Some Normal Intuitionistic Fuzzy Heronian Mean Operators Using Hamacher Operation and Their Application

Hamacher operation which is generalization of the Algebraic and Einstein operation, can widely provide a large number of arithmetical operation with respect to uncertainty information, and Heronian mean can deal with correlations of the input arguments or different criteria and don’t make calculation redundancy, meanwhile, the normal intuitionistic fuzzy numbers (NIFNs) can depict distinctively normal distribution information in practical decision making. In this paper, a multi-criteria group decision-making (MCGDM) problem is researched under the NIFNs environment, and a new MCGDM approach is introduced on the basis of the Hamacher operation. Firstly, according to Hamacher t-conorm and t-norm, some operational laws of NIFNs are presented. Secondly, it is noticed that Heronian mean can’t only once take into account mutual relation between attribute values once, but also consider the correlation between input argument and itself. Therefore, we develop some operators and study their properties in order to aggregate normal intuitionistic fuzzy numbers information, these operators include Hamacher Heronian mean (NIFHHM), Hamacher weighted Heronian mean (NIFHWHM), Hamacher geometric Heronian mean (NIFHGHM) and Hamacher weighted geometric Heronian mean (NIFHWGHM). Furthermore, we apply the proposed operators to the MCGDM problem and present a new method. The main characteristics of this new method involve that: (1) it is suitable to make decision under the normal intuitionistic fuzzy numbers environment and more reliable and reasonable to aggregate the normal distribution information. (2) it utilizes Hamacher operation which can provide more reliable and flexible decision-making results and offer an effective and powerful mathematic tool for the MAGDM under uncertainty. (3) it uses the Heronian mean operator which can considers relationships between the input arguments or the attributes and don’t brings subsequently about redundancy. Lastly, an application is given for showing the feasibility and effectiveness of the presented method in this paper.

Problematika Pembelajaran Matematika pada Pokok Bahasan Eksponen dan Alternatif Pemecahannya

<p><strong><em>. </em></strong>The aims of writing this article are to analyze the presumption regarding on exponent learning difficulty as well as to give alternative solution to resolve this problem. There are several presumptions of students’ difficulties in exponent learning difficulty, i.e. difficulty in comprehending concept, doing arithmetical operation, and students’ carelessness to do the tasks. Alternative solutions which teacher can provide to minimize the difficulties in doing exponent task are re-emphasizing the evidences and explications of the nature of exponent, relating concept with students’ daily experience taken from their natural environment to create more meaningful learning, using parables or easily accessible and inexpensive props which are represented the situation, training students to make concept mapping to assist them in arranging concept and to avoid misconception, giving more variety task, re-emphasizing the arithmetical operation of fraction, always giving information of mistakes made by the students in doing the exponent task. A lot of practice in doing task will make students have more opportunity to develop their mathematics skills. However, in order not to make students bored in taking task of exponent problem, teacher can apply games during the leaning process. One of games that can be used is Domino for learning exponent. The aims of this game are to train students’ accuracy, intelligence, creativity, as well as to enrich students’ knowledge in mathematics.</p><p> </p><p> </p>

Image Processing and Analysis System for Corneal Endothelial Cell Based on LabVIEW and MATLAB

To process corneal endothelial cell image quickly and efficiently, observe the corneal endothelial cell form and relevant calculation and analysis. This system adopts mixed programming of LabVIEW and MATLAB, to have image processing and analysis of the corneal endothelial cell. Use LabVIEW to design operation and display interface, and send the images collected to MATLAB for complex arithmetical operation, then put out data in LabVIEW. The experiment indicates the system has the advantage of intuitive interface, convenient operation, and quick arithmetic, has the practical reference value.

Application of Java-Called DLL in Crop Breeding Data Analysis System

The collected massive data during the breeding process usually cost plenty of human power. Therefore, it is urgent to create highly-efficient specific breeding data analysis software to assist breeders to screen fine varieties. For this reason, this paper developed a breeding data management analysis system by taking MyEclipse as development tool, which covers various statistical analysis techniques. In the development process of each algorithm module, JNI technology is adopted to realize Java-called DLL and complete algorithm call, improving the execution efficiency of a large number of arithmetical operations. This paper introduced Java-called DLL by aid of JNI technology in One-Way ANOVA in details and the parameter passing between Java and C++ and how to realize Java-called DLL in the operating system without C++ operating environment. Through the above-mentioned call, the advantages of C++ and Java are comprehensively considered, which not only lightens the burden of Java virtual machine and avoids the repeatability, but also improves the efficiency of arithmetical operation and the utilization rate of codes.

Study on Key Technique of Reconfigurable CNC System

FPGA has been used in CNC system, it can achieve the impulse, the count, arithmetical operation, I/O interface and so on, and therefore it can greatly simplify the design of control circuit. In this special structure mechanism, the processing and monitoring of CNC system based on FPGA instead of traditional MCU is implemented. The overall structure of reconfigurable CNC system is described, meanwhile, the DDA accurate interpolation and the control circuit of stepper motor is emphatically solved through Using the FPGA. With the result of several experiments, the performance of the CNC system is improved, reconfiguration is strengthened, besides, the peripheral interface devices and cost is greatly reduced.

Arithmetic Stroop Interference as a Function of Age: Maintenance and Modification of Automatic Processes

This experiment investigated whether well-learned “automatic” processes remain stable as a function of age, as well as whether the ability to modify automatic processes is disrupted for older adults. We used an arithmetic “Stroop” task. Nineteen young (mean 22) and 19 old adults (mean 75) participated in three sessions for a total of 450 trials. The young subjects had faster verification times, overall, than the old adults. Both young and old subjects showed significant Stroop interference. These results support the hypothesis that automatic processes, in this case access of addition and multiplication tables, are maintained for old adults. Furthermore, both groups reduced their RT with practice. For the young adults, there was a decrease in interference with practice suggesting that they were learning to inhibit the automatic process of performing the arithmetical operation. However, the old adults showed no significant decrease in interference, which implies that they were impaired in their ability to inhibit automatic processes, even when those processes interfered with performance. Theoretical and practical training implications are discussed.

On the Tables of Single and Annual Assurance Premiums published by the late Mr. William Orchard, and on a Theoretical Table of Mortality proposed by him

The values which it has been heretofore customary to tabulate for actuarial purposes, in connection with specified rates of mortality and interest, are those of annuities on single and joint lives at all ages; and from these, by operations more or less complex, and with the aid of subsidiary tables, the actuary has had to form such other values as might be required in the solution of any particular problem in hand. Of the values thus requiring to be formed, those of the single and annual premiums for assurance occur perhaps more frequently than any others; and hence the desirableness of simplifying as much as possible the operations by which these are deduced from the corresponding annuities. To effect this simplification was the object of Mr. Orchard's work, in which, as will be admitted by all competent to form an opinion on the subject, the author has been completely successful. The arithmetical operation heretofore necessary has been entirely superseded, and the required values are found simply by inspection.