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Weighted additive models are well known for dealing with multiple criteria decision making problems. Fuzzy goal programming is a branch of multiple criteria decision making which has been applied to solve real life problems. Several weighted additive models are introduced to handle fuzzy goal programming problems. These models are based on two approaches in fuzzy goal programming namely goal programming and fuzzy programming techniques. However, some of these models are not able to solve all kinds of fuzzy goal programming problems and some of them that appear in current literature suffer from a lack of precision in their formulations. This paper focuses on weighed additive models for fuzzy goal programming. It explains the oversights within some of them and proposes the necessary corrections. A new improved weighted additive model for solving fuzzy goal programming problems is introduced. The relationships between the new model and some of the existing models are discussed and proved. A numerical example is given to demonstrate the validity and strengths of the new model.

By using the restricted and complementary relationship of the principle and secondary indexes, providing the description of the compound quantification of the fuzzy number, and analyzing the essential characteristic of fuzzy decision, we propose a kind of fuzzy genetic algorithm based on the principle index (PO-FGA for short) to deal with the fuzzy optimization and programming problems with fuzzy coefficients, fuzzy variables and fuzzy constraints. The concrete solution method is presented in accordance with the strategy of the unconditional penality transformation with conditional constrains. Then consider its convergence by using Markov chain theory and analyze its performance through two examples. All these indicate that this kind of algorithm is of faster speed of convergence, smaller number of iterations, has lower chances of trapping into the state of premature convergence and can be widely used in many problems of optimization.

This paper presents a fuzzy programming method to design supply chain network, in which the customer demands and transportation costs are assumed to be fuzzy parameters. Existing researches on supply chain network design problem are either restricted on deterministic environment or only address stochastic parameters. In this paper, we consider this problem in fuzzy environment. Under different criteria, we format three types of models for the decision makers: expected cost optimization model, chance-constrained model and chance maximization model. A genetic algorithm based on fuzzy simulation is developed to solve the proposed fuzzy models. Moreover, some numerical examples are presented to illustrate the effectiveness of models and solution algorithm.

Owing to the fluctuations in the financial markets, many financial variables such as expected return, volatility, or exchange rate may occur imprecisely. But many portfolio selection models consider precise input of these values. Therefore, this paper studies a multiobjective international asset allocation problem under fuzzy environment. In our portfolio selection model, both of the return risk and the exchange risk are considered. The coefficient matrices in the objectives and constraints and the decision value are considered as fuzzy variables. The calculation of the portfolio and efficient frontier is derived by considering the exchange risk in the fuzzy environment. An empirical study is performed based on a portfolio of six securities denominated in six different currencies, i.e., USD, EUR, JPY, CNY, HKD, and GBP. The α-level closed interval portfolio and the fuzzy efficient frontier are obtained with different values of α ∈ (0, 1]. The empirical results indicate that the fuzzy asset selection method is a useful tool for dealing with the imprecise problem in the real world.

In this paper, we propose a new mathematical model to analyze bimatrix goal game under entropy environment. This new approach incorporates the entropy function of the players as an objective to the bimatrix game. The solution concepts behind this game are based on getting the probability to achieve some specified goals. We consider the solution, not only by the payoff values, but also by the probability to get them. Numerical examples are presented to illustrate the methodology in the paper.

This paper considers a multi-objective fixed-charge transportation problem (MOFCTP) in which the parameters of the objective functions are random rough variables, while the supply and the demand parameters are rough variables. In real-life situations, the parameters of a multi-objective fixed-charge transportation problem may not be defined precisely, because of globalization of the market, uncontrollable factors, etc. As such, the multi-objective fixed-charge transportation problem is proposed under rough and random rough environments. To tackle uncertain (rough and random rough) parameters, the proposed model employs an expected value operator. Furthermore, a procedure is developed for converting the uncertain multi-objective fixed-charge transportation problem into a deterministic form and then solving the deterministic model. Three different methods, namely, the fuzzy programming, global criterion, and ϵ-constrained methods, are used to derive the optimal compromise solutions of the suggested model. To provide the preferable optimal solution of the formulated problem, a comparison is drawn among the optimal solutions that are extracted from different methods. Herein, the ϵ-constrained method derives a set of optimal solutions and generates an exact Paretofront. Finally, in order to show the applicability and feasibility of the proposed model, the paper includes a real-life example of a multi-objective fixed-charge transportation problem. The main contribution of the paper is that it deals with MOFCTP using two types of uncertainties, thus making the decision making process more flexible.

This paper describes a study on bi-level multi-objective transportation problem in fuzzy environment. To alleviate a difficulty of transporting goods within nodes for long distances, we venture to formulate a transportation problem using bi-level criteria. Again, in this paper, we incorporate the real-life uncertain situation in bi-level transportation system through fuzziness. It produces a new class of transportation problem, namely fuzzy bi-level multi-objective transportation problem (FBMOTP). We solve FBMOTP with and without priority of the 1st level of transportation problem (TP) using the Vogal Approximation Method (VAM) which are called respectively Approach 1 and Approach 2. A special emphasis of this paper is to introduce a new approach namely Approach 3 for solving the FBMOTP in addition to the considered two approaches. In this regard, we incorporate an algorithm for Approach 3 to find compromise solution of the FBMOTP using VAM. Thereafter, the proposed algorithm is illustrated to show the usefulness by taking a numerical example. A comparative analysis with the existing studies is provided to understand the effectiveness of the proposed methodology. At last, conclusions are described with the lines of future study of the paper.

In a real-world production problem, some of the parameters involved, namely the availability of the resources, technological coefficients and the incomes associated with each product, may not be perfectly determined thus reflecting some ambiguity or fuzzy understanding of their nature. Therefore these parameters may admit a representation as fuzzy numbers. In this paper, we show how multi-criteria decision theory can be used to deal with a fuzzy linear production problem and with the associated fuzzy linear production game.

In this paper, we analyze the interval programming using interval and rough interval (RI). Interval programming is one of the tools to tackle uncertainty in mathematical programming. In the real world situations, we often encounter the cases where the data cannot be determined with certainty. So, the value of the data is assessed using an interval. Here, we consider that the parameters of the Fixed-Charge Transportation Problem (FCTP) are imprecise. In our proposed problem, uncertainties are considered in terms of interval and RI. We present a study of the FCTP using the interval programming. An example of the FCTP is included to show the effectiveness and usefulness of our proposed study. Finally, concluding remarks and future scopes of our paper are discussed.

In this paper a multiple objectives programming method is applied to improve the discriminating power of classical Data Envelopment Analysis (DEA) method. Unlike the classical DEA model often producing many relatively efficient decision making units (DMUs), this new approach enjoys more discriminating power, which results in less DMUs with efficiency ratio as 1. In this approach, every DMU's efficiency evaluation is viewed as one objective function to be maximized. A set of common multipliers, input and output weights, can be located not difficultly by using the fuzzy multiple objectives programming approach. In comparison to the number of programming works being same as the number of the DMUs in traditional DEA model, the new approach just needs to solving multiple objectives programming problem once no matter how many DMUs are. Apparently, the new approach is comparatively suitable to solve a problem with a large number of DMUs.

This paper proposes an exact and explicit solution algorithm to obtain the optimal solution of a fuzzy linear programming problem with the second-order cone and box constraints of decision variables. The main problem is not well-defined due to fuzziness, and so Yager’s ranking method is introduced. Then, the proposed model under Yager’s ranking method is transformed into a deterministic equivalent problem. The proposed solution algorithm is based on a parametric solution approach to determine the optimal strict region of parameters, and the main procedures are to perform deterministic equivalent transformations for the main problem and to solve the KKT condition of auxiliary problem satisfying the optimality.