Interval-Valued Intuitionistic Fuzzy Subnear Rings

Interval-Valued Intuitionistic Fuzzy Subnear Rings

Amal Kumar Adak (Ganesh Dutt College, India)
DOI: 10.4018/978-1-7998-0190-0.ch013

Abstract

The theory of interval-valued intuitionistic fuzzy sets is a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this chapter, the notion of interval-valued intuitionistic fuzzy subnear-ring is introduced, and some interesting properties are discussed. Some relations on the family of all interval-valued intuitionistic fuzzy subnear-ring are presented, and some related properties are investigated. Also, the authors represent upper and lower level set of interval-valued intuitionistic fuzzy set.
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2 Preliminaries And Definition

In this section, we recall the concept of interval arithmetics. Let D(0,1) be the set of all closed subintervals of the interval [0,1]. Then according to Zadeh's extension principle, we can popularize these operations such as ˅, ˄ and c (complement) to D(0,1). Thus ([I], ˅, ˄, c) is a complete lattice with a minimal element 978-1-7998-0190-0.ch013.m01 and a maximal element 978-1-7998-0190-0.ch013.m02 . Furthermore let 978-1-7998-0190-0.ch013.m03, 978-1-7998-0190-0.ch013.m04, where a- and a+ are lower and upper limits of 978-1-7998-0190-0.ch013.m05, be two intervals then we have 978-1-7998-0190-0.ch013.m06, a+ = b+, 978-1-7998-0190-0.ch013.m07, a+b+, and 978-1-7998-0190-0.ch013.m08, a+ < b+ and 978-1-7998-0190-0.ch013.m09.

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