The conditions of β−algebra is enforced into the structure cubic intuitionistic fuzzy settings. Furthermore, concept β− subalgebra expressed and its pertinent properties were explored. Also, discussed about level set β−subalgebras furnished some fascinating results on cartesian product β−subalgebra. Moreover, notion -normed have been introduced relevant are studied.

In this paper, employing the common property ($E.A$), we prove a common fixed theorem for weakly compatible mappings via an implicit relation in Intuitionistic fuzzy metric space. Our results generalize the results of S. Kumar [S. Kumar, {it Common fixed point theorems in Intuitionistic fuzzy metric spaces using property (E.A)}, J. Indian Math. Soc., 76 (1-4) (2009), 94--103] and C. Alaca et al...

Based on previous results that study the completion of fuzzy metric spaces, we show that every intuitionistic fuzzy quasi-metric space, using the notion of fuzzy metric space in the sense of Kramosil and Michalek to obtain a generalization to the quasi-metric setting, has a bicompletion which is unique up to isometry.

The purpose of this article is to research the concept Fibonacci lacunary ideal convergence double sequences in intuitionistic fuzzy normed linear spaces (IFNS). Additionally, a new concept, called convergence, examined. Also, I?-limit points and I?-cluster for IFNS have been defined significant results given. Cauchy I?-Cauchy are worked.

Most existing distances between intuitionistic fuzzy sets are defined in linear plane representations in 2D or 3D space. Here, we define a new interpretation of intuitionistic fuzzy sets as a restricted spherical surface in 3D space. A new spherical distance for intuitionistic fuzzy sets is introduced. We prove that the spherical distance is different from those existing distances in that it is...