This work results from my interest in the field of vector optimiza tion. I stumbled first upon this subject in 1982 during my six months visit to the Istituto di Elaborazione della Informazione in Pisa, Italy, supported by a fellowship of the (Italian) Consiglio Nationale delle Richerche. I was attracted then by a gap between vector optimiza tion used to serve as a formal model for multiple objective decision problems and the decision problems themselves, the gap nonexis tent in scalar optimization. Roughly speaking, vector optimization provides methods for ranking decisions according to a partial order whereas decision making requires a linear ordering of decisions. The book deals with vector optimization. However, vector opti mization is considered here not only as a topic of research in itself but also as a basic tool for decision making. In consequence, all results presented here are aimed at exploiting and understanding the structure of elements (decisions) framed by a vector optimiza tion problem with the underlying assumption that the results should be interpretable in terms and applicable in the context of decision making. Computational tractability of results is therefore of special concern throughout this book. A unified framework for presentation is offered by the Cone Sep aration Technique (CST) founded on the notion of cone separation."

There are numerous books on Multiple Criteria Decision Making. Soft Computing for Complex Multiple Criteria Decision Making concentrates on providing technical (meaning formal, mathematical, algorithmical) tools to make the user of Multiple Criteria Decision Making methodologies independent of bulky optimization computations. These bulky computations up to now have been a necessary, but limiting, characteristic of interactive MCDM methodologies and algorithms. This book removes these limitations of MCDM problems by reducing a problem's computational complexity. The book systematically applies the approximate, soft, treatments to major MCDM solving methodologies. As a result, it provides a wider and more functional general framework for presenting, teaching, implementing and applying a wide range of MCDM methodologies. The book seeks to provide a stimulus for a broader development and application of MCDM methods.

This textbook approaches optimization from a multi-aspect, multi-criteria perspective. By using a Multiple Criteria Decision Making (MCDM) approach, it avoids the limits and oversimplifications that can come with optimization models with one criterion. The book is presented in a concise form, addressing how to solve decision problems in sequences of intelligence, modelling, choice and review phases, often iterated, to identify the most preferred decision variant. The approach taken is human-centric, with the user taking the final decision is a sole and sovereign actor in the decision making process. To ensure generality, no assumption about the Decision Maker preferences or behavior is made. The presentation of these concepts is illustrated by numerous examples, figures, and problems to be solved with the help of downloadable spreadsheets. This electronic companion contains models of problems to be solved built in Excel spreadsheet files. Optimization models are too often oversimplifications of decision problems met in practice. For instance, modeling company performance by an optimization model in which the criterion function is short-term profit to be maximized, does not fully reflect the essence of business management. The company's managing staff is accountable not only for operational decisions, but also for actions which shall result in the company ability to generate a decent profit in the future. This calls for management decisions and actions which ensure short-term profitability, but also maintaining long-term relations with clients, introducing innovative products, financing long-term investments, etc. Each of those additional, though indispensable actions and their effects can be modeled separately, case by case, by an optimization model with a criterion function adequately selected. However, in each case the same set of constraints represents the range of company admissible actions. The aim and the scope of this textbook is to present methodologies and methods enabling modeling of such actions jointly.

This textbook approaches optimization from a multi-aspect, multi-criteria perspective. By using a Multiple Criteria Decision Making (MCDM) approach, it avoids the limits and oversimplifications that can come with optimization models with one criterion. The book is presented in a concise form, addressing how to solve decision problems in sequences of intelligence, modelling, choice and review phases, often iterated, to identify the most preferred decision variant. The approach taken is human-centric, with the user taking the final decision is a sole and sovereign actor in the decision making process. To ensure generality, no assumption about the Decision Maker preferences or behavior is made. The presentation of these concepts is illustrated by numerous examples, figures, and problems to be solved with the help of downloadable spreadsheets. This electronic companion contains models of problems to be solved built in Excel spreadsheet files. Optimization models are too often oversimplifications of decision problems met in practice. For instance, modeling company performance by an optimization model in which the criterion function is short-term profit to be maximized, does not fully reflect the essence of business management. The company's managing staff is accountable not only for operational decisions, but also for actions which shall result in the company ability to generate a decent profit in the future. This calls for management decisions and actions which ensure short-term profitability, but also maintaining long-term relations with clients, introducing innovative products, financing long-term investments, etc. Each of those additional, though indispensable actions and their effects can be modeled separately, case by case, by an optimization model with a criterion function adequately selected. However, in each case the same set of constraints represents the range of company admissible actions. The aim and the scope of this textbook is to present methodologies and methods enabling modeling of such actions jointly.

This work results from my interest in the field of vector optimiza tion. I stumbled first upon this subject in 1982 during my six months visit to the Istituto di Elaborazione della Informazione in Pisa, Italy, supported by a fellowship of the (Italian) Consiglio Nationale delle Richerche. I was attracted then by a gap between vector optimiza tion used to serve as a formal model for multiple objective decision problems and the decision problems themselves, the gap nonexis tent in scalar optimization. Roughly speaking, vector optimization provides methods for ranking decisions according to a partial order whereas decision making requires a linear ordering of decisions. The book deals with vector optimization. However, vector opti mization is considered here not only as a topic of research in itself but also as a basic tool for decision making. In consequence, all results presented here are aimed at exploiting and understanding the structure of elements (decisions) framed by a vector optimiza tion problem with the underlying assumption that the results should be interpretable in terms and applicable in the context of decision making. Computational tractability of results is therefore of special concern throughout this book. A unified framework for presentation is offered by the Cone Sep aration Technique (CST) founded on the notion of cone separation.

This book concentrates on providing technical tools to make the user of Multiple Criteria Decision Making (MCDM) methodologies independent of bulky optimization computations. These bulky computations have been a necessary, but limiting, characteristic of interactive MCDM methodologies and algorithms. The book removes these limitations of MCDM problems by reducing a problem's computational complexity. The result is a wider and more functional general framework for presenting, teaching, implementing and applying a wide range of MCDM methodologies.