Interval Linear Algebra

TL;DR

This book systematically develops the theory of interval linear algebras and vector spaces using special interval types, providing numerous examples, properties, and potential applications across various algebraic structures.

Contribution

It introduces new types of interval linear algebras and vector spaces, including fuzzy and bialgebra variants, with comprehensive theoretical development and practical examples.

Findings

Over 350 examples illustrating concepts

Introduction of set interval linear algebras of multiple types

Discussion of applications and problem sets

Abstract

In this book we use only special types of intervals and introduce the notion of different types of interval linear algebras and interval vector spaces using the intervals of the form [0, a] where the intervals are from Zn or Z+ \cup {0} or Q+ \cup {0} or R+ \cup {0}. A systematic development is made starting from set interval vector spaces to group interval vector spaces. Vector spaces are taken as interval polynomials or interval matrices or just intervals over suitable sets or semigroups or groups. Main feature of this book is the authors have given over 350 examples. This book has six chapters. Chapter one is introductory in nature. Chapter two introduces the notion of set interval linear algebras of type one and two. Set fuzzy interval linear algebras and their algebras and their properties are discussed in chapter three. Chapter four introduces several types of interval linear bialgebras and bivector spaces and studies them. The possible applications are given in chapter five. Chapter six suggests nearly 110 problems of all levels.