Dhanasekar et al. (International Journal of Fuzzy Systems 19 (2017) 1479-1491) proposed a fuzzy Hungarian MODI algorithm to solve fully fuzzy transportation problems. Dhanasekar et al. have used the standard multiplication of trapezoidal fuzzy numbers in their proposed method. In this paper, it is pointed out that the method, proposed by Dhanasekar et al., is not valid for standard multiplication of trapezoidal fuzzy numbers and is valid only if a special type of multiplication of fuzzy numbers is used. [ABSTRACT FROM AUTHOR]
*FUZZY numbers, *MATHEMATICAL optimization, *PROBLEM solving, *ALGORITHMS, *PROBABILITY theory
Abstract
This paper addresses a selective maintenance optimization problem for a fuzzy multi-state system composed of fuzzy multi-state elements. Due to insufficient data and unpredictable external working conditions, both the performance capacity and states transition intensities of multi-state elements cannot be known precisely, but are represented by fuzzy numbers. Additionally, both the durations of a break and a succeeding mission are also treated as fuzzy values. To maximize the fuzzy probability of a system successfully completing a succeeding mission, a selective maintenance model is proposed to identify an optimal subset of maintenance activities to be performed on some elements in the system. A solution algorithm containing three rules to eliminate inferior solutions and narrowdown elements' states combinations is proposed to resolve the new selective maintenance model in a computationally efficient manner. An illustrative example of an archibald is presented to demonstrate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]
In this paper, we generalize the bounded dual simplex algorithm for solving minimum cost flow problem with fuzzy cost, which its aim is to find the least fuzzy cost of a commodity through a capacitated network in order to satisfy demands at certain nodes using available supplies at other nodes. This algorithm begins with dual feasibility and iterates between dual and primal problems until optimality is achieved. Here, we use the linear ranking functions to compare fuzzy numbers. By using the proposed method the optimal solution of minimum cost flow problems with fuzzy costs can be easily obtained. To illustrate the proposed method a numerical example is solved and the obtained results are discussed. [ABSTRACT FROM AUTHOR]