount of ε can be effectively used to differentiate between strongly and weakly efficient decision making units (DMUs). The problem of weak dominance particularly occurs when the reference set is fully or partially defined in terms of fuzzy numbers. In this paper, we propose a new four-step fuzzy DEA method to re-shape weakly efficient frontiers along with revisiting the efficiency score of DMUs in terms of perturbing the weakly efficient frontier. This approach eliminates the non-zero slacks in fuzzy DEA while keeping the strongly efficient frontiers unaltered. In comparing our proposed algorithm to an existing method in the recent literature we show three important flaws in their approach that our method addresses. Finally, we present a numerical example in banking with a combination of crisp and fuzzy data to illustrate the efficacy and advantages of the proposed approach

Towards Structural Classification of Proteins based on Contact Map Overlap

A multitude of measures have been proposed to quantify the similarity between protein 3-D structure. Among these measures, contact map overlap (CMO) maximization deserved sustained attention during past decade because it offers a fine estimation of the natural homology relation between proteins. Despite this large involvement of the bioinformatics and computer science community, the performance of known algorithms remains modest. Due to the complexity of the problem, they got stuck on relatively small instances and are not applicable for large scale comparison. This paper offers a clear improvement over past methods in this respect. We present a new integer programming model for CMO and propose an exact B &B algorithm with bounds computed by solving Lagrangian relaxation. The efficiency of the approach is demonstrated on a popular small benchmark (Skolnick set, 40 domains). On this set our algorithm significantly outperforms the best existing exact algorithms, and yet provides lower and upper bounds of better quality. Some hard CMO instances have been solved for the first time and within reasonable time limits. From the values of the running time and the relative gap (relative difference between upper and lower bounds), we obtained the right classification for this test. These encouraging result led us to design a harder benchmark to better assess the classification capability of our approach. We constructed a large scale set of 300 protein domains (a subset of ASTRAL database) that we have called Proteus 300. Using the relative gap of any of the 44850 couples as a similarity measure, we obtained a classification in very good agreement with SCOP. Our algorithm provides thus a powerful classification tool for large structure databases

A Constructive Proof of Fundamental Theory for Fuzzy Variable Linear Programming Problems

Two existing methods for solving fuzzy variable linear programming problems based on ranking functions are the fuzzy primal simplex method proposed by Mahdavi-Amiri et al. (2009) and the fuzzy dual simplex method proposed by Mahdavi-Amiri and Nasseri (2007). In this paper, we prove that in the absence of degeneracy these fuzzy methods stop in a finite number of iterations. Moreover, we generalize the fundamental theorem of linear programming in a crisp environment to a fuzzy one. Finally, we illustrate our proof using a numerical example

Risk assessment of blasting operations in open pit mines using FAHP method

Purpose. In the mining blasting operation, fragmentation is the most important output. Fly rock, ground vibration, air blast, and environmental effects are detrimental effects of blasting operations. Identifying and ranking the risk of blasting operations is considered as the most important stage in project management. Methods. In this research, the problem of identifying and ranking the factors constituting the risk in blasting operations is considered with the methodology of the Fuzzy Analytical Hierarchy Process (FAHP). Criteria and sub-criteria have been determined based on historical research studies, field studies, and expert opinions for designing a hierarchical process. Findings. Based on FAHP scores, non-control of the sub-criterion of health and safety (C3), blast operation results (C18) and knowledge, and skill and staffing (C2) with a score of 0.377, 0.334, and 0.294 respectively are the most effective sub-criterion for the creation of blasting operations risk. According to the score, the sub-criterion C18 is the most effective sub-criterion in providing the blasting operations risk. Effects and results of blasting operations (D8), with a score of 0.334 as the most effective criterion, and natural hazards (D10), with a score of 0.015, were the last priorities in the factors causing blasting operations risk. Originality. Regarding the risk rating of blasting operations, the control of the sub-criteria C3, C18, and C2, and the D8 criterion, is of particular importance in reducing the risk of blasting operations and improving project management. Practical implications. The evaluation of human resource performance and increase in the level of knowledge and skills and occupational safety and control of all outputs of blasting operations is necessary. Therefore, selecting the most important project risks and taking actions to remove them is essential for risk management.Мета. Визначення ризиків проведення вибухових робіт та їх оцінка на основі використанням нечіткого методу аналізу ієрархій (НМАІ) для покращення управління якістю проектів. Методика. В рамках даного дослідження, проблеми визначення та оцінки ризиків вибухових робіт розглядалися із застосуванням нечіткого методу аналізу ієрархій. На базі аналізу історичних даних і польового дослідження з урахуванням експертних оцінок були визначені критерії та підкритерії для побудови ієрархій. Результати. За результатами НМАІ, неконтролюючий підкритерій здоров’я та безпеки (С3), підкритерій результатів вибухових робіт (С18), знань, умінь і кадрів (С2) зі значеннями 0.377, 0.334 і 0.294 відповідно найбільш ефективні в появі ризику проведення вибухових робіт. Підкритерій С18 чинить найбільший вплив на ризик проведення вибухових робіт. Критерій результатів і наслідків вибухових робіт (D8) з найефективнішим значенням 0.334 та критерій природних катастроф (D10) зі значенням 0.015 є останніми пріоритетами серед чинників, які визначають ризик проведення вибухових робіт. Наукова новизна. Отримав доповнення та подальший розвиток науково-методичний підхід до визначення ризиків при проведенні вибухових робіт, заснований на їх ранжуванні з використанням системи виявлених критеріїв і підкритеріїв методом НМАІ. Практична значимість. Для успішного керування проектом важливо визначати найсерйозніші ризики проекту й вжити заходів щодо їх усунення. Відносно ранжирування ризиків проведення вибухових робіт управління підкритеріями C3, C18 і C2, а також критерієм D8, особливо важливо для зниження цих ризиків та покращення якості управління проектом.Цель. Определение рисков проведения взрывных работ и их оценка на основе использования нечеткого метода анализа иерархий (НМАИ) для улучшения управления качеством проектов. Методика. В рамках данного исследования, проблемы определения и оценки рисков взрывных работ рассматривались с применением нечеткого метода анализа иерархий. На базе анализа исторических данных и полевого исследования с учетом экспертных оценок были определены, критерии и подкритерии для построения иерархий. Результаты. По результатам НМАИ, неконтролирующий подкритерий здоровья и безопасности (С3), подкритерий результатов взрывных работ (С18), знаний, умений и кадров (С2) со значениями 0.377, 0.334 и 0.294 соответственно наиболее эффективны в появлении риска проведения взрывных работ. Подкритерий С18 оказывает самое большое влияние на риск проведения взрывных работ. Критерий результатов и последствий взрывных работ (D8) с самым эффективным значением 0.334 и критерий природных катастроф (D10) со значением 0.015 являются последними приоритетами среди факторов, которые определяют риск проведения взрывных работ. Научная новизна. Получил дополнение и дальнейшее развитие научно-методический подход к определению рисков при проведении взрывных работ, основанный на их ранжировании с использованием системы выявленных критериев и подкритериев методом НМАИ. Практическая значимость. Для успешного руководства проектом важно определять самые серьезные риски проекта и предпринять действия по их устранению. В отношении ранжирования рисков проведения взрывных работ управление подкритериями C3, C18 и C2, а также критерием D8, особенно важно для снижения этих рисков и улучшения руководства проектом.The authors would like to thank Mining Engineering Department, Islamic Azad University (South Tehran Branch) for supporting this research

Fuzzy linear programming problems : models and solutions

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, alpha-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately

A new computational method for solving fully fuzzy nonlinear matrix equations

Multi formulations and computational methodologies have been suggested to extract solution of fuzzy nonlinear programming problems. However, in some cases the methods which have been utilised in order to find the solution of these problems involve greater complexity. On the basis of the mentioned reason, the current research work is intended towards introduction of a simple method for finding the fuzzy optimal solution related to fuzzy nonlinear issues. The proposed method is validated and is confirmed to be applicable by suggesting some demonstrated examples. The results confirm that the proposed method is so easy to understand and to apply for solving fully fuzzy nonlinear system (FFNS)

Multilevel Weighted Support Vector Machine for Classification on Healthcare Data with Missing Values

This work is motivated by the needs of predictive analytics on healthcare data as represented by Electronic Medical Records. Such data is invariably problematic: noisy, with missing entries, with imbalance in classes of interests, leading to serious bias in predictive modeling. Since standard data mining methods often produce poor performance measures, we argue for development of specialized techniques of data-preprocessing and classification. In this paper, we propose a new method to simultaneously classify large datasets and reduce the effects of missing values. It is based on a multilevel framework of the cost-sensitive SVM and the expected maximization imputation method for missing values, which relies on iterated regression analyses. We compare classification results of multilevel SVM-based algorithms on public benchmark datasets with imbalanced classes and missing values as well as real data in health applications, and show that our multilevel SVM-based method produces fast, and more accurate and robust classification results.Comment: arXiv admin note: substantial text overlap with arXiv:1503.0625

Lexicographic Methods for Fuzzy Linear Programming

Fuzzy Linear Programming (FLP) has addressed the increasing complexity of real-world decision-making problems that arise in uncertain and ever-changing environments since its introduction in the 1970s. Built upon the Fuzzy Sets theory and classical Linear Programming (LP) theory, FLP encompasses an extensive area of theoretical research and algorithmic development. Unlike classical LP, there is not a unique model for the FLP problem, since fuzziness can appear in the model components in different ways. Hence, despite fifty years of research, new formulations of FLP problems and solution methods are still being proposed. Among the existing formulations, those using fuzzy numbers (FNs) as parameters and/or decision variables for handling inexactness and vagueness in data have experienced a remarkable development in recent years. Here, a long-standing issue has been how to deal with FN-valued objective functions and with constraints whose left- and right-hand sides are FNs. The main objective of this paper is to present an updated review of advances in this particular area. Consequently, the paper briefly examines well-known models and methods for FLP, and expands on methods for fuzzy single- and multi-objective LP that use lexicographic criteria for ranking FNs. A lexicographic approach to the fuzzy linear assignment (FLA) problem is discussed in detail due to the theoretical and practical relevance. For this case, computer codes are provided that can be used to reproduce results presented in the paper and for practical applications. The paper demonstrates that FLP that is focused on lexicographic methods is an active area with promising research lines and practical implications.Spanish Ministry of Economy and CompetitivenessEuropean Union (EU) TIN2017-86647-