Fuzzy Efficiency Measures in Data Envelopment Analysis Using Lexicographic Multiobjective Approach

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.There is an extensive literature in data envelopment analysis (DEA) aimed at evaluating the relative efficiency of a set of decision-making units (DMUs). Conventional DEA models use definite and precise data while real-life problems often consist of some ambiguous and vague information, such as linguistic terms. Fuzzy sets theory can be effectively used to handle data ambiguity and vagueness in DEA problems. This paper proposes a novel fully fuzzified DEA (FFDEA) approach where, in addition to input and output data, all the variables are considered fuzzy, including the resulting efficiency scores. A lexicographic multi-objective linear programming (MOLP) approach is suggested to solve the fuzzy models proposed in this study. The contribution of this paper is fivefold: (1) both fuzzy Constant and Variable Returns to Scale models are considered to measure fuzzy efficiencies; (2) a classification scheme for DMUs, based on their fuzzy efficiencies, is defined with three categories; (3) fuzzy input and output targets are computed for improving the inefficient DMUs; (4) a super-efficiency FFDEA model is also formulated to rank the fuzzy efficient DMUs; and (5) the proposed approach is illustrated, and compared with existing methods, using a dataset from the literature

Research Agenda on Multiple-Criteria Decision-Making: New Academic Debates in Business and Management

[EN] Systemic disruptions are becoming more continuous, intense, and persistent. Their effects have a severe impact on the economy in volatile, uncertain, complex, and ambiguous (VUCA) environments that are increasingly transversal to productive sectors and activities. Researchers have intensified their academic production of multiple-criteria decision-making (MCDM) in recent years. This article analyzes the research agenda through a systematic review of scientific articles in the Web of Science Core Collection according to the Journal Citation Report (JCR), both in the Social Sciences Citation Index (SSCI) and in the Science Citation Index Expanded (SCIE). According to the selected search criteria, 909 articles on MCDM published between 1979 and 2022 in Web of Science journals in the business and management categories were located. A bibliometric analysis of the main thematic clusters, the international collaboration networks, and the bibliographic coupling of articles was carried out. In addition, the analysis period is divided into two subperiods (1979¿2008 and 2009¿2022), establishing 2008 as the threshold, the year of the Global Financial Crisis (GFC), to assess the evolution of the research agenda at the beginning of systemic disruptions. The bibliometric analysis allows the identification of the motor, basic, specialized, and emerging themes of each subperiod. The results show the similarities and differences between the academic debate before and after the GFC. The evidence found allows academics to be guided in their high-impact research in business and management using MCDM methodologies to address contemporary challenges. An important contribution of this study is to detect gaps in the literature, highlighting unclosed gaps and emerging trends in the field of study for journal editors.Castello-Sirvent, F.; Meneses-Eraso, C. (2022). Research Agenda on Multiple-Criteria Decision-Making: New Academic Debates in Business and Management. Axioms. 11(10):1-37. https://doi.org/10.3390/axioms11100515137111

A Heuristic Algorithm for Nonlinear Lexicography Goal Programming with an Efficient Initial Solution

In this paper,  a heuristic algorithm is proposed in order to solve a nonlinear lexicography goal programming (NLGP) by using an efficient initial point. Some numerical experiments showed that the search quality by the proposed heuristic in a multiple objectives problem depends on the initial point features, so in the proposed approach the initial point is retrieved by Data Envelopment Analysis to be selected as an efficient solution. There are some weaknesses in classic NLGP algorithm that lead to trapping into the local optimum, so a simulated annealing concept is implemented during the searching stage to increase the diversity of search in the solution space. Some numerical examples with different sizes were generated and comparison of results confirms that the proposed solution heuristic is more efficient than the classic approach. Moreover the proposed approach was extended for cases with ordinal weights of inputs or outputs. The computational experiments for 5 numerical instances and the statistical analysis indicate that the proposed heuristic algorithm is a robust procedure to find better preferred solution comparing to the classic NLGP

Defuzzification of groups of fuzzy numbers using data envelopment analysis

Defuzzification is a critical process in the implementation of fuzzy systems that converts fuzzy numbers to crisp representations. Few researchers have focused on cases where the crisp outputs must satisfy a set of relationships dictated in the original crisp data. This phenomenon indicates that these crisp outputs are mathematically dependent on one another. Furthermore, these fuzzy numbers may exist as a group of fuzzy numbers. Therefore, the primary aim of this thesis is to develop a method to defuzzify groups of fuzzy numbers based on Charnes, Cooper, and Rhodes (CCR)-Data Envelopment Analysis (DEA) model by modifying the Center of Gravity (COG) method as the objective function. The constraints represent the relationships and some additional restrictions on the allowable crisp outputs with their dependency property. This leads to the creation of crisp values with preserved relationships and/or properties as in the original crisp data. Comparing with Linear Programming (LP) based model, the proposed CCR-DEA model is more efficient, and also able to defuzzify non-linear fuzzy numbers with accurate solutions. Moreover, the crisp outputs obtained by the proposed method are the nearest points to the fuzzy numbers in case of crisp independent outputs, and best nearest points to the fuzzy numbers in case of dependent crisp outputs. As a conclusion, the proposed CCR-DEA defuzzification method can create either dependent crisp outputs with preserved relationship or independent crisp outputs without any relationship. Besides, the proposed method is a general method to defuzzify groups or individuals fuzzy numbers under the assumption of convexity with linear and non-linear membership functions or relationships

Methodological review of multicriteria optimization techniques: aplications in water resources

Multi-criteria decision analysis (MCDA) is an umbrella approach that has been applied to a wide range of natural resource management situations. This report has two purposes. First, it aims to provide an overview of advancedmulticriteriaapproaches, methods and tools. The review seeks to layout the nature of the models, their inherent strengths and limitations. Analysis of their applicability in supporting real-life decision-making processes is provided with relation to requirements imposed by organizationally decentralized and economically specific spatial and temporal frameworks. Models are categorized based on different classification schemes and are reviewed by describing their general characteristics, approaches, and fundamental properties. A necessity of careful structuring of decision problems is discussed regarding planning, staging and control aspects within broader agricultural context, and in water management in particular. A special emphasis is given to the importance of manipulating decision elements by means ofhierarchingand clustering. The review goes beyond traditionalMCDAtechniques; it describes new modelling approaches. The second purpose is to describe newMCDAparadigms aimed at addressing the inherent complexity of managing water ecosystems, particularly with respect to multiple criteria integrated with biophysical models,multistakeholders, and lack of information. Comments about, and critical analysis of, the limitations of traditional models are made to point out the need for, and propose a call to, a new way of thinking aboutMCDAas they are applied to water and natural resources management planning. These new perspectives do not undermine the value of traditional methods; rather they point to a shift in emphasis from methods for problem solving to methods for problem structuring. Literature review show successfully integrations of watershed management optimization models to efficiently screen a broad range of technical, economic, and policy management options within a watershed system framework and select the optimal combination of management strategies and associated water allocations for designing a sustainable watershed management plan at least cost. Papers show applications in watershed management model that integrates both natural and human elements of a watershed system including the management of ground and surface water sources, water treatment and distribution systems, human demands,wastewatertreatment and collection systems, water reuse facilities,nonpotablewater distribution infrastructure, aquifer storage and recharge facilities, storm water, and land use

A compromise programming approach for target setting in DEA

This paper presents a new data envelopment analysis (DEA) target setting approach that uses the compromise programming (CP) method of multiobjective optimization. This method computes the ideal point associated to each decision making unit (DMU) and determines an ambitious, efficient target that is as close as possible (using an lp metric) to that ideal point. The specific cases p = 1, p = 2 and p = ∞ are separately discussed and analyzed. In particular, for p = 1 and p = ∞, a lexicographic optimization approach is proposed in order to guarantee uniqueness of the obtained target. The original CP method is translation invariant and has been adapted so that the proposed CP-DEA is also units invariant. An lp metric-based efficiency score is also defined for each DMU. The proposed CP-DEA approach can also be utilized in the presence of preference information, non-discretionary or integer variables and undesirable outputs. The proposed approach has been extensively compared with other DEA approaches on a dataset from the literature

The Use of AR-IDEA Approach for Supplier Selection Problems

Abstract: To select the best suppliers in the presence of both cardinal and ordinal data and considering weight restrictions, this paper proposes a method, which is based on Assurance RegionImprecise Data Envelopment Analysis (AR-IDEA). A numerical example demonstrates the application of the proposed method

The state of the art development of AHP (1979-2017): A literature review with a social network analysis

Although many papers describe the evolution of the analytic hierarchy process (AHP), most adopt a subjective approach. This paper examines the pattern of development of the AHP research field using social network analysis and scientometrics, and identifies its intellectual structure. The objectives are: (i) to trace the pattern of development of AHP research; (ii) to identify the patterns of collaboration among authors; (iii) to identify the most important papers underpinning the development of AHP; and (iv) to discover recent areas of interest. We analyse two types of networks: social networks, that is, co-authorship networks, and cognitive mapping or the network of disciplines affected by AHP. Our analyses are based on 8441 papers published between 1979 and 2017, retrieved from the ISI Web of Science database. To provide a longitudinal perspective on the pattern of evolution of AHP, we analyse these two types of networks during the three periods 1979?1990, 1991?2001 and 2002?2017. We provide some basic statistics on AHP journals and researchers, review the main topics and applications of integrated AHPs and provide direction for future research by highlighting some open questions

The state of the art development of AHP (1979-2017): a literature review with a social network analysis

Although many papers describe the evolution of the analytic hierarchy process (AHP), most adopt a subjective approach. This paper examines the pattern of development of the AHP research field using social network analysis and scientometrics, and identifies its intellectual structure. The objectives are: (i) to trace the pattern of development of AHP research; (ii) to identify the patterns of collaboration among authors; (iii) to identify the most important papers underpinning the development of AHP; and (iv) to discover recent areas of interest. We analyse two types of networks: social networks, that is, co-authorship networks, and cognitive mapping or the network of disciplines affected by AHP. Our analyses are based on 8441 papers published between 1979 and 2017, retrieved from the ISI Web of Science database. To provide a longitudinal perspective on the pattern of evolution of AHP, we analyse these two types of networks during the three periods 1979–1990, 1991–2001 and 2002–2017. We provide some basic statistics on AHP journals and researchers, review the main topics and applications of integrated AHPs and provide direction for future research by highlighting some open questions