Problem In Fuzzy Environment Research Articles

A novel three-way classification and ranking approach based on regret theory and TOPSIS

In multi-attribute decision-making (MADM) problems, attribute types typically include benefit attributes and cost attributes. In most existing MADM studies, attribute types are converted to the same type to reduce the effect of diverse attribute types on decision results, inevitably leading to the loss of original information. In view of this, this paper presents a novel three-way decision (TWD) approach based on regret theory (RT) and TOPSIS to handle MADM problems in fuzzy environments without converting attribute types. Firstly, RT is employed to analyze the process of acquiring the relative revenue function for benefit attributes and the relative loss function for cost attributes. Then, we combine RT and TOPSIS method to estimate the conditional probability. Based on two attribute types, we develop the corresponding TWD models. One is to establish a TWD model that maximizes expected revenues based on benefit attributes, and the other is to establish a TWD model that minimizes expected losses based on cost attributes. Subsequently, we introduce the notion of integrated decision domains and investigate the ranking methods for alternatives that belong to the same (or different) integrated decision domains. Finally, we validate the effectiveness and performance of our method through case study and experimental analyses.

Multi-Attribute Group Decision-Making Problem Based On Q-Rung Orthopair Fuzzy Set Under Confidence Environment

Emergency decision-making for communities and countries is an important and critical tool. It improves the effectiveness and reliability to response emergencies which minimizes the rate of casualties, environmental damages and economic losses. In the event of emergency decision-making, the main issue is extreme imprecision, ambiguity, and fuzziness. This paper is devoted to the study of q‐rung orthopair fuzzy aggregation operators under the confidence levels and their applications to multiple-attribute group decision making (MAGDM) problems. The concept of q-rung orthopair fuzzy set (q-ROFS) is used as tool to describe undetermined information and is superior to the intuitionistic set (IFS) and Pythagorean fuzzy set (PFS). The distinguishing feature of the q-ROFS is that the sum of the q-th power of the membership degree and the q-th power of non-membership degree is bounded by 1. As a result, the range of uncertain information that it may describe is expanded. In this work, we focus on MAGDM problems under the fuzzy environment. First, based on aggregation operators some drawbacks of the already existing MAGDM methods are analyzed. Moreover, we present some modified operational laws and some of their properties to overcome these drawbacks. Next, related to q-ROFS fuzzy-weighted averaging (q-ICROFWA) and fuzzy-weighted power averaging (q-ICROFWPA) aggregation operator under confidence levels along with their properties are presented. By using these operators’ q-ICROFWA and q-ICROFWPA an advanced method is proposed to deal with MAGDM problems in fuzzy environment. At last, the validity and feasibility of this method is illustrated with some numerical examples.

The Composite Approach for Linear Fractional Programming Problem in Fuzzy Environment

The Composite Approach for Linear Fractional Programming Problem in Fuzzy Environment

Geometric Mean Method Combined With Ant Colony Optimization Algorithm to Solve Multi-Objective Transportation Problems in Fuzzy Environments

The transportation problem (TP) is a well-known subject in the field of optimization and a very prevalent challenge for businesspeople. The goal is to reduce the total transportation cost, of delivering resources from sources to destinations. The literature demonstrates that various approaches have been designed with a single goal in mind, although TPs are not always developed with a bi-goal in mind. Solving transportation difficulties with several objectives is a common task. In this study, a new method for addressing multi-criteria TP using geometric means, along with a novel approach of the Ant Colony Optimization algorithm (ACO) for solving multi-objective TP in a fuzzy environment. Fuzzy numbers have been used to solve real-world problems in various domains, including operations research and optimization. The ACO Algorithm has long been recognized as a viable alternative strategy for solving optimization problems. The purpose of this study is to provide a unique approach for organizing fuzzy numbers as well as enhancements to the ACO algorithm for solving the Multi-Objective TP model. Our method, such as Geometric Mean Ant Colony Optimization Algorithm (GMACOA), outperforms other methods in terms of objective values. Numerical examples are provided to demonstrate the method in comparison to various current methods.

A multi-objective berth allocation problem in fuzzy environment

The Berth Allocation Problem (BAP) is an important seaside problem in port logistics, which involves the determination of berthing times and positions of arriving vessels in a wharf. Most studies have considered that vessels arrival and handling times are known fixed quantities available to wharves operators beforehand. However, due to many uncontrollable factors that can affect vessels arrival and handling times, those quantities are highly uncertain and may have a significant impact in the wharf operation. This paper takes fuzzy uncertainty into account and presents a fully fuzzy BAP with two objective functions. Specifically, it is considered the minimisation of the total waiting time of vessels and the makespan of the wharf operation. The problem is solved by using two lexicographic methods for fully fuzzy multi-objective linear programming (FFMOLP). Multiple Pareto optimal fuzzy solutions are obtained using a fuzzy epsilon-constraint method. Results demonstrate the effectiveness of the proposed approaches in handling fuzziness and conflicting objectives in a BAP. Moreover, from a methodological point of view, results show that it is best to use lexicographic ranking criteria instead of linear ranking functions for solving the associated FFMOLP problem.

Optimal Replenishment Policies and Trade Credit for Integrated Inventory Problems in Fuzzy Environment

In this highly volatile, uncertain, complex, and ambiguous (VUCA) environment, a fuzzy inventory optimization problem is a hot topic that received the most attention from both academicians and practitioners. In this paper, the authors have studied the integrated inventory problems under trade credit in fuzzy environments, where the demand rate and deterioration rate are taken here as triangular fuzzy numbers. Accordingly, three types of fuzzy programming models as fuzzy expected cost minimization model, fuzzy α-cost minimization model, and credibility maximization model are built according to different management goals. Since the problem is shown to be NP-hard, this research focuses on proposing a hybrid intelligent algorithm by integrating fuzzy simulation, neural network, and genetic algorithm for solving these models. Then, some numerical examples are presented to illustrate the benefits of the models and evaluate the efficiency of the algorithms. The computational experiments show that the trade credit strategy has a positive impact on improving the supply chain’s performance and reducing its total cost. In addition, the maximum relative error of the objective values is less than 1%, which implies that the hybrid intelligent algorithm is robust to the parameter settings and effective in solving our models. Finally, the practical implications are discussed and useful managerial insights are given.

Optimal fuzzy based economic emission dispatch of combined heat and power units using dynamically controlled Whale Optimization Algorithm

The significance and purpose of this multi-objective Combined Heat and Power Economic Emission Dispatch (MO-CHPEED) problem aims to determine the optimal generator output of the co-generation systems, in which two conflicting objectives of the fuel cost and mass of emissions are to be simultaneously minimized. The nonlinear and nonconvex nature of the objective functions needs a good optimization technique to handle it. This paper proposes a Dynamically Controlled Whale Optimization Algorithm (DCWOA) to solve the multi-objective non-convex MO-CHPEED problem in fuzzy environment. The proposed DCWOA is an improved variant of the traditional WOA method by adding dynamically controlled constriction function. Both the conflicting objectives of fuel cost and mass of emissions are handled using Fuzzy Framework. To highlight the performance of the proposed technique, it is tested on the latest CEC test functions and three different MO-CHPEED case studies. The results obtained by proposed DCWOA after 100 independent trails on latest CEC test functions and compared with latest different published methods show the effectiveness and robustness of the proposed method for getting better average and STD values. Moreover, proposed DCWOA is also tested on different dimensioned MO-CHPEED test functions after 100 independent trails and compared with latest techniques. Again the most compromise results given by proposed DCWOA highlights the supremacy of the proposed method in terms of the getting better fitness and best compromise solution obtained and the convergence traits of the MO-CHPEED problem.

On the Application of a Lexicographic Method to Fuzzy Linear Programming Problems

The literature on fuzzy variable linear programming (FVLP) and fuzzy number linear programming (FNLP) is prolific in terms of the number of available solution methods. In FVLP problems, only the decision variables and right-hand side values of the constraints are fuzzy numbers. In FNLP problems, except forthe decision variables, all parameters are fuzzy numbers. A widespread approach for solving problemsin FVLP and FNLP is to use linear ranking functions in order to transform the fuzzy problems into conventional ones. Previous studies have shown that linear ranking functions do not guarantee uniqueness of the optimal fuzzy objective values. In this paper, we use a lexicographic method to find unique optimal fuzzy objective values of such problems and compare the results with those obtained via linear ranking function approaches. The paper also discusses applications of the lexicographic method in diet and time–cost trade-off problems in fuzzy environments.

Error bound analysis for split weak vector mixed quasi-variational inequality problems in fuzzy environment

In this paper, we consider a new class of split weak vector mixed quasi-variational inequality problems in fuzzy environments (for short, SWQVIP). Our aim is to establish error bounds for the underlying problem SWQVIP via regularized gap functions. We first propose some regularized gap functions of the problem SWQVIP using the method of nonlinear scalarization functions. Then, error bounds for the problem SWQVIP are investigated based on regularized gap functions with some suitable conditions without monotonicity. Finally, some examples are given to illustrate our results. The main results obtained in this paper are new and extend some corresponding known results in the literature.

Extension of particle swarm optimization algorithm for solving transportation problem in fuzzy environment

Transportation problem is one of the most common real life optimization problems seeking to minimize the total transportation cost while delivering a product from a number of sources to a number of destinations. In this paper, the transportation costs have been considered as generalized trapezoidal fuzzy numbers representing the uncertainty therein whereas the supply and the demand levels are crisp numbers. Particle Swarm Optimization has been extended to solve this fuzzy transportation problem. To illustrate the proposed extension of PSO, two numerical examples from existing literature have been solved and the results have been compared with those of the existing approaches. A few randomly generated problems of different dimensions have also been solved and the convergence rate of the proposed PSO has also been studied with respect to the variants of inertia weight, population size and the number of iterations. It has been observed that the proposed PSO works efficiently to obtain the optimal solutions and also removes the barricades of the traditional solution techniques.

Solving Bi-Level Multi-Objective Transportation Problem under Fuzziness

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.

On Multi-Objective Multi-Item Solid Transportation Problem in Fuzzy Environment

This paper discusses the reliability of multi-objective multi-item solid transport (F-MOMIST) problem with the transportation of penalties represented by the trapezoidal fuzzy numbers. We extended the existing F-MOMIST by introducing the fuzzy efficient concept and fuzzy crisp. We propose a weighting Tchebycheff approach to efficiently solve F-MOMIST. In the proposed approach, we first describe the first type of stability set corresponding to the optimal $$\alpha $$ -Pareto solution and then use the proposed approach to evaluate the first type of stability set corresponding to the $$\alpha $$ -optimal compromise solutions. A numerical case study to check the validity of the proposed approach is presented. The results of comparative experiments show that the proposed method is sufficiently effective in solving F-MOMIST and has better performance than the existing methods.

Solving Fuzzy Bi-Criteria Fixed Charge Transportation Problem Using a New Fuzzy Algorithm

The bi-criteria fixed charge transportation problem is an extension of the classical transportation problem. The bi-criteria fixed charge transportation problem in a crisp environment is, often, not effective in dealing with imprecision or vagueness in the values of the problem parameters. To deal with such situations, it has been proposed that the parameters should be represented as fuzzy numbers. Hence, bi-criteria fixed charge transportation problem in fuzzy environment is considered here. In existing approaches, the programming problems in fuzzy environment are solved by converting them into crisp environment by choosing appropriate membership functions and thus, the solutions are also crisp numbers. However, in this paper, a new algorithm is proposed to solve the above said problem using a linear ranking function, without converting it into crisp environment and the solutions derived are fuzzy numbers. The algorithm is suitably illustrated with a numerical example. Numerical results are compared for both fuzzy and crisp versions of the problem.

Maximal flow problem in fuzzy environment

Maximal flow problem in fuzzy environment

Fractile criterion iterative-interactive optimisation process for multi-objective stochastic linear programming problems in fuzzy environment

Present article focuses on one general fractile criterion iterative-interactive optimisation process in order to obtain the preferable Pareto optimal solution, subject to specified main objective function to multi-objective stochastic linear programming problems in fuzzy environment. This asks the managers to identify the main objective function among all objective functions without specifying any weights or utility functions. Unlike existing articles, the reference membership levels to conflicting objective functions are analytically determined by employing the trade-off ratios among objective functions in this process. Moreover, the necessity of only very few interactions with decision-makers saves the precious time and money of organisations. Numerical applications demonstrate the efficiency of proposed process. Finally, conclusions are drawn.

Fuzzy multi-objective decision making approach for nuclear power plant installation

Due to the increase in energy demand, many countries suffer from energy poverty because of insufficient and expensive energy supply. Plans to use alternative power like nuclear power for electricity generation are being revived among developing countries. Decisions for installation of power plants need to be based on careful assessment of future energy supply and demand, economic and financial implications and requirements for technology transfer. Since the problem involves many vague parameters, a fuzzy model should be an appropriate approach for dealing with this problem. This study develops a Fuzzy Multi-Objective Linear Programming (FMOLP) model for solving the nuclear power plant installation problem in fuzzy environment. FMOLP approach is recommended for cases where the objective functions are imprecise and can only be stated within a certain threshold level. The proposed model attempts to minimize total duration time, total cost and maximize the total crash time of the installation project. By using FMOLP, the weighted additive technique can also be applied in order to transform the model into Fuzzy Multiple Weighted-Objective Linear Programming (FMWOLP) to control the objective values such that all decision makers target on each criterion can be met. The optimum solution with the achievement level for both of the models (FMOLP and FMWOLP) are compared with each other. FMWOLP results in better performance as the overall degree of satisfaction depends on the weight given to the objective functions. A numerical example demonstrates the feasibility of applying the proposed models to nuclear power plant installation problem.

Enhancement of Capacitated Transportation Problem in Fuzzy Environment

This research work aims to study a capacitated transportation problem (CTP) with penalty cost, supplies, and demands represented by hexagonal fuzzy numbers. Based on ranking function, the supplies and demands are converted to the crisp form. Through the use of the α‐level, the problem is converted into interval linear programming. To optimize the interval objective function, we define the order relations represented by policy maker’s choice between intervals. The maximization (minimization) problem considering the interval objective function is transformed to multiobjective optimization problem based on order relations introduced by the preference of policy makers between interval profits (costs). A numerical example is given for illustration and to check the validity of the suggested approach.

A new class of strong mixed vector GQVIP-generalized quasi-variational inequality problems in fuzzy environment with regularized gap functions based error bounds

In this paper, we introduce and study a new class of strong mixed vector generalized quasi-variational inequality problems (GQVIP) in fuzzy environment. Then, using the method of the nonlinear scalarization function, the regularized gap functions for GQVIP is established. In addition, error bounds are provided for GQVIP via those regularized gap functions under suitable assumptions. The main results obtained in this paper are new and extend some corresponding known results. Some examples are given for the illustration of our results.

On Solving Transportation Problem in Fuzzy Environment Using Ranking Function

On Solving Transportation Problem in Fuzzy Environment Using Ranking Function

Dynamic variational inequality in fuzzy environments

This paper introduces a class of differential fuzzy variational inequalities, the model provides an efficient approach for solving many dynamic multi-objective optimization problems in fuzzy environments. An existence theorem of the Caratheodory weak solution for the model is established under some suitable assumptions. An algorithm, supported by the convergence analysis, is developed to find the solution. In addition, some examples are given to illustrate the application and the algorithm.