Mathematics and Computer Science, Volume 1

12Complete Generalized Soft Lattice

Manju John* and Susha D.

Department of Mathematics, Catholicate College, Pathanamthitta, Kerala, India

Abstract

A soft set is a representation of vague data and can be used to study real-life problems containing various types of uncertainty. Complete lattices have many applications in various fields. Here, we introduce the concepts of complete gs-lattice, s-closure system and s-Moore family. Here, we discuss some ways to construct complete gs-lattices and a representation of a complete gs-lattice as an s-closure system. Fixed point theory is a useful tool in applied mathematics. We conclude this study with Tarski’s fixed point theorem in generalized soft lattices (gs-lattices).

Keywords: Complete gs lattice, s-closure system, s-Moore family

12.1 Introduction

Theories of probability, fuzzy set, rough set [18], vague set, etc. are very useful for dealing with different kind of uncertainty. Zadeh’s fuzzy set theory [20] is most applicable and useful among all these theories, which was proposed in 1965. A soft set is a fairly accurate description of an object, and this description can be made convenient by choosing parametrization as words, sentences, real numbers, functions, etc., which reduces the problems like setting membership functions. Molodstov showed that this theory has various applications in the fields, like theory of games, integration, and the theory of measure. Many researchers like Maji [15], Shabir [19], Cagman [1, 5] and Feng ...