Cubic Intuitionistic Fuzzy Gamma-m-Normed Linear Space

Abstract

Objectives: The purpose of this research is to take the lead in foggiest  idea of  convergence in cubic intuitionistic fuzzy Gamma-m normed linear space(CCIFGMNLS). According to the theory of fuzzy m-Normed Linear Space(FMNLS),we offer the conception  of Cauchy's sequence and convergence in cubic  intuitionistic fuzzy Gamma-m Normed  Linear Space (CIFGMNLS). We have reviewed the  certain results, and this paper proposes the hypothesis  of completeness in CIFGMNLS.

Methods: In this research paper we defined the   intuitionistic fuzzy Gamma gamma ring, intuitionistic fuzzy gamma ideals,  left and right intuitionistic fuzzy gamma vector space which are using to approach the theory of intuitionistic fuzzy gamma-2-normed linear space, intuitionistic fuzzy Gamma-m-Normed Linear Space and its axioms.  And the CCIFGMNLS can be approached using the IFGMNLS.

Findings: In this research paper  from CCIFGMNLS construct a norm function that satisfies the properties of IFGMNLS, and   provided  that example with proof  of a sequence is cauchy sequence and convergence in IFGMNLS if and only  it is cauchy sequence and convergence sequence in CCIFGMNLS. Also derived a theorem and its proof for completeness of a  sequence   in CCIFGMNLS.

Novelty: Already gamma ring and fuzzy n-normed linear space has been defined. we   originated  the notion  of  IFGMNLS using this also  put forwarded  the  CCIFGMNLS and  some results obtained from its properties  . we provided  a necessary axioms  to  completeness of  a sequence in CCIFGMNLS.