Incorporating Parameter Uncertainty into Copula Models: A Fuzzy Approach

On the calculation of a membership function for the solution of a fuzzy linear optimization problem

The existing results on the variational inequality problems for fuzzy mappings and their applications were based on Zadeh’s decomposition theorem and were formally characterized by the precise sets which are the fuzzy mappings’ cut sets directly. That is, the existence of the fuzzy variational inequality problems in essence has not been solved. In this paper, the fuzzy variational-like inequality problems is incorporated into the framework of n-dimensional fuzzy number space by means of the new ordering of two n-dimensional fuzzy-number-valued functions we proposed [Fuzzy Sets and Systems 295 (2016) 19-36]. As a theoretical basis, the existence and the basic properties of the fuzzy variational inequality problems are discussed. Furthermore, the relationship between the variational-like inequality problems and the fuzzy optimization problems is discussed. Finally, we investigate the optimality conditions for the fuzzy multiobjective optimization problems.

In order to solve the problem of fuzzy multiobjective optimization of basketball match appearance lineup in complex situations, this paper proposes a fuzzy multiobjective optimization model (FMOM) of basketball match appearance lineup relying on optimal matching for the individual. This method considers the players’ fuzzy conditions concerning the satisfaction degree, priority degree etc for the basketball match cost, utilization, adjacency requirements etc, relies on the theory of optimal matching for individual, fuzzifies the fuzzy multiobjective optimization model, designs the fuzzy multiobjective function, and according to the preference of players optimizes fuzzy multiobjective optimization model of appearance lineup. It improves the basketball match appearance lineup mode in the fuzzy multiobjective optimization model so to raise the practicality and efficiency of the model. Finally, with actual cases, it proves the effectiveness of the model.

Fuzzy generation scheduling for a generation company (GenCo) with large scale wind farms

In the present paper, we consider fuzzy optimization problems which involve fuzzy sets only in the objective mappings, and give two concepts of optimal solutions which are non-dominated solutions and weak non-dominated solutions based on orderings of fuzzy sets. First, by using level sets of fuzzy sets, the fuzzy optimization problems treated in this paper are reduced to set optimization problems, and relationships between (weak) non-dominated solutions of the fuzzy optimization problems and the reduced set optimization problems are derived. Next, the set optimization problems are reduced to scalar optimization problems which can be regarded as scalarization of the fuzzy optimization problems. Then, relationships between non-dominated solutions of the fuzzy optimization problems and optimal solutions of the reduced scalar optimization problems are derived.

Fuzzy particle swarm optimization for conjunctive use of groundwater and reclaimed wastewater under uncertainty

Increasing evaluation indexes have been involved in the network modeling, and some parameters cannot be described precisely. Fuzzy set theory becomes a promising mathematical method to characterize such uncertain parameters. This study investigates the fuzzy multi-objective path optimization problem (FMOPOP), in which each arc has multiple crisp and fuzzy weights simultaneously. Fuzzy weights are characterized by triangular fuzzy numbers or trapezoidal fuzzy numbers. We adopt two fuzzy number ranking methods based on their fuzzy graded mean values and distances from the fuzzy minimum number. Motivated by the ripple spreading patterns on the natural water surface, we propose a novel ripple-spreading algorithm (RSA) to solve the FMOPOP. Theoretical analyses prove that the RSA can find all Pareto optimal paths from the source node to all other nodes within a single run. Numerical examples and comparative experiments demonstrate the efficiency and robustness of the newly proposed RSA. Moreover, in the first numerical example, the processes of the RSA are illustrated using metaphor-based language and ripple spreading phenomena to be more comprehensible. To the best of our knowledge, the RSA is the first algorithm for the FMOPOP that can adopt various fuzzy numbers and ranking methods while maintaining optimality.

New preference order relationships and their application to multiobjective interval and fuzzy interval optimization problems

The solving strategy of GA-Based Multi-objective Fuzzy Matter-Element optimization is put forward in this paper to the kind of characters of product optimization such as multi-objective, fuzzy nature, indeterminacy, etc. Firstly, the model of multi-objective fuzzy matter-element optimization is created in this paper, and then it defines the matter-element weightily and changes solving multi-objective optimization into solving dependent function K(x) of the single objective optimization according to the optimization criterion. In addition, modified adaptive macro genetic algorithms (MAMGA) are adopted to solve the optimization problem. It emphatically modifies crossover and mutation operator. By the comparing MAMGA with adaptive macro genetic algorithms (AMGA), not only the optimization is a little better than the latter, but also it reaches the extent to which the effective iteration generation is 62.2% of simple genetic algorithms (SGA). Lastly, three optimization methods, namely fuzzy matter-element optimization, linearity weighted method and fuzzy optimization, are also compared. It certifies that this method is feasible and valid.

Study on fuzzy optimization methods based on quasi-linear fuzzy number and genetic algorithm

This article presents an algorithm for solving fully fuzzy multi-objective linear fractional (FFMOLF) optimization problem. Some computational algorithms have been developed for the solution of fully fuzzy single-objective linear fractional optimization problems. Veeramani and Sumathi (Appl Math Model 40:6148–6164, 2016) pointed out that no algorithm is available for solving a single-objective fully fuzzy optimization problem. Das et al. (RAIRO-Oper Res 51:285–297, 2017) proposed a method for solving single-objective linear fractional programming problem using multi-objective programming. Moreover, it is the fact that no method/algorithm is available for solving a FFMOLF optimization problem. In this article, a fully fuzzy MOLF optimization problem is considered, where all the coefficients and variables are assumed to be the triangular fuzzy numbers (TFNs). So, we are proposing an algorithm for solving FFMOLF optimization problem with the help of the ranking function and the weighted approach. To validate the proposed fuzzy intelligent algorithm, three existing classical numerical problems are converted into FFMOLF optimization problem using approximate TFNs. Then, the proposed algorithm is applied in an asymmetric way. Since there is no algorithm available in the existing literature for solving this difficult problem, we compare the obtained efficient solutions with corresponding existing methods for deterministic problems.

Performance analysis and fuzzy optimization of a two-stage fermentation process with cell recycling including an extractor for lactic acid production

Fuzzy Optimization for an Integrated Process of Extractive Fermentation Including Cell Recycle for Lactic Acid Production

This work develops two approaches based on the fuzzy set theory to solve a class of fuzzy mathematical optimization problems with uncertainties in the objective function and in the set of constraints. The first approach is an adaptation of an iterative method that obtains cut levels and later maximizes the membership function of fuzzy decision making using the bound search method. The second one is a metaheuristic approach that adapts a standard genetic algorithm to use fuzzy numbers. Both approaches use a decision criterion called satisfaction level that reaches the best solution in the uncertain environment. Selected examples from the literature are presented to compare and to validate the efficiency of the methods addressed, emphasizing the fuzzy optimization problem in some import-export companies in the south of Spain.

Investment portfolio optimization (IPO) is one of the most important problems in the financial area. Also, one of the most important features of financial markets is their embedded uncertainty. Thus, it is essential to propose a novel IPO model that can be employed in the presence of uncertain data. Accordingly, the main goal of this paper is to propose a novel fuzzy multi-period multi-objective portfolio optimization (FMPMOPO) model that is capable to be used under data ambiguity and practical constraints including budget constraint, cardinality constraint, and bound constraint. It should be noted that three objectives including terminal wealth, risk, and liquidity as well as practical constraints are considered in proposed FMPMOPO model. Also, the alpha-cut method is employed to deal with fuzzy data. Finally, the proposed fuzzy multi-period wealth-risk-liquidity (FMPWRL) model is implemented in real-world case study from Tehran stock exchange (TSE). The experimental results show the applicability and efficacy of the proposed FMPWRL model for fuzzy multi-period multi-objective investment portfolio optimization problem under fuzzy environment.