A Constructive Proof of Fundamental Theory for Fuzzy Variable Linear Programming Problems

Two existing methods for solving fuzzy variable linear programming problems based on ranking functions are the fuzzy primal simplex method proposed by Mahdavi-Amiri et al. (2009) and the fuzzy dual simplex method proposed by Mahdavi-Amiri and Nasseri (2007). In this paper, we prove that in the absence of degeneracy these fuzzy methods stop in a finite number of iterations. Moreover, we generalize the fundamental theorem of linear programming in a crisp environment to a fuzzy one. Finally, we illustrate our proof using a numerical example

Bi-objective supply chain problem using MOPSO and NSGA-II

The increase competition and decline economy has increased the relevant importance of having reliable supply chain. The primary objective of many supply chain problems is to reduce the cost of services and, at the same time, to increase the quality of services. In this paper, we present a multi-level supply chain network by considering multi products, single resource and deterministic cost and demand. The proposed model of this paper is formulated as a mixed integer programming and we present two metaheuristics namely MOPSO and NSGA-II to solve the resulted problems. The performance of the proposed models of this paper has been examined using some randomly generated numbers and the results are discussed. The preliminary results indicate that while MOPSO is able to generate more Pareto solutions in relatively less amount of time, NSGA-II is capable of providing better quality results

System reliability using generalized intuitionistic fuzzy Rayleigh lifetime distribution

Reliability analysis as one of the important research topics in engineering has been researched by a number of authors. Reliability in classical distributions is based on precise parameters. It is usually assumed that parameters of distributions are precise real numbers. However, in the real world, the data sometimes cannot be measured and recorded precisely. In this paper, the concept of fuzzy reliability is extended by the idea of generalized intuitionistic fuzzy reliability. We investigate the reliability characteristics of systems using Rayleigh lifetime distribution, in which the lifetime parameter is assumed to be generalized intuitionistic fuzzy number. Generalized intuitionistic fuzzy reliability, generalized intuitionistic fuzzy hazard function, generalized intuitionistic fuzzy mean time to failure and their cut sets are discussed when the systems follow generalized intuitionistic fuzzy Rayleigh lifetime distribution. In this approach, for every special cut set, reliability curve and hazard curve are like a band with upper and lower bound. A numerical example is given to illustrate the proposed approach. Further, reliability analysis of the series and parallel systems are done

Multiscale Entropic Regularization for MTS on General Metric Spaces

We present an $O((\log n)^2)$-competitive algorithm for metrical task systems (MTS) on any $n$-point metric space that is also $1$-competitive for service costs. This matches the competitive ratio achieved by Bubeck, Cohen, Lee, and Lee (2019) and the refined competitive ratios obtained by Coester and Lee (2019). Those algorithms work by first randomly embedding the metric space into an ultrametric and then solving MTS there. In contrast, our algorithm is cast as regularized gradient descent where the regularizer is a multiscale metric entropy defined directly on the metric space. This answers an open question of Bubeck (Highlights of Algorithms, 2019).Comment: 23 pages, 1 figure, to appear in ITCS '2