Fuzzy Programming Approach Research Articles

Linear fractional transportation problem in bipolar fuzzy environment

This article proposes a solution methodology for the Linear Fractional Transportation Problem (LFTP) by incorporating bipolar fuzzy sets (BFSs) to accommodate both positive and negative judgmental perspectives. The approach explores Zimmermann's extension within bipolar fuzzy environment to compare outcomes. In this context, the cost function and constraint coefficients are depicted using interval-valued trapezoidal bipolar fuzzy numbers (IVTrBFNs) and defuzzified by (s, t)-cut. The initial approach employs the simplex method and fuzzy optimization method, renowned for its effectiveness in obtaining optimal solutions. In the alternative method, Bipolar fuzzy programming approach (BFPA) is utilized for better outcome. In this method the LFTP is altered to a Multi-Objective Transportation Problem (MOTP), and BFPA extends Zimmermann's technique under suitable positive and negative membership functions, converting MOTP to a one-objective transportation problem (TP) and solved using LINGO software. Supporting this proposed method some theorems are formulated to demonstrate that the most effective solution of the single-objective TP is a Pareto optimal solution for the corresponding MOTP. A quantitative example is provided for better understanding of the proposed BFPA method alongside two other approaches.

A new Fermatean fuzzy multi‐objective indefinite quadratic transportation problem with an application to sustainable transportation

AbstractIn this work, a Fermatean fuzzy (FF) multi‐objective indefinite quadratic transportation problem (TP) is introduced. Due to some unavoidable reasons, real‐life transportation parameters such as supply, demand and costs are indeterminate in nature and cannot be expressed in crisp terms. We represent these parameters using FF numbers, an extension of fuzzy numbers, which are capable of representing indeterminacy efficiently. A multi‐objective indefinite quadratic TP where each objective is a product of two linear factors (cost functions) is considered. Defuzzification of FF numbers is accomplished by the introduction of ‐cut for the first time. The obtained crisp TP is solved using the intuitionistic fuzzy programming approach and FF programming approach to arrive at a compromise solution. To substantiate the work, solution methodology based on defuzzification using the ranking function is also deliberated. The applicability of the model is demonstrated through a sustainable TP, which simultaneously minimizes transportation cost with depreciation cost and packaging cost with wastage cost. The resulting value of the objective functions and the aspiration levels are compared to depict the efficacy of the proposed method over the ranking function method. The concluding section summarizes the work, and future avenues along with some limitations of the work are also specified.

Resilient and sustainable semiconductor supply chain network design under trade credit and uncertainty of supply and demand

Supply Chain (SC) performance appraisal extends beyond economic evaluation to encompass environmental and social impacts, as well as resilience to supply and demand disruptions. Thus, SC network design decisions should simultaneously optimize all these performance metrics as a primary objective. However, existing studies optimized these objectives independently or in a limited scope, failing to comprehensively address the interconnected nature of these performance metrics. Therefore, this study proposes a mixed integer linear programming (MILP) model with four objectives to address a multi-tier resilient and sustainable semiconductor SC network design problem under trade credit, supply, and demand uncertainties. The model aims to determine the optimal number and location of various facilities, the amount to order from suppliers, economic production quantities, quantity allocation between SC entities, and ideal supplier selections. The proposed supply chain network contributes to the global effort to reduce carbon emissions and enhance the circular economy by considering carbon trading, recycling, and the proper disposal of end-of life products. Uncertainties in input parameters are addressed using a fuzzy programming approach, while lexicographic optimization and the ɛ-constraint method are used to solve the proposed model. This paper presents a numerical example to illustrate the applicability of the proposed model and provide managerial insights. The numerical analysis results show that provided an appropriate confidence level for the uncertain parameters, the sets of Pareto optimal solutions can be generated. And it also shows that the total SC cost increases with decreasing carbon emissions level and increasing job opportunities created. This research advances sustainable and resilient supply chain management practices while offering practical guidance for decision-makers in real-world contexts.

Compromise optimum allocation in neutrosophic multi-character survey under stratified random sampling using neutrosophic fuzzy programming

Survey sampling has wide range of applications in social and scientific investigation to draw inference about the unknown parameter of interest. In complex surveys, the sample information about the study variable cannot be expressed by a precise number under uncertain environment due fuzziness and indeterminacy. Therefore, this information is expressed by neutrosophic numbers rather than the classical numbers. The neutrosophic statistics, which is generalization of classical statistics, deals with the neutrosophic data that has some degree of indeterminacy and fuzziness. In this study, we investigate the compromise optimum allocation problem for estimating the population means of the neutrosophic study variables in a multi-character stratified random sampling under uncertain per unit measurement cost. We proposed the intuitionistic fuzzy cost function, modeling the fuzzy uncertainty in stratum per unit measurement cost. The compromise optimum allocation problem is formulated as a multi-objective intuitionistic fuzzy optimization problem. The solution methodology is suggested using neutrosophic fuzzy programming and intuitionistic fuzzy programming approaches. A numerical study includes the means estimation of atmospheric variables is presented to explore the real-life application, explain the mathematical formulation, and efficiency comparison with some existing methods. The results show that the suggested methods produce more precise estimates with less utilization of survey resources as compared to some existing methods. The Python is used for statistical analysis, graphical designing and numerical optimization problems are solved using GAMS.

Çok Seviyeli Rekabetçi Kapalı Döngü Tedarik Zinciri Ağ Tasarımı: Karşılaştırmalı Bir Analiz

Kısıtlı doğal kaynaklar ve bunların bilinçsizce tüketilmesi, son yıllarda hammadde yerine atık malzemenin işlenme oranının artmasına yol açmış ve endüstriyel ortamı daha rekabetçi hale getirerek, Tedarik Zinciri Yönetiminin (TZY) dinamiklerini değiştirmiştir. Kullanım ömrü sonu ürün sayısının artması ve bunlarla ilgili çevresel kaygılar, aynı zamanda müşteri baskılarına cevap verebilmek adına lojistiğin tersine çevrilmesine büyük özen gösterilerek Kapalı Döngü Tedarik Zinciri (KDTZ) tasarımı ve optimizasyonu üzerine ilgi artmıştır. KDTZ, geniş bir literatüre sahiptir ve bu çerçevede tedarik zinciri maliyetlerini optimize etmek için pek çok model geliştirilmiştir. Literatürün çoğu tekil tedarik zinciri ile ilgilidir ve mevcut rakip tedarik zincirlerini görmezden gelir. Ancak, günümüzün rekabetçi pazarlarında, tedarik zincirleri birkaç rekabetçi şirket tarafından birbirine entegre şeklinde oluşturulmakta ve daha fazla pazar payı elde etmek için birlikte rekabet ederek çalışmaktadır. Böyle bir ortamda, tedarik zincirleri içinde ve arasında farklı rekabet biçimleri vardır. Bu bağlamda, makale ürün geri kazanımı için bir takım teşviklerle kullanılmış ürünleri iade etme isteğini artırarak sürdürülebilir tüketimi iyileştirmeye çalışan iki üretici, bir toplama&geri dönüşüm merkezi ve müşterilerden oluşan çok seviyeli rekabetçi KDTZ yönetiminde dağıtım ağlarının tasarımı ve optimizasyonu problemini ele almaktadır. KDTZ yönetiminde farklı amaçlara sahip karar vericiler için uzlaşık çözüme ulaşmak için dört farklı Etkileşimli Bulanık Programlama (EBP) yaklaşımı kullanılmış ve sonuçlar analiz edilmiştir.

A novel fuzzy programming approach for piece selection problem in P2P content distribution network.

Piece selection policy in dynamic P2P networks play crucial role and avoid the last piece problem. BitTorrent uses rarest-first piece selection mechanism to deal with this problem, but its efficacy is limited because each peer only has a local view of piece rareness. The problem of piece section is multiple objectives. A novel fuzzy programming approach is introduced in this article to solve the multiple objectives piece selection problem in P2P network, in which some of the factors are fuzzy in nature. Piece selection problem has been prepared as a fuzzy mixed integer goal programming piece selection problem that includes three primary goals such as minimizing the download cost, time, maximizing speed and useful information transmission subject to realistic constraints regarding peer's demand, capacity and dynamicity. The proposed approach has the ability to handle practical situations in a fuzzy environment and offers a better decision tool to each peer to select optimal pieces to download from other peers in dynamic P2P network. Extensive simulations are carried out to demonstrate the effectiveness of the proposed model. It is proved that proposed system outperforms existing with respect to download cost, time and meaningful exchange of useful information.

Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution

In this paper, a bi-level chance constrained programming problem is considered when the coefficients of the objective function is presented as neutrosophic numbers and the right- hand side of the constraints is normal variables and the constraints have a joint probability distribution. While the probability problem and applying the score and accurate functions the problem is converted into an equivalent deterministic non- linear programming problem, a fuzzy programming approach is applied by defining membership function. A linear membership function is used for obtaining optimal compromise solution. A numerical example is given to illustrate the proposed methodology.

A pythagorean hesitant fuzzy programming approach and its application to multi objective reliability optimization problem

Decision-making problems can often be effectively solved using traditional optimization methods that have a clearly defined configuration. However, in real-world scenarios, decision-makers frequently encounter doubt or hesitation, making it challenging to precisely specify certain parameters. As a result, they often seek input from different experts, leading to conflicting values and varying levels of satisfaction among decision-makers. This uncertainty and lack of crisp values make decision-making problems inherently non-deterministic. In this paper, a novel Pythagorean hesitant fuzzy (PHF) programming method is designed to address the challenges of optimization problems with multiple objectives. Here PHF aggregation operators are used to aggregate the PHF memberships and non-memberships of the objectives. Additionally, to account the uncertainties of the parameters of the optimization problem Parabolic Pythagorean fuzzy number is used and centroid method is applied for defuzzification. We solved an example of multi objective optimization problem of manufacturing system to demonstrate our proposed method and finally, presented a case study on reliability optimization model for Life Support Systems, where the primary objectives are to maximize system reliability and minimize cost. The result is compared with other existing methods by degree of closeness.

A deterministic multi-item inventory model with quadratic demand under neutrosophic and pythagorean hesitant fuzzy programming approach

In this paper, a deterministic fuzzy inventory model with quadratic demand pattern, time-dependent holding cost, and time-dependent deterioration has been created. We have taken the rate of shortage as fully backlogged. In traditional inventory model, most of the cost parameters were taken as crisp. But in real world, fuzzy cost parameters are more realistic to appear instead of crisp parameters. Due to uncertainty we have considered all the cost parameters as hexagonal fuzzy number. We have regarded all of the cost parameters as hexagonal fuzzy numbers due to uncertainty. Our primary goal is to reduce the total average cost, and for that we've covered two optimization techniques: the Pythagorean Hesitant Fuzzy Programming Approach (PHFPA) and the Neutrosophic Hesitant Fuzzy Programming approach (NHFP).Through extensive numerical experiments and sensitivity analysis, the effectiveness and practicality of the proposed model are demonstrated. Comparative studies with traditional inventory models underscore the advantages of the Neutrosophic and Pythagorean Hesitant Fuzzy Programming Approach in managing multi-item inventory systems with quadratic demand patterns, highlighting its robustness in handling uncertain and ambiguous information.

Fuzzy Programming Approach to Solve Multi-Objective Fully Fuzzy Transportation Problem

The aim of this study is presenting the solution methodology of multi-objective fuzzy transportation problem with fuzzy decision variables, where all the input parameters and decisions variables of the programming problems are assumed to be triangular fuzzy number and triangular fuzzy decision variables respectively. Moreover the objectives under considerations are minimization of cost of transportation and minimization of shipping time under fuzzy environment. The fuzziness of the objective functions and the fuzzy constraints of the programming problem are defuzzified using the ranking function and the equality property between two fuzzy numbers, respectively. The consequent crisp multi-objective fuzzy transportation problem is tackled by employing fuzzy mathematical programming approach. Finally fuzzy decision is made after solving the resultant mathematical programming problem using LINGO(Schrage and LINDO Systems (1997)) software. Illustrative numerical example is presented in support of the proposed methodology.

Dynamic-chance-constrained-based Fuzzy Programming Approach for Optimizing Wastewater Facultative Ponds for Multi-period Case

In this article, a novel optimization model that was specifically designed as a dynamic-chance-constrained fuzzy uncertain programming framework is introduced. This model serves the purpose of optimizing the efficiency of facultative ponds utilized in domestic wastewater treatment. The primary focus of this study was maximizing the amount of the wastewater treated in the facility subject to quality requirements via the assessment of wastewater quality through the measurement of Biological Oxygen Demand (BOD). The model's development was grounded in a real-world scenario, where decision-makers encountered uncertainties in various parameters, such as the rate of BOD degradation and the incoming wastewater load, both characterized by fuzzy membership functions. In light of this uncertainty, the decision-maker aimed to maximize the wastewater treatment capacity while maintaining a suitable safety margin for both objective and constraint functions, employing policies founded on probability and chance. A case study was carried out at the Bantul domestic wastewater treatment plant, situated in Yogyakarta, Indonesia. The study successfully identified optimal decisions regarding wastewater flow rates and processing times. As a result, it can be concluded that the proposed model effectively resolved the problem at hand, making it a valuable tool for decision-makers in similar contexts.

Modeling the robust facility layout problem for unequal space considering health and environmental safety criteria under uncertain parameters

This study examines the robust facility layout problem (RFLP) while taking into account unpredictable health and environmental safety standards. This problem's major goal is to arrange the departments in various departments of a hall, allot each department the appropriate amount of space, and identify the kind of amenities and equipment needed for each chosen sector. To accomplish the aforementioned objective, five criteria were taken into account: the total cost of department transfer and selection; access to more facilities and equipment; access to firefighting equipment; access to favorable climatic conditions; and the separation of noisy departments from one another. The fuzzy programming approach is utilized in this research to regulate the uncertainty parameters due to the uncertainty of the transfer cost and transfer time parameters. Additionally, by supplying an appropriate chromosome, the precise Epsilon constraint approach, NSGA II, and MOPSO have been employed to tackle the issue. The computational sizes of larger-sized sample problems solved demonstrate the strong performance of the NSGA II in quickly finding effective solutions.

Intuitionistic fuzzy multi-objective transportation model during pandemic COVID-19

The given paper discusses an intuitionistic fuzzy discrete time-space optimization model while taking into account the COVID-19 pandemic. The novelty of this study is characterized by the proposal of a distinctive multi-objective intuitionistic fuzzy transportation model in which the demand function varies with time as the number of infected, exposed and susceptible persons increase. Forecasting of demand is executed using the epidemic diffusion model. Also, a new approach to defuzzify triangular intuitionistic fuzzy numbers, depending upon the concept of the golden ratio, is presented. Intuitionistic fuzzy programming approach is used to obtain the pareto-optimal solution. A real-life numerical illustration is explained using the proposed methodology to examine its practical suitability. Outperforming the existing traditional method of solving a transportation problem verifies its proficiency.

Sustainable group tourist trip planning: An adaptive large neighborhood search algorithm

The tourism industry is a key driver of economic growth and contributes to the achievement of sustainability goals. This paper presents a multi-objective group tourist planning problem that considers economic, environmental, and social dimensions simultaneously. The proposed model minimizes total cost and environmental impacts while maximizing the total collected prizes from tourists' interests. We introduce the lost profit opportunity for the cost of tours from an economic perspective for the first time. From an environmental perspective, the model minimizes both carbon emissions for transportation and the waste produced by tourists. Social satisfaction is addressed by considering tourists' preferences for visiting tourist sites and their interests in participating in group tours, maximizing total collected prizes. Uncertainties in travel time and prize values are addressed by using a fuzzy programming approach. A multi-objective adaptive large neighborhood search (ALNS) algorithm is developed to solve the proposed multi-objective group tourist planning problem, offering various removal, insertion, and local search heuristic procedures. Extensive analyses and computations are conducted to demonstrate the performance of the proposed multi-objective optimization model and the ALNS metaheuristic algorithm in solving large-scale instances. The results demonstrate the effectiveness of our approach in aiding tourism managers to make informed decisions that balance economic, environmental, and social objectives.

Stochastic Transportation Problem with Multichoice Random Parameter

This paper deals with the situation of multiple random choices along with multiple objective functions of the transportation problem. Due to the uncertainty in the environment, the choices of the cost coefficients are considered multichoice random parameters. The other parameters (supply and demand) are replaced by random variables with Gaussian distributions, and each multichoice parameter alternative is treated as a random variable. In this paper, the Newton divided difference interpolation technique is used to convert the multichoice parameter into a single choice in the objective function. Then, the chance-constrained method is applied to transform the probabilistic constraints into deterministic constraints. Due to the consideration of multichoices in the objective function, the expectation minimization model is used to get the deterministic form. Moreover, the fuzzy programming approach with the membership function is utilized to convert the multiobjective function into a single-objective function. A case study is also illustrated for a better understanding of the methodology.

An aspect of bilevel interval linear fractional transportation problem with disparate flows: a fuzzy programming approach

An aspect of bilevel interval linear fractional transportation problem with disparate flows: a fuzzy programming approach

A multi-objective q-rung orthopair fuzzy programming approach to heterogeneous group decision making

In allusion to heterogeneous multi-criteria group decision making (MCGDM) problems with incomplete weights and q-rung orthopair fuzzy (q-ROF) truth degrees, where many kinds of criteria values, i.e., crisp values, intervals, trapezoidal fuzzy values, hesitant fuzzy values and q-ROF values (q-ROFVs), and multiple types of interactions exist, i.e., positive synergetic interactions, negative synergetic interactions and independence, a novel multi-objective q-ROF programming approach is proposed. In particular, in order to globally capture the interactions among criteria, Choquet-based relative closeness degrees are developed based on the technique for order performance by similarity to ideal solution (TOPSIS) and the Choquet integral. Then, the q-ROF Choquet-based group consistency index (q-ROFCGCI) and the q-ROF Choquet-based group inconsistency index (q-ROFCGII) are defined. Next, to derive optimal 2-additive fuzzy measures on the criteria set and optimal experts' weights, a new multi-objective q-ROF mathematical programming model is established by minimizing the q-ROFCGII and maximizing the q-ROFCGCI. Subsequently, an algorithm based on the adaptive non-dominated sorting genetic algorithm III (A-NSGA-III) is designed to solve the established model. Afterwards, the Choquet-based overall relative closeness degrees of the alternatives are used to obtain their preferred ordering. Finally, the effectiveness and advantage of the proposed approach is verified using four real cases concerning the evaluation of social commerce.

Fermatean Fuzzy Programming with New Score Function: A New Methodology to Multi-Objective Transportation Problems

The aim of this work is to establish a new methodology to tackle the multi-objective transportation problems [MOTP] in a Fermatean fuzzy environment that can deal with all the parameters that possess a conflicting nature. In our research work, we developed a new score function in the context of a fermatean nature for converting fuzzy data into crisp data with the help of the Fermatean fuzzy technique. Then, we introduced an algorithm-based methodology, i.e., the Fermatean Fuzzy Programming approach to tackle transportation problems with multi-objectives. The main purpose of this research work is to give an alternate fuzzy programming approach to handle the MOTP. To justify the potential and validity of our work, numerical computations have been carried out using our proposed methodology.

Decision-making support for optimizing pollutant degradation processes in domestic wastewater treatment plants involving uncertain parameters via fuzzy programming approaches

A fuzzy optimization model was implemented in this study as a decision-making approach to optimize pollutant degradation processes in facultative ponds of domestic wastewater treatment plants. The fuzzy parameters are due to uncertain situations, which eliminate the need for managers to collect data, particularly when the data are no longer represent the real situation. The managers formulate the fuzzy parameters in the problem based on their intuition and experience in using the provided decision-making tool. Also, the fuzzy optimization model proposed in this study was solved using the fuzzy-based programming approach with the generalized gradient algorithm performed in LINGO 19.0 optimization software. In addition, the numerical experiment was conducted with secondary and generated data for the certain and fuzzy parameters, respectively. The results showed that optimal decisions were achieved and the manager can then use the proposed model in managing domestic wastewater treatment plants.

A Multi Objective Epq Model with Uniform Demand and Productıon Rate Along Wıth Shortages Under Intuitioistic Fuzzy Programmıng Approach

In this paper we have described a multi-objective economic production quantity (EPQ) model with uniform demand rate as well as shortages. In this model we have considered the production rate as finite. Due to uncertainty in the various cost parameters, most of the costs parameters are taken as pentagonal fuzzy number. The model has been solved by Fuzzy Non-Linear Programming Problem (FNLP), Fuzzy Additive Goal Programming Problem (FAGP) and Intuitionistic fuzzy programming approach (IFP).To demonstrate the validity of this model some numerical examples have been given lastly. The sensitivity analysis for some cost parameters has also been given.