A study on multiplication operation on triangular fuzzy numbers

The arithmetic operations on fuzzy number are basic content in fuzzy mathematics. But still the operations of fuzzy arithmetic operations are not established. There are some arithmetic operations for computing fuzzy number. Certain are analytical methods and further are approximation methods. In this paper we, compare the multiplication operation on triangular fuzzy number between α-cut method and standard approximation method and give some examples.

Towards the Construction of Reed-Muller Code Based Symmetric Key FHE

Homomorphic encryption (HE) schemes became popular cryptographic primitives and very useful in variety of security applications. Homomorphic encryption based on coding theory have the advantages of faster computations due to the structural properties of the codes used. Several schemes are supporting unlimited Mod2 addition operations in literature. The present paper introduces Reed-Muller (RM) code based Mod2 multiplication operation thereby making RM code based HE scheme fully homomorphic. The representation of the codeword with necessary adaption to support unlimited number of Mod2​ multiplication operations is presented along with the scheme first. The correctness proof of the homomorphic operations along with experimental evaluation is also presented to demonstrate the practical aspects of the proposal.

DNA Matrix Operation Based on the Mechanism of the DNAzyme Binding to Auxiliary Strands to Cleave the Substrate

Numerical computation is a focus of DNA computing, and matrix operations are among the most basic and frequently used operations in numerical computation. As an important computing tool, matrix operations are often used to deal with intensive computing tasks. During calculation, the speed and accuracy of matrix operations directly affect the performance of the entire computing system. Therefore, it is important to find a way to perform matrix calculations that can ensure the speed of calculations and improve the accuracy. This paper proposes a DNA matrix operation method based on the mechanism of the DNAzyme binding to auxiliary strands to cleave the substrate. In this mechanism, the DNAzyme binding substrate requires the connection of two auxiliary strands. Without any of the two auxiliary strands, the DNAzyme does not cleave the substrate. Based on this mechanism, the multiplication operation of two matrices is realized; the two types of auxiliary strands are used as elements of the two matrices, to participate in the operation, and then are combined with the DNAzyme to cut the substrate and output the result of the matrix operation. This research provides a new method of matrix operations and provides ideas for more complex computing systems.

A note on almost prime submodule of CSM module over principal ideal domain

An almost prime submodule is a generalization of prime submodule introduced in 2011 by Khashan. This algebraic structure was brought from an algebraic structure in ring theory, prime ideal, and almost prime ideal. This paper aims to construct similar properties of prime ideal and almost prime ideal from ring theory to module theory. The problem that we want to eliminate is the multiplication operation, which is missing in module theory. We use the definition of module annihilator to bridge the gap. This article gives some properties of the prime submodule and almost prime submodule of CMS module over a principal ideal domain. A CSM module is a module that every cyclic submodule. One of the results is that the idempotent submodule is an almost prime submodule.

Naive Bayes modification for intrusion detection system classification with zero probability

One of the methods used in detecting the intrusion detection system is by implementing Naïve Bayes algorithm. However, Naïve Bayes has a problem when one of the probabilities is 0, it will cause inaccurate prediction, or even no prediction was found. This paper proposed two modifications for Naïve Bayes algorithm. The first modification eliminated the variable that has 0 probability and the second modification changed the multiplication operations to addition operations. This modification is only applied when the Naïve Bayes algorithm does not find any prediction results caused by zero probabilities. The results of this research show that the value of precision, recall, and accuracy in the modification made tends to increase and better than the original Naïve Bayes algorithm. The highest precision, recall, and accuracy are obtained from modification by changing the multiplication operation to the addition. Increasing precision can reach 4%, increasing recall reaches 2% and increasing accuracy reaches 2%.

TURKISH PRE-SERVICE MATHEMATICS TEACHERS’ BELIEFS IN MULTIPLICATION

Mathematics teachers’ beliefs play an important role in the mathematics teaching practices. However, the instruments used to measure the mathematics on certain contents are still limited. Thus, this study was conducted to develop a Multiplication Beliefs Questionnaire (MBQ) to identify and examine the profile of Turkish pre-service mathematics teachers’ beliefs. The samples of this study consisted of 414 four-year pre-service primary mathematics teachers from 18 different universities in Turkey collected using a convenience sampling technique. The validity of the questionnaire was analyzed using an exploratory factor analysis (EFA). We obtained four components of beliefs in multiplication covering, remote belief in multiplication (C1), multiplication operation belief in mathematics textbooks (C2), dynamic belief in multiplication learning (C3), and self-efficacy belief in multiplication problems (C4). The results showed that the pre-service mathematics teachers’ beliefs in components C1, C3, and C4 were positive, while component C2 was neutral. This study had an essential contribution to the mathematics literature since developing a questionnaire on multiplication distributed to the pre-service teachers. The previous studies showed that belief was subjective yet objectively influenced knowledge. Thus, identifying the pre-service teachers’ beliefs in teacher education may provide various benefits in reforming mathematics teaching.

Analisis Kebutuhan Pengembangan Permainan Kartu Domino sebagai Media Pembelajaran Operasi Hitung Perkalian Siswa Kelas IV SD

Keterampilan operasi perkalian sangat penting dalam pendidikankarena operasi perkalian merupakan inti dasar mata pelajaran matematika hingga tingkat tinggi. Fungsi media pada pembelajaran yakni menyampaikan informasi selama pembelajaransehingga menginspirasi siswa untuk belajar. Terdapat banyak variasi media pembelajaran operasi perkalian, di antaranya media permainan kartu. Permainan kartu ini disebut domino. Penelitian ini menggunakan survei kuesioner dengan teknik pengumpulan data melalui kuesioner dan angket dikategorikan sesuai dengan kebutuhan target yang diujicobakan kepada siswa kelas IV SD dengan latar sekolah yang berbeda. Tujuan pada penelitian ini yakni ingin mengetahui kebutuhan dalam pengembangan permainan kartu domino, media pembelajaran yang digunakan oleh guru pada pembelajaran operasi perkalian, dan tingkat ketahuan para siswa terkait dengan media kartu domino tersebut. Adapun hasil penelitian menunjukkan tingkat implementasi media pada pembelajaran mendapatkan skor sebesar 78,1% dan respons positif terhadap permainan kartu sebesar 78,1%. Multiplication operation skills are very important in education, because multiplication operations are the basic core of mathematics subjects to a high level. The function of the media in the learning is to convey information during learning, so that it inspires students to learn. There are many variations of multiplication operation learning media, including card game media. This study used a questionnaire survey with data collection techniques through questionnaires and questionnaires categorized according to the needs of the target were tested on fourth grade elementary school students with different school backgrounds. The purpose of this study is to find out the needs in the development of domino card games, the learning media used by teachers in learning multiplication operations, and the level of discovery by students related to the domino card media. The results of the study show that the level of media implementation in learning gets a score of 78,1% and a positive response to card games is 78,1%.

Modified Binary Vedic Multiplication Using Carry Save Adder

This paper presents modified binary Vedic multiplication using carry save adder. The suggested modified binary Vedic multiplication technique is more efficient in terms of delay. The proposed circuit is implemented in Verilog HDL. The Xilinx ISE Design Suite 14.6 is used for circuit synthesis. The simulation done for 4-bit ,8-bit 16-bit multiplication operations. In this paper, the simulation waveforms are shown only for 4-bit and 8-bit multiplication operation based on the modified Vedic multiplication technique using carry save adder. The vedic multiplication method can be extended for a larger bit size. The delay compared with normal multiplication technique.

Arbitrary Coupled Trapezoidal Fully Fuzzy Sylvester Matrix Equation

There are many applications where couple of Sylvester matrix equations (CSME) are required to be solved simultaneously, especially in analyzing the stability of control systems. However, there are some situations in which the crisp CSME are not well equipped to deal with the uncertainty problem during the process of stability analysis in control system engineering. Thus, in this paper a new method for solving a coupled trapezoidal fully fuzzy Sylvester matrix equation (CTrFFSME) with arbitrary coefficients is proposed. The arithmetic fuzzy multiplication operation is applied to convert the CTrFFSME into a system of non-linear equations. Then the obtained non-linear system is reduced and converted to a system of absolute equations where the fuzzy solution is obtained by solving that system. The proposed method can solve many unrestricted fuzzy systems such as Sylvester and Lyapunov fully fuzzy matrix equations with triangular and trapezoidal fuzzy numbers. We illustrate the proposed methods by solving numerical example.

Digital Signature Scheme with Hidden Group Possessing Two-Dimensional Cyclicity

A method is proposed for constructing digital signature schemes based on the hidden discrete logarithm problem, which meet ageneral criterion of post-quantum resistance. The method provides a relatively small size of the public key and signature. Based on the method, a practical digital signature scheme has been developed, in which the exponentiation operation in a hidden group with two-dimensional cyclicity is the basic cryptographic primitive. The algebraic support of a cryptoscheme is a four-dimensional finite non-commutative algebra with associative multiplication operation. By specifying algebra using abasis vector multiplication table with half of empty cells, the performance of signature generation and authentication procedures is improved. A public key is a triple of four-dimensional vectors calculated as images of elements of a hidden group which are mapped using two types of masking operations: 1) mutually commutative with the exponentiation operation and 2) not having this property.