Algebraic Structures Using Super Interval Matrices

By Kandasamy, W. B. Vasantha

Book Id: WPLBN0002828092
Format Type: PDF eBook:
File Size: 2.68 MB
Reproduction Date: 7/2/2013

Title:	Algebraic Structures Using Super Interval Matrices
Author:	Kandasamy, W. B. Vasantha
Volume:
Language:	English
Subject:	Non Fiction, Education, Super Interval Matrices
Collections:	Authors Community, Mathematics
Historic Publication Date:	2013
Publisher:	World Public Library

Member Page:	Florentin Smarandache
Citation APA MLA Chicago B. Vasantha Kandasam, B. W., & Smarandache, F. (2013). Algebraic Structures Using Super Interval Matrices. Retrieved from http://gutenberg.cc/

Description
In this book authors for the first time introduce the notion of super interval matrices using the special intervals of the form [0, a], a belongs to Z+ ∪ {0} or Zn or Q+ ∪ {0} or R+ ∪ {0}.

Excerpt
SUPER INTERVAL SEMILINEAR ALGEBRAS In this chapter we for the first time introduce the notion of semilinear algebra of super interval matrices over semifields of type I (super semilinear algebra of type I) and semilinear algebra of super interval matrices over interval semifields of type II (super semilinear algebra of type II) and study their properties and illustrate them with examples. DEFINITION 4.1: Let V be a semivector space of super interval matrices defined over the semifield S of type I. If on V we for every pair of elements x, y ∈ V; x . y is in V where ‘.’ is the product defined on V, then we call V a semilinear algebra of super interval matrices over the semifield S of type I. We will illustrate this situation by some examples. Example 4.1: Let V = {([0, a1] [0, a2] | [0, a3] [0, a4] | [0, a5] [0, a6] | [0,a7]) | ai ∪ Z+ ∪ {0}; 1 ≤ i ≤ 7} be a semivector space of super interval matrices defined over the semifield S = Z+ ∪ {0} of type I. Consider x = ([0, 5] [0, 3] | [0, 9] [0, 1] [0, 2] [0, 8] | [0, 6]) and y =([0, 1] [0, 2] | [0, 3] [0, 5] [0, 3] [0, 1] | [0, 5]) in V. We define the product ‘.’ on V as x.y =([0, 5] [0, 6] | [0, 27] [0, 5] [0, 6] [0, 8] | [0, 30]) ∈ V. Thus V is a super semilinear algebra of super interval row matrices over the semifield S of type II.

Table of Contents
CONTENTS Preface 5 Chapter One INTRODUCTION 7 Chapter Two INTERVAL SUPERMATRICES 9 Chapter Three SEMIRINGS AND SEMIVECTOR SPACES USING SUPER INTERVAL MATRICES 83 Chapter Four SUPER INTERVAL SEMILINEAR ALGEBRAS 137 Chapter Five SUPER FUZZY INTERVAL MATRICES 203 5.1 Super Fuzzy Interval Matrices 203 5.2 Special Fuzzy Linear Algebras Using Super Fuzzy Interval Matrices 246 Chapter Six APPLICATION OF SUPER INTERVAL MATRICES AND SET LINEAR ALGEBRAS BUILT USING SUPER INTERVAL MATRICES 255 Chapter Seven SUGGESTED PROBLEMS 257 FURTHER READING 281 INDEX 285 ABOUT THE AUTHORS 287