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An Approach to Solve a possibilistic Linear Programming Problem

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Applied Mathematics 2014年第2期5卷 226-233页

作者： Ritika Chopra Ratnesh R. Saxena Department of Mathematics DeenDayalUpadhyay College Delhi University Delhi India Department of Mathematics Delhi University Delhi India

The objective of the paper is to deal with a kind of possibilistic linear programming (PLP) problem involving multiple objectives of conflicting nature. In particular, we have considered a multi objective linear programming (MOLP) problem whose objective is to simultaneously minimize cost and maximize profit in a supply chain where cost and profit coefficients, and related parameters such as available supply, forecast demand and budget are fuzzy with trapezoidal fuzzy numbers. An example is given to illustrate the strategy used to solve the aforesaid PLP problem.

关键词： Multi Objective Linear Programming Problem Fuzzy Set Theory Trapezoidal Fuzzy Numbers possibilistic Linear Programming Problem

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可能性扩展规则的推理和知识编译

软件学报 2010年第11期21卷 2826-2837页

作者：殷明浩孙吉贵林海吴瑕东北师范大学计算机学院吉林长春130117 吉林大学计算机科学与技术学院吉林长春130012 吉林大学符号计算与知识工程教育部重点实验室吉林长春130012

在扩展规则的基础上提出了可能性扩展规则.给出了基于可能性扩展规则的可能性逻辑推理方法,利用互补因子的概念来估价推理问题的复杂度.扩展了经典逻辑的蕴含可控制类和可满足可控制类的定义,提出了可能性蕴含可控制类、不一致性程度计... 详细信息

在扩展规则的基础上提出了可能性扩展规则.给出了基于可能性扩展规则的可能性逻辑推理方法,利用互补因子的概念来估价推理问题的复杂度.扩展了经典逻辑的蕴含可控制类和可满足可控制类的定义,提出了可能性蕴含可控制类、不一致性程度计算可控制类的概念.在可能性扩展规则的基础上提出了EPPCCCL(each pair of possibilistic clauses contains complementary literals)理论,并证明了该理论是在最优化形式蕴含可控制类和不一致性程度计算可控制类中的,可以作为可能性知识编译的目标语言.

关键词：扩展规则可能性逻辑知识编译 EPPCCCL(each pair of possibilistic clauses contains complementary literals)理论

Fuzzy Mathematical Model for Solving Supply Chain Problem

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Journal of Computer and Communications 2018年第9期6卷 73-105页

作者： Yi-Shian Chin Hsin-Vonn Seow Lai Soon Lee Rajprasad Kumar Rajkumar Nottingham University Business School University of Nottingham Malaysia Campus Semenyih Malaysia Laboratory Computational Statistics and Operations Research Institute for Mathematical Research University Putra Malasia Serdang Malaysia Department of Mathematics Faculty of Science University Putra Malaysia Serdang Malaysia Department of Mechanical Materials and Manufacturing Engineering Faculty of Engineering University of Nottingham Malaysia Campus Semenyih Malaysia

In a real world application supply chain, there are many elements of uncertainty such as supplier performance, market demands, product price, operation time, and shipping method which increases the difficulty for manufacturers to quickly respond in order to fulfil the customer requirements. In this paper, the authors developed a fuzzy mathematical model to integrate different operational functions with the aim to provide satisfy decisions to help decision maker resolve production problem for all functions simultaneously. A triangular fuzzy number or possibilistic distribution represents all the uncertainty parameters. A comparison between a fuzzy model, a possibilistic model and a deterministic model is presented in this paper in order to distinguish the effectiveness of model in dealing the uncertain nature of supply chain. The proposed models performance is evaluated based on the operational aspect and computational aspect. The fuzzy model and the possibilistic model are expected to be more preferable to respond to the dynamic changes of the supply change network compared to the deterministic model. The developed fuzzy model seems to be more flexible in undertaking the lack of information or imprecise data of a variable in real situation whereas possibilistic model is more practical in solving an existing systems problem that has available data provided.

关键词： Supply Chain Fuzzy Model possibilistic Model Undertainty Triangular Fuzzy Number

Finding a Link between Randomness and Fuzziness

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Applied Mathematics 2014年第9期5卷 1369-1374页

作者： Fokrul Alom Mazarbhuiya College of Computer Science and IT Albaha University Albaha KSA

If sample realizations are intervals, if the upper and the lower boundaries of such intervals are realizations of two independently distributed random variables, the two probability laws together lead to some interesting assertions. In this article, we shall attempt to remove certain confusions regarding the relationship between probability theory and fuzzy mathematics.

关键词： Probability Possibility Fuzzy Sets possibilistic Events Uniform Probability Law Triangular Fuzzy Number Order Statistics