The relationship between the intuitionistic fuzzy sets and the algebraic hyperstructures is described in this paper. The concept of the quasi-coincidence of an intuitionistic fuzzy interval valued with an interval-valued intuitionistic fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of an intuitionistic fuzzy point in intuitionistic fuzzy sets. By using thi...

and Applied Analysis 3 x ν αx, t ν x, t/|α| for each α/ 0, xi ν x, t ν y, s ≥ ν x y, t s , xii ν x, · : 0,∞ → 0, 1 is continuous, xiii limt→∞ν x, t 0 and limt→ 0ν x, t 1. In this case μ, ν is called an intuitionistic fuzzy norm. Example 1.4 cf. 37 . Let X, ‖·‖ be a normed space, a∗b ab, and a b min a b, 1 for all a, b ∈ 0, 1 . For all x ∈ X and every t > 0 and k 1, 2, consider μk x, t ⎧ ⎨ ⎩ t t...

in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...

Based on the theory of intuitionistic fuzzy sets, the concepts of intuitionistic fuzzy subalgebras with thresholds (λ, μ) and intuitionistic fuzzy ideals with thresholds (λ, μ) of BCI-algebras are introduced and some properties of them are discussed. Keywords—BCI-algebra, intuitionistic fuzzy set, intuitionistic fuzzy subalgebra with thresholds (λ, μ), intuitionistic fuzzy ideal with thresholds...

In this paper, we introduce the concept of an intuitionistic fuzzy graph structure (IFGS). We discuss certain notions, including intuitionistic fuzzy Bi-cycles, intuitionistic fuzzy Bi-trees and φ-complement of an intuitionistic fuzzy graph structure with several examples. We also present φ-complement of an intuitionistic fuzzy graph structure along with self-complementary and strong self-compl...

Abstract: In this paper, similar to the extension from intuitionistic fuzzy numbers (IFNs) to neutrosophic numbers (NNs), we propose the normal neutrosophic numbers (NNNs) based on the normal intuitionistic fuzzy numbers (NIFNs) to handle the incompleteness, indeterminacy and inconsistency of the evaluation information. In addition, because Heronian mean (HM) operators can consider capture the ...

Intuitionistic fuzzy special sets is a special case of intuitionistic fuzzy sets. In this paper, under the framework of information systems, the relationship between intuitionistic fuzzy special sets and rough sets is analyzed. Based on basic intuitionistic fuzzy special sets of information systems, intuitionistic fuzzy special σ-algebra are generated, and rough sets are embedded in the intuiti...

Similarity of intuitionistic fuzzy sets is an important measure to indicate the similarity degree between intuitionistic fuzzy sets. Based on the information carried by transforming intuitionistic fuzzy sets into their lower, upper and middle fuzzy sets, we propose a new construction for similarity measures between intuitionistic fuzzy sets. The proposed construction method on similarity measur...

The mounting escalation of multimedia content in information indexing and retrieval has made a high venture for extracting the text from videos. In this paper a new approach has been made using Stroke Width Transform (SWT) with intuitionistic fuzzy set theory for detecting text from images. The proposed methodology uses a fuzzy based edge detection method instead of the conventional edge detect...

This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we an...