Classical data envelopment analysis (DEA) models use crisp data to measure the inputs and outputs of a given system. In cases such as manufacturing systems, production processes, service systems, etc., the inputs and outputs may be complex and difficult to measure with classical DEA models. Crisp input and output data are fundamentally indispensable in the conventional DEA models. If these models contain complex uncertain data, then they will become more important and practical for decision makers.Uncertainty in Data Envelopment Analysis introduces methods to investigate uncertain data in DEA models, providing a deeper look into two types of uncertain DEA methods, fuzzy DEA and belief degree-based uncertainty DEA, which are based on uncertain measures. These models aim to solve problems encountered by classical data analysis in cases where the inputs and outputs of systems and processes are volatile and complex, making measurement difficult. Introduces methods to deal with uncertain data in DEA models, as a source of information and a reference book for researchers and engineers Presents DEA models that can be used for evaluating the outputs of many reallife systems in social and engineering subjects Provides fresh DEA models for efficiency evaluation from the perspective of imprecise data Applies the fuzzy set and uncertainty theories to DEA to produce a new method of dealing with the empirical data

Classical data envelopment analysis (DEA) models use crisp data to measure the inputs and outputs of a given system. In cases such as manufacturing systems, production processes, service systems, etc., the inputs and outputs may be complex and difficult to measure with classical DEA models. Crisp input and output data are fundamentally indispensable in the conventional DEA models. If these models contain complex uncertain data, then they will become more important and practical for decision makers.Uncertainty in Data Envelopment Analysis introduces methods to investigate uncertain data in DEA models, providing a deeper look into two types of uncertain DEA methods, fuzzy DEA and belief degree-based uncertainty DEA, which are based on uncertain measures. These models aim to solve problems encountered by classical data analysis in cases where the inputs and outputs of systems and processes are volatile and complex, making measurement difficult.- Introduces methods to deal with uncertain data in DEA models, as a source of information and a reference book for researchers and engineers- Presents DEA models that can be used for evaluating the outputs of many reallife systems in social and engineering subjects- Provides fresh DEA models for efficiency evaluation from the perspective of imprecise data- Applies the fuzzy set and uncertainty theories to DEA to produce a new method of dealing with the empirical data

This book offers a comprehensive review of the different types of fuzzy sets that have been developed in the last few years. Each chapter is dedicated to a type of fuzzy set, which is at first introduced and described in detail, together with its properties. In turn, its application in an optimization and/or decision-making problem is discussed. In particular, the book highlights current research gaps and future research directions on fuzzy numbers in decision analysis and transportation problems. It is intended as a self-contained reference guide for scientists and engineers interested in applying fuzzy set theory for solving optimization problems.

Classical data envelopment analysis (DEA) models use crisp data to measure the inputs and outputs of a given system. In cases such as manufacturing systems, production processes, service systems, etc., the inputs and outputs may be complex and difficult to measure with classical DEA models. Crisp input and output data are fundamentally indispensable in the conventional DEA models. If these models contain complex uncertain data, then they will become more important and practical for decision makers.Uncertainty in Data Envelopment Analysis introduces methods to investigate uncertain data in DEA models, providing a deeper look into two types of uncertain DEA methods, fuzzy DEA and belief degree-based uncertainty DEA, which are based on uncertain measures. These models aim to solve problems encountered by classical data analysis in cases where the inputs and outputs of systems and processes are volatile and complex, making measurement difficult. Introduces methods to deal with uncertain data in DEA models, as a source of information and a reference book for researchers and engineers Presents DEA models that can be used for evaluating the outputs of many reallife systems in social and engineering subjects Provides fresh DEA models for efficiency evaluation from the perspective of imprecise data Applies the fuzzy set and uncertainty theories to DEA to produce a new method of dealing with the empirical data

Classical data envelopment analysis (DEA) models use crisp data to measure the inputs and outputs of a given system. In cases such as manufacturing systems, production processes, service systems, etc., the inputs and outputs may be complex and difficult to measure with classical DEA models. Crisp input and output data are fundamentally indispensable in the conventional DEA models. If these models contain complex uncertain data, then they will become more important and practical for decision makers.Uncertainty in Data Envelopment Analysis introduces methods to investigate uncertain data in DEA models, providing a deeper look into two types of uncertain DEA methods, fuzzy DEA and belief degree-based uncertainty DEA, which are based on uncertain measures. These models aim to solve problems encountered by classical data analysis in cases where the inputs and outputs of systems and processes are volatile and complex, making measurement difficult.- Introduces methods to deal with uncertain data in DEA models, as a source of information and a reference book for researchers and engineers- Presents DEA models that can be used for evaluating the outputs of many reallife systems in social and engineering subjects- Provides fresh DEA models for efficiency evaluation from the perspective of imprecise data- Applies the fuzzy set and uncertainty theories to DEA to produce a new method of dealing with the empirical data

This book offers a comprehensive review of the different types of fuzzy sets that have been developed in the last few years. Each chapter is dedicated to a type of fuzzy set, which is at first introduced and described in detail, together with its properties. In turn, its application in an optimization and/or decision-making problem is discussed. In particular, the book highlights current research gaps and future research directions on fuzzy numbers in decision analysis and transportation problems. It is intended as a self-contained reference guide for scientists and engineers interested in applying fuzzy set theory for solving optimization problems.