Generalized Weak Forms of Irresolute Mappings in Intuitionistic Topological Spaces

Samer Yaseen,Suham Aziz,Nabila Aziz

doi:10.32894/kujss.2018.13.4.3

Samer Yaseen, Suham Aziz + Show 1 more

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https://doi.org/10.32894/kujss.2018.13.4.3

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Abstract

The purpose of this paper is to study a new classes of irresolute mappings called Intuitionistic Generalized Pre irresolute mappings, Intuitionistic Generalized Semi irresolute mappings, Intuitionistic Generalized α-irresolute mappings and Intuitionistic Generalized β-irresolute mappings with study of their properties. Then we investigate relationships between them..

Highlights

In 1965, Zadeh [8] introduced the concept of fuzzy set. later Atanassov introduced the concept of Intuitionistic fuzzy set [1,2] using generalized of fuzzy set, this concept used to defined intuitionistic fuzzy special sets and "intuitionistic fuzzy topological spaces which introduced by Coker [4,5]
In 2000, Coker [6] introduced the concept of intuitionistic topological spaces In this paper we introduce a new classes of weak irresolute mapping with study their properties
Intuitionistic Generalized Pre Irresolute & Semi Irresolute Mappings: In this part we introduce Intuitionistic Generalized pre irresolute, Intuitionistic

Summary

Introduction

In 1965, Zadeh [8] introduced the concept of fuzzy set. later Atanassov introduced the concept of Intuitionistic fuzzy set [1,2] using generalized of fuzzy set, this concept used to defined intuitionistic fuzzy special sets and "intuitionistic fuzzy topological spaces which introduced by Coker [4,5]. . An Intuitionistic topology ( ITS, for short ) on is a collection of an Intuitionistic sets in with the following conditions: 1) ̇ , ̇ . The complement of an Intuitionistic open set is called Intuitionistic closed set Denoted by "ICS". An intuitionistic setof X is said to be : 1) Intuitionistic generalizes semi-open set(IGSOS , for short) if U ISCS s.t Uthen U int( ̃ ). 2) Intuitionistic generalizes pre-open set (IGPOS , for short) if U IPCS s.t. Uthen U int( ̃ ). The complement of IGPOS is called IGPCS . Proposition 3.2: Let ( ) ( ) and ( ) ( ) be IGPIr mapping. Proof: Letbe ICS in . ( ( ̃ )) is IGSCS in and mapping. The implication among some types of mappings are given by the following diagram

IG Ir

IG Ir IG Ir

Define a mapping