New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis

The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods.     

AN APPLICATION OF TOPOLOGICAL ANALYSIS TO STUDYING THE THREE-DIMENSIONAL FLOW IN CASCADES; PART I—TOPOLOGICAL RULES FOR SKIN-FRICTION LINES AND SECTION STREAMLINES

Based on the working of Lighthill and Hunt et al., in the present paper the author has established the topological rules adapting to analysing the skin-friction lines and the section streamlines in cascades. These rules are (1) for a rotor cascade without shroud band, the total number of nodal points equals that the saddle points on the skin-friction line vector fields in each pitch range; (2) for an annular or straight cascade with no clearances at blade ends, the total number of saddle points is two more than that of nodal points on the skin-friction line fields in a pitch; (3) the total number of saddles in the secondary flow fields on cross-sections in cascade is one less than that of nodes; (4) in the section streamline vector fields on a meridian surface penetrating a flow passage, and on leading and trailing edge sections, the total number of nodes is equal to that of saddles; (5) on the streamline vector fields of a blade-to-blade surface, the total number of nodes is one less than that of saddles.     

Global Solvability of Linear Differential Operators with Multiple Characteristics

In this paper, we first introduce the irreducible unitary representation of nilpotent Lie groups, then by using the irreducible unitary representation we construct a fundamental solution to a class of left invariant differential operators and thus obtain the global solvability of this kind of operators.     

试论岩石力学的最新进展

本文综述了目前岩石力学测试技术、理论探讨与工程应用情况,并对今后的发展提出一些意见和建议。      

图象增强的模糊集合方法

本文论述了图象的模糊集合表示和利用模糊性质进行图象增强的基本原理,讨论了一级模糊增强方法,提出了自适应二级模糊增强模型,并同Pal, S K模型作了比较,提出了它们各自的优缺点,实验结果令人满意     

Fuzzy多胞形及其表示定理

本文首先引进Fuzzy多胞形的概念,建立了Fuzzy多胞形的表示定理,特别地,得到Fuzzy单纯形的表示定理([4]),对于Fuzzy集,引遍了Fuzzy极点的概念,并证明了Fuzzy多胞形是其Fuzzy极点的Fuzzy凸胞。这些定义和结论是普通凸集理论中相应定义和结论的推广。     

高等学校校报微机管理系统

本文介绍利用软件工程,数据库技术和模糊检索开发高等学校校报微机管理系统。该系统具有很好的通用性,可应用于高校校报的现代化管理,为办报提供科学依据。     

聚能射流三维数值模拟

研究三维多介质界面处理及数值模拟问题。采用拉格朗日法、欧拉法相结合的方法在矩形网格上离散差分基本方程组;在欧拉步中引入模糊方法处理界面,计算各输运量;编写了数值模拟程序,并对线型装药金属罩聚能射流模型进行模拟。证明模糊界面描述和模糊输运计算有效、可行。     

Application of shooting methods for two-point boundary value problems of ordinary differential equations with parameters in hydrodynamics

In this paper. first we introduce the shooting method (including the method of adjoints and the method of quasilinearization) for two-point boundary value problems of ordinary differential equations with parameters, and give out an example of solving hydrodynamic lubrication equation by using the shooting method. The calculated results are satisfactory.     

有链条件的非奇异环

本文先引入 C:一环、Br ·环等等若干环类并给出它们成为 G ol ide环的一个充要 条件.本文还给出半质右G old ie 环为左G ol id环的一个刻划