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.

Fuzzy technology has emerged as one of the most exciting new concepts available. Fuzzy Logic and its Applications... covers a wide range of the theory and applications of fuzzy logic and related systems, including industrial applications of fuzzy technology, implementing human intelligence in machines and systems. There are four main themes: intelligent systems, engineering, mathematical foundations, and information sciences. Both academics and the technical community will learn how and why fuzzy logic is appreciated in the conceptual, design and manufacturing stages of intelligent systems, gaining an improved understanding of the basic science and the foundations of human reasoning.

In the last ten years, a true explosion of investigations into fuzzy modeling and its applications in control, diagnostics, decision making, optimization, pattern recognition, robotics, etc. has been observed. The attraction of fuzzy modeling results from its intelligibility and the high effectiveness of the models obtained. Owing to this the modeling can be applied for the solution of problems which could not be solved till now with any known conventional methods. The book provides the reader with an advanced introduction to the problems of fuzzy modeling and to one of its most important applications: fuzzy control. It is based on the latest and most significant knowledge of the subject and can be used not only by control specialists but also by specialists working in any field requiring plant modeling, process modeling, and systems modeling, e.g. economics, business, medicine, agriculture,and meteorology.

In recent years it has become apparent that an important part of the theory of artificial intelligence is concerned with reasoning on the basis of uncertain, incomplete, or inconsistent information. A variety of formalisms have been developed, including nonmonotonic logic, fuzzy sets, possibility theory, belief functions, and dynamic models of reasoning such as belief revision and Bayesian networks. Several European research projects have been formed in the area and the first European conference was held in 1991. This volume contains the papers accepted for presentation at ECSQARU-93, the European Conference on Symbolicand Quantitative Approaches to Reasoning and Uncertainty, held at the University of Granada, Spain, November 8-10, 1993.

Operations Research is a field whose major contribution has been to propose a rigorous fonnulation of often ill-defmed problems pertaining to the organization or the design of large scale systems, such as resource allocation problems, scheduling and the like. While this effort did help a lot in understanding the nature of these problems, the mathematical models have proved only partially satisfactory due to the difficulty in gathering precise data, and in formulating objective functions that reflect the multi-faceted notion of optimal solution according to human experts. In this respect linear programming is a typical example of impressive achievement of Operations Research, that in its detenninistic fonn is not always adapted to real world decision-making : everything must be expressed in tenns of linear constraints ; yet the coefficients that appear in these constraints may not be so well-defined, either because their value depends upon other parameters (not accounted for in the model) or because they cannot be precisely assessed, and only qualitative estimates of these coefficients are available. Similarly the best solution to a linear programming problem may be more a matter of compromise between various criteria rather than just minimizing or maximizing a linear objective function. Lastly the constraints, expressed by equalities or inequalities between linear expressions, are often softer in reality that what their mathematical expression might let us believe, and infeasibility as detected by the linear programming techniques can often been coped with by making trade-offs with the real world.

This volume contains selected papers covering a wide range of topics, including theoretical and methodological advances relating to data gathering, classification and clustering, exploratory and multivariate data analysis, and knowledge seeking and discovery. The result is a broad view of the state of the art, making this an essential work not only for data analysts, mathematicians, and statisticians, but also for researchers involved in data processing at all stages from data gathering to decision making.

The last few years have seen important advances in the use ofgenetic algorithms to address challenging optimization problems inindustrial engineering. Genetic Algorithms and Engineering Designis the only book to cover the most recent technologies and theirapplication to manufacturing, presenting a comprehensive and fullyup-to-date treatment of genetic algorithms in industrialengineering and operations research. Beginning with a tutorial on genetic algorithm fundamentals andtheir use in solving constrained and combinatorial optimizationproblems, the book applies these techniques to problems in specificareas--sequencing, scheduling and production plans, transportationand vehicle routing, facility layout, location-allocation, andmore. Each topic features a clearly written problem description,mathematical model, and summary of conventional heuristicalgorithms. All algorithms are explained in intuitive, rather thanhighly-technical, language and are reinforced with illustrativefigures and numerical examples. Written by two internationally acknowledged experts in the field,Genetic Algorithms and Engineering Design features originalmaterial on the foundation and application of genetic algorithms,and also standardizes the terms and symbols used in othersources--making this complex subject truly accessible to thebeginner as well as to the more advanced reader. Ideal for both self-study and classroom use, this self-containedreference provides indispensable state-of-the-art guidance toprofessionals and students working in industrial engineering,management science, operations research, computer science, andartificial intelligence. The only comprehensive, state-of-the-arttreatment available on the use of genetic algorithms in industrialengineering and operations research . . . Written by internationally recognized experts in the field ofgenetic algorithms and artificial intelligence, Genetic Algorithmsand Engineering Design provides total coverage of currenttechnologies and their application to manufacturing systems.Incorporating original material on the foundation and applicationof genetic algorithms, this unique resource also standardizes theterms and symbols used in other sources--making this complexsubject truly accessible to students as well as experiencedprofessionals. Designed for clarity and ease of use, thisself-contained reference: * Provides a comprehensive survey of selection strategies, penaltytechniques, and genetic operators used for constrained andcombinatorial optimization problems * Shows how to use genetic algorithms to make production schedules,solve facility/location problems, make transportation/vehiclerouting plans, enhance system reliability, and much more * Contains detailed numerical examples, plus more than 160auxiliary figures to make solution procedures transparent andunderstandable

As of today, Evolutionary Computing and Fuzzy Set Computing are two mature, wen -developed, and higbly advanced technologies of information processing. Bach of them has its own clearly defined research agenda, specific goals to be achieved, and a wen setUed algorithmic environment. Concisely speaking, Evolutionary Computing (EC) is aimed at a coherent population -oriented methodology of structural and parametric optimization of a diversity of systems. In addition to this broad spectrum of such optimization applications, this paradigm otTers an important ability to cope with realistic goals and design objectives reflected in the form of relevant fitness functions. The GA search (which is often regarded as a dominant domain among other techniques of EC such as evolutionary strategies, genetic programming or evolutionary programming) delivers a great deal of efficiency helping navigate through large search spaces. The main thrust of fuzzy sets is in representing and managing nonnumeric (linguistic) information. The key notion (whose conceptual as weH as algorithmic importance has started to increase in the recent years) is that of information granularity. It somewhat concurs with the principle of incompatibility coined by L. A. Zadeh. Fuzzy sets form a vehic1e helpful in expressing a granular character of information to be captured. Once quantified via fuzzy sets or fuzzy relations, the domain knowledge could be used efficiently very often reducing a heavy computation burden when analyzing and optimizing complex systems.

Comprising papers presented at an international symposium on fuzzy engineering technology, this volume provides information on the current state-of-the-art in the field of fuzzy theories and applications, and their importance in the areas of industry, medicine, artificial intelligence, management, socio-economics, ecology, agriculture, behavioural science and education. The results of recent research of LIFE (Laboratory for International Fuzzy Engineering Research) are also included.