DEVELOPMENT OF LEARNING TRAJECTORY ON THE SET TOPIC FOR 7TH GRADE IN THE CONTEXT OF SEDEKAH LAUT TRADITION

Set is an important topic to be mastered by students because it influences the development of mathematics in daily life. However, many students still have difficulty learning the topic. Therefore, it is necessary to design a learning trajectory using the appropriate approach, context, and media. This research resulted in the learning development using Sedekah Laut context to create meaningful learning and increase students' understanding of sets. The method used in this study was design research proposed by Gravemeijer & Cobb with three stages: preliminary design, experimental design (pilot experiments and teaching experiments), and retrospective analysis. However, this article only presented the results from the Preliminary design stage. The participants involved in this study were 7th-grade students of SMP Negeri 6 Semarang. The resulting hypothetical learning trajectory consists of a series of learning processes: observing context videos to find the concepts of sets, non-sets, empty sets, universal sets, and Venn diagrams; explaining the properties of the set; defining set operations; and solving problems related to sets.

A Large-Size HfO2 Based RRAM Structure Suitable for Integration of One RRAM with One InGaZnO Thin Film Transistor for Large-Area Applications

This work aims at finding a HfO2-based resistive random-access memory (RRAM) structure suitable for the integration of one RRAM with one InGaZnO thin film transistor (TFT) for large-area applications such as flexible electronic circuits. One of the major concerns is that the compliance current (CC) required for the formation of stable and strong conductive filaments in the forming and set processes as well as the maximum current required in the reset process in a large-size RRAM should be lower than that of the maximum current a TFT can deliver. In this work, an ultrathin Al2O¬3 layer of 2 nm was inserted between the HfO2 switching layer and the reactive Ti layer of the top electrode in the RRAM with the structure of Pt (bottom electrode)/HfO2/Al2O3/Ti/TiN (top electrode). With the ultrathin Al2O¬3 layer, the forming voltage was greatly reduced, and the CC for stable forming and set operations and maximum reset current can reach a low current level that an InGaZnO TFT is able to provide, while the device-to-device variation of the forming operation and cycle-to-cycle resistance variations of the set and reset operations are improved significantly.

(3, 2)-Fuzzy Sets and Their Applications to Topology and Optimal Choices

The purpose of this paper is to define the concept of (3, 2)-fuzzy sets and discuss their relationship with other kinds of fuzzy sets. We describe some of the basic set operations on (3, 2)-fuzzy sets. (3, 2)-Fuzzy sets can deal with more uncertain situations than Pythagorean and intuitionistic fuzzy sets because of their larger range of describing the membership grades. Furthermore, we familiarize the notion of (3, 2)-fuzzy topological space and discuss the master properties of (3, 2)-fuzzy continuous maps. Then, we introduce the concept of (3, 2)-fuzzy points and study some types of separation axioms in (3, 2)-fuzzy topological space. Moreover, we establish the idea of relation in (3, 2)-fuzzy set and present some properties. Ultimately, on the basis of academic performance, the decision-making approach of student placement is presented via the proposed (3, 2)-fuzzy relation to ascertain the suitability of colleges to applicants.

Footvector Representation of Curves and Surfaces

This paper proposes a foot mapping-based representation of curves and surfaces which is a geometric generalization of signed distance functions. We present a first-order characterization of the footvector mapping in terms of the differential geometric invariants of the represented shape and quantify the dependence of the spatial partial derivatives of the footvector mapping with respect to the principal curvatures at the footpoint. The practical applicability of foot mapping representations is highlighted by several fast iterative methods to compute the exact footvector mapping of the offset surface of CSG trees. The set operations for footpoint mappings are higher-order functions that map a tuple of functions to a single function, which poses a challenge for GPU implementations. We propose a code generation framework to overcome this that transforms CSG trees to the GLSL shader code.

N-Fuzzy Sets and Their Applications

The purpose of this paper is to define n-Fuzzy sets and study their relationship with intuitionistic fuzzy sets, Pythagorean fuzzy sets and Fermatean fuzzy sets. The n-Fuzzy sets can deal with more uncertain situations than intuitionistic fuzzy sets, Pythagorean fuzzy sets and Fermatean fuzzy sets because of its larger range of describing the membership grades. The set operations, score function, accuracy function and Euclidean distance of n-Fuzzy sets will study. Finally, we study the Sanchez$^{,}$s approach for medical diagnosis and extend this concept with the notion of n-Fuzzy set.

A Set of Integral Grid-Coding Algebraic Operations Based on GeoSOT-3D

As the amount of collected spatial information (2D/3D) increases, the real-time processing of these massive data is among the urgent issues that need to be dealt with. Discretizing the physical earth into a digital gridded earth and assigning an integral computable code to each grid has become an effective way to accelerate real-time processing. Researchers have proposed optimization algorithms for spatial calculations in specific scenarios. However, a complete set of algorithms for real-time processing using grid coding is still lacking. To address this issue, a carefully designed, integral grid-coding algebraic operation framework for GeoSOT-3D (a multilayer latitude and longitude grid model) is proposed. By converting traditional floating-point calculations based on latitude and longitude into binary operations, the complexity of the algorithm is greatly reduced. We then present the detailed algorithms that were designed, including basic operations, vector operations, code conversion operations, spatial operations, metric operations, topological relation operations, and set operations. To verify the feasibility and efficiency of the above algorithms, we developed an experimental platform using C++ language (including major algorithms, and more algorithms may be expanded in the future). Then, we generated random data and conducted experiments. The experimental results show that the computing framework is feasible and can significantly improve the efficiency of spatial processing. The algebraic operation framework is expected to support large geospatial data retrieval and analysis, and experience a revival, on top of parallel and distributed computing, in an era of large geospatial data.

Contribution of Student Level of Understanding in The Concept of Calculated Operations And Their Relationship to Set Operations

The problem in this study is: whether there is a contribution to the level of understanding of the concept of calculated operations against the operation of the association in students of SMP Negeri 1 Balikpapan. This study aims to find out if there is a contribution to the level of understanding of the concept of calculated operations against the operation of the association in students of SMP Negeri 1 Balikpapan. The population of this study is all students of grade VII-A SMP Negeri 1 Balikpapan consisting of 34 students. And as a sample in this study is the whole student. The data analysis technique used is to use non-premetric statistics "sign test". The results of the data analysis showed that tcount < htable or 1 < 1, this means that there is a positive contribution between the mastery of the counting operations against the operation of the student association of SMP Negeri 1 balikpapan. From these results, it is expected that the teachers of mathematics lessons generally and the teachers who teach in grade VII in order to further improve the learning of hitung operations to students so that the learning of the association operations ismore understandable to students

Suitable interval-valued intuitionistic fuzzy topological spaces

In the present paper, a characterization of the intuitionistic fuzzy sets, the interval-valued intuitionistic fuzzy sets and their set-operations are given. By making use of these characterizations, the relationships between the interval-valued intuitionistic fuzzy topology and four fuzzy topologies associated to it are studied. For this reason, some subclasses of the family of interval-valued intuitionistic fuzzy topologies on a set which we call pre-suitable and suitable are introduced. Furthermore, the concepts of homeomorphism functions and compactness in the framework of interval-valued intuitionistic fuzzy topological spaces are introduced and studied.

On the Binarization of Grey Wolf Optimizer‎: ‎A Novel Binary Optimizer Algorithm

‎Grey Wolf Optimizer (GWO) is a population-based evolutionary algorithm inspired by the hunting behaviour of grey wolves‎. ‎GWO‎, ‎in its basic form‎, ‎is a real coded algorithm‎, ‎therefore‎, ‎it needs modifications to deal with binary optimization problems‎. ‎In this paper‎, ‎we review previous works on binarization of GWO‎, ‎and classify them with respect to their encoding scheme‎, ‎updating strategy‎, ‎and transfer function‎. ‎Then‎, ‎we propose a novel binary GWO algorithm (named SetGWO)‎, ‎which is based on set encoding and uses set operations in its updating strategy‎. ‎Experimental results on different real-world combinatorial optimization problems and different datasets‎, ‎show that SetGWO outperforms other existing binary GWO algorithms in terms of quality of solutions‎, ‎running time‎, ‎and scalability‎.