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GENERATING EXACT NONLINEAR ranking functionS BY SYMBOLIC-NUMERIC HYBRID METHOD

Journal of Systems Science & Complexity 2013年第2期26卷 291-301页

作者： SHEN Liyong WU Min YANG Zhengfeng ZENG Zhenbing School of Mathematical Sciences Graduate University of Chinese Academy of Sciences Shanghai Key Laboratory of Trustworthy Computing East China Normal University

This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial *** authors first transform the problem into a parameterized polynomial optimization problem,and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming(SDP).A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function,and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop *** last,the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.

关键词： Program verification ranking function semidefinite programming symbolic-numeric hybrid method.

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Application of Intuitionistic Z-Numbers in Supplier Selection

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Intelligent Automation & Soft Computing 2023年第1期35卷 47-61页

作者： Nik Muhammad Farhan Hakim Nik Badrul Alam Ku Muhammad Naim Ku Khalif Nor Izzati Jaini Centre for Mathematical Sciences College of Computing and Applied SciencesUniversiti Malaysia PahangLebuhraya Tun RazakGambangKuantan26300PahangMalaysia Faculty of Computer and Mathematical Sciences Universiti Teknologi MARA PahangJengka CampusBandar Tun Abdul Razak Jengka26400PahangMalaysia

Intuitionistic fuzzy numbers incorporate the membership and non-membership *** contrast,Z-numbers consist of restriction components,with the existence of a reliability component describing the degree of certainty for the *** combination of intuitionistic fuzzy numbers and Z-numbers produce a new type of fuzzy numbers,namely intuitionistic Z-numbers(IZN).The strength of IZN is their capability of better handling the uncertainty compared to Zadeh's Z-numbers since both components of Z-numbers are charac-terized by the membership and non-membership functions,exhibiting the degree of the hesitancy of *** paper presents the application of such numbers in fuzzy multi-criteria decision-making problems.A decision-making model is proposed using the trapezoidal intuitionistic fuzzy power ordered weighted average as the aggregation function and the ranking function to rank the *** proposed model is then implemented in a supplier selection *** obtained ranking is compared to the existing models based on *** results show that the ranking order is slightly different from the existing *** analysis is performed to validate the obtained *** sensitivity analysis result shows that the best supplier is obtained using the proposed model with 80%to 100%consistency despite the drastic change of criteria *** Z-numbers play a very important role in describing the uncertainty in the decision makers’opinions in solving decision-making problems.

关键词： Intuitionistic Z-number fuzzy decision making ranking function supplier selection sensitivity analysis

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Bi-level Programming for Stackelberg Game with Intuitionistic Fuzzy Number: a ranking Approach

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Journal of the Operations Research Society of China 2021年第1期9卷 131-149页

作者： Sumit Kumar Maiti Sankar Kumar Roy School of Applied Sciences and Humanities Haldia Institute of TechnologyPurba MidnaporeWB 721657India Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeWB 721102India

This paper introduces a ranking function procedure on a bi-level programming for Stackelberg game involving intuitionistic fuzzy *** fuzzy num-ber is considered in many real-life situations,so it makes perfect sense to address decision-making problem by using some specified intuitionistic fuzzy *** this paper,intuitionistic fuzziness is characterized by a normal generalized triangular intuitionistic fuzzy number.A defuzzification method is introduced based on the pro-portional probability density function associated with the corresponding membership function,as well as the complement of non-membership *** the proposed ranking technique,a methodology is presented for solving bi-level programming for Stackelberg *** application example is provided to demonstrate the applica-bility of the proposed methodology,and the achieved results are compared with the existing methods.

关键词： Bi-levelprogramming Triangular intuitionistic fuzz ynumber ranking function Nonlinear programming Optimal solution

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New Methods to Solve Fuzzy Shortest Path Problems

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Journal of Southeast University(English Edition) 2001年第1期17卷 18-21页

作者：刘春林何建敏施建军南京大学商学院南京210093 东南大学经济管理学院南京210096

This paper discusses the problem of finding a shortest path from a fixed origin s to a specified node t in a network with arcs represented as typical triangular fuzzy numbers (TFN). Because of the characteristic of TFNs, the length of any path p from s to t , which equals the extended sum of all arcs belonging to p , is also TFN. Therefore, the fuzzy shortest path problem (FSPP) becomes to select the smallest among all those TFNs corresponding to different paths from s to t (specifically, the smallest TFN represents the shortest path). Based on Adamo's method for ranking fuzzy number, the pessimistic method and its extensions - optimistic method and λ combination method, are presented, and the FSPP is finally converted into the crisp shortest path problems.

关键词： triangular fuzzy number fuzzy shortest path ranking function

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