Interval Linear Algebra

Interval Arithmetic, or Interval Mathematics, was developed in the 1950s and 1960s as an approach to rounding errors in mathematical computations. However, there was no methodical development of interval algebraic structures to this date. This book provides a systematic analysis of interval algebraic structures, viz. interval linear algebra, using intervals of the form [0, a]. CONTENTS 4 DEDICATION 6 PREFACE 8 Chapter One: INTRODUCTION 10 Chapter Two: SET INTERVAL LINEAR ALGEBRAS OF 12 2.1 Set Interval Linear Algebras of Type I 12 2.2 Semigroup Interval Vector Spaces 30 Chapter Three: SET FUZZY INTERVAL LINEAR 58 3.1 Set Fuzzy Interval Vector Spaces and Their Properties 58 3.2 Set Fuzzy Interval Vector Spaces of Type II and TheirProperties 77 Chapter Four: SET INTERVAL BIVECTOR SPACES AND 104 4.1 Set Interval Bivector Spaces and Their Properties 104 4.2 Semigroup Interval Bilinear Algebras and TheirProperties 137 4.3 Group Interval Bilinear Algebras and their Properties 154 4.4 Bisemigroup Interval Bilinear Algebras and TheirGeneralization 177 Chapter Five: APPLICATIONS OF THE SPECIAL CLASSES 220 Chapter Six: SUGGESTED PROBLEMS 222 FURTHER READING 238 INDEX 243 ABOUT THE AUTHORS 248