On the fixed point theory of soft metric spaces

Mujahid Abbas,Salvador Romaguera,Ghulam Murtaza

doi:10.1186/s13663-016-0502-y

Abstract

AbstractThe aim of this paper is to show that a soft metric induces a compatible metric on the collection of all soft points of the absolute soft set, when the set of parameters is a finite set. We then show that soft metric extensions of several important fixed point theorems for metric spaces can be directly deduced from comparable existing results. We also present some examples to validate and illustrate our approach.

Highlights

It is a usual practice to use mathematical tools to study the behavior of different aspects of a system and its different subsystems
Different kind of difficulties arise in dealing with the uncertainties and imprecision either already existing in the data or due to the mathematical tools used to solve the model featuring various situations
Theories such as probability theory and rough set theory have been introduced by mathematicians and computer scientists to handle the problems associated with the uncertainties and imprecision of real world models

Summary

Introduction

It is a usual practice to use mathematical tools to study the behavior of different aspects of a system and its different subsystems. Fuzzy set theory, initiated by Zadeh [ ], has evolved as an important tool to solve the issues of uncertainties and ambiguities Theories such as probability theory and rough set theory have been introduced by mathematicians and computer scientists to handle the problems associated with the uncertainties and imprecision of real world models. The contribution made by probability theory, fuzzy set theory, vague sets, rough sets, and interval mathematics to deal with uncertainty is of vital importance but these theories have their own limitations. To overcome these peculiarities, in , Molodtsov introduced in [ ] soft sets as a mathematical tool to handle the uncertainty associated with real world data based problems. The distinguishing attribute of soft set theory is that unlike probability and fuzzy set theory, it does not uphold a precise quantity

Objectives

Conclusion