EDUCATUM JSMT Vol. 6 No. 1 (2019) ISSN 2289-7070 / eISSN 2462-2451 (41-46) http://ojs.upsi.edu.my/index.php/EJSMT/index 41 Visualization of Intuitionistic Fuzzy B-Spline Space Curve and Its Properties M. I. E Zulkifly, 1* and A. F. Wahab, 1 1 School of Informatics and Applied Mathematics, University Malaysia Terengganu, 21030, Kuala Nerus, Terengganu, Malaysia *Corresponding author: emirzul@gmail.com DOI: https://doi.org/10.37134/ejsmt.vol6.1.6.2019 Received: 13 June 2019; Accepted: 15 June 2019; Published: 28 June 2019 Abstract In this paper, an intuitionistic fuzzy B-spline space curve is defined and some of its properties is introduced. Firstly, intuitionistic fuzzy control point is defined based on intuitionistic fuzzy and geometrical modeling concepts. Each of the control point relation that consists of three function is find and shown. Later, the control point is blended with B- spline basis function and intuitionistic fuzzy B-spline curve is visualized. Some of the control point and space curve properties in the Euclidean space is also discussed throughout this paper. Keywords Intuitionistic fuzzy B-spline, intuitionistic fuzzy control point, intuitionistic fuzzy set, space curve, control point relation INTRODUCTION Curve is an important tools used to visualize collected data or information provided. It is a necessary and inevitable in order to represent data point [1]. The data need to visualize as it can show the trend and nature of the data studied. A curve can be visualized depends on the conditions of the data obtained. The curve became harder and challenging to visualize when there exist uncertainty features in the data. In normal situation, an uncertainty data is remove from a set of data regardless of its effect on the resulting curve. Therefore, the evaluation and analyzing process from the data visualized will be incomplete. The data set should be filtered if there exist an element of uncertainty so that the data can be used to generate curves or surfaces of a model that want to be investigated. To overcome this matter, intuitionistic fuzzy set (IFS) is used. IFS is a generalization of fuzzy set theory from [2] and was introduced by in [3][4]. The set consists of three component namely degree of membership, non-membership and uncertainty (non-determinacy). Intuitionistic fuzzy set (IFS) have been studied and applied in different fields of science, mathematics, engineering and much more such as in [5][6]. IFS is generally defined by three functions consists of membership, non-membership and uncertainty with the constraint that the sum of these three functions must be equal to one [7]. Research of IFS related to curve and surface have been done by Zulkifly & Wahab. In [8], they introduced an idea of IFS in spline curve and surface which focused on Bézier spline where the curve and surface are blended with intuitionistic fuzzy control point. Wahab et. al [9] discussed intuitionistic fuzzy Bézier model and generated intuitionistic fuzzy Bézier curve using interpolation method. They visualized intuitionistic fuzzy Bézier curve that consists of membership, non-membership and uncertainty curve by blending the Bernstein polynomial with intuitionistic fuzzy control point that have been defined. Later, Zulkifly & Wahab defined intuitionistic fuzzy control point relation (IFCPR) through intuitionistic fuzzy concept with some properties. They illustrate intuitionistic fuzzy bicubic Bézier surface through the approximation method by using data point with intuitionistic features [10]. By using IFCPR, they also generate cubic Bézier curve through interpolation method and intuitionistic fuzzy B-spline curve (IFB-SC) using approximation method [12][13].