Fuzzy Preference Ordering Of Interval Numbers In Decision Problems

In conventional mathematical programming, coefficients of problems are usually determined by the experts as crisp values in terms of classical mathematical reasoning. But in reality, in an imprecise and uncertain environment, it will be utmost unrealistic to assume that the knowledge and representation of an expert can come in a precise way. The wider objective of the book is to study different real decision situations where problems are defined in inexact environment. Inexactness are mainly generated in two ways – (1) due to imprecise perception and knowledge of the human expert followed by vague representation of knowledge as a DM; (2) due to huge-ness and complexity of relations and data structure in the definition of the problem situation. We use interval numbers to specify inexact or imprecise or uncertain data. Consequently, the study of a decision problem requires answering the following initial questions: How should we compare and define preference ordering between two intervals?, interpret and deal inequality relations involving interval coefficients?, interpret and make way towards the goal of the decision problem? The present research work consists of two closely related fields: approaches towards defining a generalized preference ordering scheme for interval attributes and approaches to deal with some issues having application potential in many areas of decision making.

In conventional mathematical programming, coefficients of problems are usually determined by the experts as crisp values in terms of classical mathematical reasoning. But in reality, in an imprecise and uncertain environment, it will be utmost unrealistic to assume that the knowledge and representation of an expert can come in a precise way. The wider objective of the book is to study different real decision situations where problems are defined in inexact environment. Inexactness are mainly generated in two ways – (1) due to imprecise perception and knowledge of the human expert followed by vague representation of knowledge as a DM; (2) due to huge-ness and complexity of relations and data structure in the definition of the problem situation. We use interval numbers to specify inexact or imprecise or uncertain data. Consequently, the study of a decision problem requires answering the following initial questions: How should we compare and define preference ordering between two intervals?, interpret and deal inequality relations involving interval coefficients?, interpret and make way towards the goal of the decision problem? The present research work consists of two closely related fields: approaches towards defining a generalized preference ordering scheme for interval attributes and approaches to deal with some issues having application potential in many areas of decision making.

In this book international expert authors provide solutions for modern fundamental problems including the complexity of computing of critical points for set-valued mappings, the behaviour of solutions of ordinary differential equations, partial differential equations and difference equations, or the development of an abstract theory of global attractors for multi-valued impulsive dynamical systems. These abstract mathematical approaches are applied to problem-solving in solid mechanics, hydro- and aerodynamics, optimization, decision making theory and control theory. This volume is therefore relevant to mathematicians as well as engineers working at the interface of these fields.

This book shows how common operation management methods and algorithms can be extended to deal with vague or imprecise information in decision-making problems. It describes how to combine decision trees, clustering, multi-attribute decision-making algorithms and Monte Carlo Simulation with the mathematical description of imprecise or vague information, and how to visualize such information. Moreover, it discusses a broad spectrum of real-life management problems including forecasting the apparent consumption of steel products, planning and scheduling of production processes, project portfolio selection and economic-risk estimation. It is a concise, yet comprehensive, reference source for researchers in decision-making and decision-makers in business organizations alike.

This book describes novel algorithms based on interval-valued fuzzy methods that are expected to improve classification and decision-making processes under incomplete or imprecise information. At first, it introduces interval-valued fuzzy sets. It then discusses new methods for aggregation on interval-valued settings, and the most common properties of interval-valued aggregation operators. It then presents applications such as decision making using interval-valued aggregation, and classification in case of missing values. Interesting applications of the developed algorithms to DNA microarray analysis and in medical decision support systems are shown. The book is intended not only as a timely report for the community working on fuzzy sets and their extensions but also for researchers and practitioners dealing with the problems of uncertain or imperfect information.

This book is a printed edition of the Special Issue "Fuzzy Techniques for Decision Making" that was published in Symmetry

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