Application of Neutrosophic Filters in Lattice Implication Algebra

V. S. Naga Malleswari^*1, Kiran kumar¹, K. Bhagya Lakshmi², G. Luka³, T. Srinivasa Rao⁴     

¹Department of Freshman Engineering, Pvp Siddhartha institute of Technology, Vijayawada, India

²Department of Mathematics,KKR&KSR Institute of technology,Guntur, India

³ Department of Mathematics, Government polytechnic for minorities,Guntur, India

⁴Department of Mathematics, KL university, Vaddeswaram, India.

Emails: vsnm.maths@gmail.com; kkumark2005@yahoo.co.in; mblakshmi12@gmail.com;gunturuluka@gmail.com; tsr_2505@kluniversity.in

Abstract

Neutrosophic set theory is applied to lattice implication algebra, and the concept of neutrosophic filters and neutrosophic lattice filters in lattice implication algebra are introduced. Several properties are investigated.  Characterizations of a neutrosophic filter are discussed. Finally, we proved that every neutrosophic filter is a neutrosophic lattice filter, but the converse is invalid.

Keywords: Neutrosophic set(NS); Lattice implication algebra (LIA); Neutrosophic filter(NF); Neutrosophic lattice filter(NLF)