Military Academy

Abstract: Many ranking methods have been proposed so far. However, there is yet no method that can always give a satisfactory solution to every situation; some are counterintuitive, not discriminating; some use only the local information of fuzzy values; some produce different rankings for the same situation. For overcoming the above problems, we propose a new method for ranking fuzzy numbers by distance method. Our method is based on calculating the centroid point, where the distance means from original point to the centroid point ( x 0 , y 0 ), and the x 0 index is the same as Murakami et al.'s x 0 . However, the y 0 index is integrated from the inverse functions of an LR-type fuzzy number. Thus, we use ranking function R( A ) = √ x 2 + y 2 (distance index) as the order quantities in a vague environment. Our method can rank more than two fuzzy numbers simultaneously, and the fuzzy numbers need not be normal. Furthermore, we also propose the coefficient of variation (CV index) to improve Lee and Li's method [Comput. Math. Appl.15 (1988) 887–896]. Lee and Li rank fuzzy numbers based on two different criteria, namely, the fuzzy mean and the fuzzy spread of the fuzzy numbers, and they pointed out that human intuition would favor a fuzzy number with the following characteristics: higher mean value and at the same time lower spread. However, when higher mean value and at the same time higher spread/or lower mean value and at the same time lower spread exists, it is not easy to compare its orderings clearly. Our CV index is defined as CV = σ (standard error)/μ (mean), which can overcome Lee and Li's problem efficiently. In this way, our proposed method can also be easily calculated by the “Mathematica” package to solve problems of ranking fuzzy numbers. At last, we present three numerical examples to illustrate our proposed method, and compare with other ranking methods.

Abstract: The as-prepared cobalt oxide (assigned as CoO x ) was fabricated by precipitation–oxidation from aqueous cobalt nitrate solution using sodium hydroxide and oxidation with hydrogen peroxide. Another series of pure cobalt oxides was refined by the decomposition of CoO x in a nitrogen environment at temperatures of 280, 450 and 950 °C (D-280, D-450 and D-950, respectively). Phase transformation, structural properties and red-ox properties were characterized by thermogravimetry-mass spectrometry (TG-MS), X-ray diffraction (XRD), infrared spectroscopy (IR), Raman spectroscopy and temperature-programmed decomposition/reduction (TPD/TPR). Analysis of the thermal behavior on CoO x revealed that a series of pure cobalt oxide with particle sizes of 10–20 nm could be obtained easily. The results demonstrated that the refined samples D-280, D-450 and D-950 were CoO(OH), Co 3 O 4 and CoO, respectively.

Abstract: To face the reality of practical multiple criteria problems usually possessing characters of fuzziness, and to consider group decision making with various subjective–objective backgrounds usually participating in decision-making process. In this paper, the experts' opinions are described by linguistic terms which can be expressed in trapezoidal (or triangular) fuzzy numbers. To make the consensus of the experts consistent, we utilize fuzzy Delphi method to adjust the fuzzy rating of every expert to achieve the consensus condition. For the aggregate of many experts' opinions, we take the operation of fuzzy numbers to get the mean of fuzzy rating, x ij and the mean of weight, w •j . In multi-alternatives and multi-attributes cases, the fuzzy decision matrix X =[ x ij ] m×n is constructed by the mean of the fuzzy rating, x ij . Then, we can derive the aggregate fuzzy numbers by multiplying the fuzzy decision matrix with the corresponding fuzzy attribute weights. The final results become a problem of ranking fuzzy numbers. We also propose an easy procedure of using fuzzy numbers to rank aggregate fuzzy numbers A i . In this way, we can obtain the best selection for evaluating system. For practical application, we propose an algorithm for evaluating the best main battle tank by fuzzy decision theory and compare it with other method.

Abstract: Many decision making problems which are complicated and fuzzy in nature exist in modern society. How to solve them is becoming increasingly important for human society. For solving multiple criteria's decision making in a fuzzy environment, in this paper, we will propose a new algorithm for evaluating naval tactical missile systems by the fuzzy Analytical Hierarchy Process based on grade value of membership function. Generally, we are given scores by experience of experts to represent judgmental objects. In this paper, from viewpoint of many experts, we will build membership functions of judgement criteria for all sub-items. When the membership function is built, we can calculate the grade value by data of missile performance. The grade value is called performance score. Our methods can be summarized in the following. 1. 1. Building membership function of judgement criteria for all sub-items, it is called fuzzy standard. 2. 2. Calculate the grade of membership function by practical data to represent performance scores. 3. 3. Use fuzzy AHP method and entropy concepts to calculate aggregate weights. Finally, for a simple and efficient computation, we have developed a systematic and practical program to calculate all algorithms, and apply the new algorithm to a naval tactical missile systems valuation and selection problem.

Abstract: In the team orienteering problem, start and end points are specified along with other locations which have associated scores. Given a fixed amount of time for each of the M members of the team, the goal is to determine M paths from the start point to the end point through a subset of locations in order to maximize the total score. In this paper, a fast and effective heuristic is presented and tested on 353 problems ranging in size from 21 to 102 points. The computational results are presented in detail.