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The shortest path (SP) problem constitutes one of the most prominent topics in graph theory and has practical applications in many research areas such as transportation, network communications, emergency services, and fire stations services, to name just a few. In most real-world applications, the arc weights of the corresponding SP problems are represented by fuzzy numbers. The current paper presents a fuzzy-based Ant Colony Optimization (ACO) algorithm for solving shortest path problems with different types of fuzzy weights. The weights of the fuzzy paths involving different kinds of fuzzy arcs are approximated using the α -cut method. In addition, a signed distance function is used to compare the fuzzy weights of paths. The proposed algorithm is implemented on three increasingly complex numerical examples and the results obtained compared with those derived from a genetic algorithm (GA), a particle swarm optimization (PSO) algorithm and an artificial bee colony (ABC) algorithm. The results confirm that the fuzzy-based enhanced ACO algorithm could converge in about 50% less time than the alternative metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

Supplier selection and order allocation constitute vital strategic decisions that must be made by managers within supply chain management environments. In this paper, we propose a multi-objective fuzzy model for supplier selection and order allocation in a two-level supply chain with multi-period, multi-source, and multi-product characteristics. The supplier evaluation objectives considered in this model include cost, delay, and electronic-waste (e-waste) minimization, as well as coverage and weight maximization. A signal function is used to model the price discount offered by the suppliers. Triangular fuzzy numbers are used to deal with the uncertainty of delay and e-waste parameters while the fuzzy Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) is used to obtain the weights of the suppliers. The resulting NP-hard problem, a Pareto-based meta-heuristic algorithm called controlled elitism non-dominated sorting genetic algorithm (CENSGA), is developed. The Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO) are used to validate the applicability of the CENSGA algorithm and the Taguchi technique to tune the parameters of the algorithms. The results are analysed using graphical and statistical comparisons illustrating how the proposed CENSGA dominates NSGA-II and MOPSO in terms of mean ideal solution distance (MID) and spacing metrics. [ABSTRACT FROM AUTHOR]

Shortest path (SP) optimization problems arise in a wide range of applications such as telecommunications and transportation industries. The main purpose of these problems is to find a path between two predetermined nodes within a network as cheaply or quickly as possible. Conventional SP problems generally assume that the arc weights are defined by crisp variables, though imprecise data have been lately incorporated into the analysis. The present study formulates the SP problem in a directed interval-valued triangular fuzzy network. The resulting interval-valued fuzzy SP (IVFSP) problem is converted into a multi objective linear programming (MOLP) problem. Then, a lexicographic optimization structure is used to obtain the efficient solution of the resulting MOLP problem. The optimization process confirms that the optimum interval-valued fuzzy shortest path weight preserves the form of an interval-valued triangular fuzzy number. The applicability of the proposed approach is illustrated through an example dealing with wireless sensor networks. [ABSTRACT FROM AUTHOR]

The increase in the amount and variety of evaluations provided by the users of different websites regarding the products displayed is becoming an increasingly familiar scenario. That is, decision makers (DMs) constantly receive linguistic evaluations (LEs) from unknown evaluators when considering different choice alternatives. The imprecision of the LEs and the fact that the evaluators may have biased interests when describing a product must be considered by the DMs when computing their expected utilities. We define a Bayesian-updated probability (BUP) function that accounts for the fuzziness inherent in the LEs and the reputation of the evaluator to represent the beliefs of DMs. The proposed BUP process allows the DMs to subjectively adjust the probability mass that is shifted across evaluation intervals when updating their beliefs and computing their corresponding expected utilities. We illustrate the behavior of the BUP function numerically and describe potential decision support applications. [ABSTRACT FROM AUTHOR]