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This paper proposes a bi-objective hub-and-spoke (H&S) network design problem with type-2 (T2) fuzzy transportation cost and travel time described by parametric secondary possibility distributions, which are obtained using three types of mean value (MV) reduction methods. The considered objectives jointly minimize the generalized expectation of the total transportation costs and the maximum travel time requirement in terms of generalized value-at-risk (VaR). To solve the fuzzy bi-objective H&S network design problem, we develop a two-phase approach, where in the first phase we convert the proposed model into its equivalent parametric mixed-integer programming problems by applying an equivalent transformation method. This is followed by the second phase using a fuzzy linear programming approach implemented with an augmented max-min operator to obtain a non-dominated solution that has an equal satisfactory degree on both objectives. Finally, a case study based on the Civil Aeronautics Board (CAB) data set is conducted to demonstrate the effectiveness of the proposed model and solution approach. [ABSTRACT FROM AUTHOR]

Abstract: This paper aims to solve the problem of multiple-objective linear optimization model subject to a system of inf- composition fuzzy relation equations, where is R-, S- or QL-implications generated by continuous Archimedean t-norm (s-norm). Since the feasible domain of inf- relation equations constraint is nonconvex, these traditional mathematical programming techniques may have difficulty in computing efficient solutions for this problem. Therefore, we firstly investigate the solution sets of a system of inf- composition fuzzy relation equations in order to characterize the feasible domain of this problem. And then employing the smallest solution of constraint equation, we yield the optimal values of linear objective functions subject to a system of inf- composition fuzzy relation equations. Secondly, the two-phase approach is applied to generate an efficient solution for the problem of multiple-objective linear optimization model subject to a system of inf- composition fuzzy relation equations. Finally, a procedure is represented to compute the optimal solution of multiple-objective linear programming with inf- composition fuzzy relation equations constraint. In addition, three numerical examples are provided to illustrate the proposed procedure. [Copyright &y& Elsevier]

Abstract: In the real-world manufacturing/distribution planning decision (MDPD) integration problems in supply chains, the environmental coefficients and parameters are normally imprecise due to incomplete and/or unavailable information. This work presents a fuzzy linear programming approach based on the possibility theory. It applies this approach to solve multi-product and multi-time period MDPD problems with imprecise goals and forecast demand by considering the time value of money of related operating cost categories. The proposed approach attempts to minimize the total manufacturing and distribution costs by considering the levels of inventory, subcontracting and backordering, the available machine capacity and labor levels at each source, forecast demand and available warehouse space at each destination. This study utilizes an industrial case study to demonstrate the feasibility of applying the proposed approach to practical MDPD problems. The primary contribution of this paper is a fuzzy mathematical programming methodology for solving the MDPD integration problems in uncertain environments. [ABSTRACT FROM AUTHOR]

Abstract: This paper is an amendment to Hop’s paper [N.V. Hop, Solving linear programming problems under fuzziness and randomness environment using attainment values, Information Sciences 177 (2007) 2971–2984], in solving linear programming problems under fuzziness and randomness environments. Hop introduced a new characterization of relationship, attainment values, to enable the conversion of fuzzy (stochastic) linear programming models into corresponding deterministic linear programming models. The purpose of this paper is to provide a correction and an improvement of Hop’s analytical work through rationalization and simplification. More importantly, it is shown that Hop’s analysis does not support his demonstration or the solution-finding mechanism; the attainment values approach as he had proposed does not result in superior performance as compared to other existing approaches because it neglects some relevant and inevitable theoretical essentials. Two numerical examples from Hop’s paper are also employed to show that his approach, in the conversion of fuzzy (stochastic) linear programming problems to corresponding problems, is questionable and can neither find the maximum nor the minimum in the examples. The models of the examples are subsequently amended in order to derive the correct optimal solutions. [Copyright &y& Elsevier]

Abstract: In this paper, the author presents a model to measure attainment values of fuzzy numbers/fuzzy stochastic variables. These new measures are then used to convert the fuzzy linear programming problem or the fuzzy stochastic linear programming problem into the corresponding deterministic linear programming problem. Numerical comparisons are provided to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, the author presents a model to measure the superiority and inferiority of fuzzy numbers/fuzzy stochastic variables. Then, the new measures are used to convert the fuzzy (stochastic) linear program into the corresponding deterministic linear program. Numerical examples are provided to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

In this paper, we present a tabu search technique to approximately solve fuzzy optimization problems. We demonstrate the performance of the proposed method by applying it to an elementary fuzzy optimization problem. Other applications of the method to fuzzy linear programming, fuzzy regression and the training of fuzzy neural networks are also presented. [Copyright &y& Elsevier]