Intuitionistic Fuzzy Transportation Problem Research Articles

A New Approach for Solving a Heptagonal Intuitionistic Fuzzy Transportation Problem by Using Proposed Method

In this paper, we approach the transportation problem whose supplies and demands are in intuitionistic fuzzy number. We formulate and utilize the heptagonal intuitionistic fuzzy number to deal with uncertainty. We discuss about the new ranking function for intuitionistic fuzzy number. Finally, we approach an algorithm for finding the optimal solution of heptagonal intuitionistic fuzzy transportation problem with relevant numerical example.

An approach for solving fully generalized intuitionistic fuzzy transportation problems

An approach for solving fully generalized intuitionistic fuzzy transportation problems

An ε-Constraint Method for Multiobjective Linear Programming in Intuitionistic Fuzzy Environment

Effective decision-making requires well-founded optimization models and algorithms tolerant of real-world uncertainties. In the mid-1980s, intuitionistic fuzzy set theory emerged as another mathematical framework to deal with the uncertainty of subjective judgments and made it possible to represent hesitancy in a decision-making problem. Nowadays, intuitionistic fuzzy multiobjective linear programming (IFMOLP) problems are a topic of extensive research, for which a considerable number of solution approaches are being developed. Among the available solution approaches, ranking function-based approaches stand out for their simplicity to transform these problems into conventional ones. However, these approaches do not always guarantee Pareto optimal solutions. In this study, the concepts of dominance and Pareto optimality are extended to the intuitionistic fuzzy case by using lexicographic criteria for ranking triangular intuitionistic fuzzy numbers (TIFNs). Furthermore, an intuitionistic fuzzy ε-constraint method is proposed to solve IFMOLP problems with TIFNs. The proposed method is illustrated by solving two intuitionistic fuzzy transportation problems addressed in two studies (S. Mahajan and S. K. Gupta’s, “On fully intuitionistic fuzzy multiobjective transportation problems using different membership functions,” Ann Oper Res, vol. 296, no. 1, pp. 211–241, 2021, and Ghosh et al.’s, “Multi-objective fully intuitionistic fuzzy fixed-charge solid transportation problem,” Complex Intell Syst, vol. 7, no. 2, pp. 1009–1023, 2021). Results show that, in contrast with Mahajan and Gupta’s and Ghosh et al.’s methods, the proposed method guarantees Pareto optimality and also makes it possible to obtain multiple solutions to the problems.

On solving fully intuitionistic fuzzy transportation problem via branch and bound technique

In dealing with real world transportation problems, several issues are frequently encountered as a result of uncontrollable factors. To deal this uncertainties, many authors have suggested transportation problems with intuitionistic fuzzy parameters. In this article, fully intuitionistic fuzzy transportation problem (InFTP) is considered in which the parameters are triangular intuitionistic fuzzy numbers. To solve this, initially intuitionistic fuzzy branch and bound technique are applied to get the initial basic feasible solution and then intuitionistic fuzzy modified distribution (InFMODI) method is applied to acquire the optimal solution of the fully InFTP. Also, a new ordering is developed here in which some properties of compensation, linearity, additive and partial order relations are satisfied. The optimal solution obtained from the proposed method satisfies the condition of optimality and feasibility. Finally, two numerical examples are provided to show the effectiveness of the proposed method.

An approach to solve interval valued intuitionistic fuzzy transportation problem of Type-2

An approach to solve interval valued intuitionistic fuzzy transportation problem of Type-2

A novel approach to interval-valued variables using new interval arithmetic to solve an intuitionistic fuzzy transportation problem

This paper is concerned with the solution mechanism to solve the transportation problem under unpredictability by using interval valued intuitionistic fuzzy parameters. The parameters are chosen as intervals in which costs are modeled by intuitionistic fuzzy numbers, whereas source and destination are taken as crisp values. Various methods of transportation problem like VAM, Monalisha’s Approximation method, Zero point method are used to illustrate the cost in interval numbers by using the interval arithmetic operations. For each method, a solution is derived without converting into crisp expression followed by a graphical representation.

Intuitionistic fuzzy TOPSIS for non-linear multi-objective transportation and manufacturing problem

The given study intends to propose a new approach, named intuitionistic fuzzy TOPSIS, to solve a non-linear multi-objective intuitionistic fuzzy problem, whose application is not confined to only one type but has a wider scope. Considering the distance of positive and negative ideal solutions from the optimal values directly in terms of triangular intuitionistic fuzzy numbers makes the study unique. Along with this, a new technique, based upon barycentric coordinates of a triangle, to defuzzify triangular intuitionistic fuzzy numbers has been proposed. Two different types of substantive illustrations viz., non-linear multi-objective intuitionistic fuzzy transportation problem and non-linear multi-objective intuitionistic fuzzy manufacturing problem, are solved and compared with the paradigmatic approaches existing in the literature.

Stability of Parametric Intuitionistic Fuzzy Multi-Objective Fractional Transportation Problem

In this study, a parametric intuitionistic fuzzy multi-objective fractional transportation problem (PIF-MOFTP) is proposed. The current PIF-MOFTP has a single-scalar parameter in the objective functions and an intuitionistic fuzzy supply and demand. Based on the (α,β)-cut concept a parametric (α,β)-MOFTP is established. Then, a fuzzy goal programming (FGP) approach is utilized to obtain (α,β)-Pareto optimal solution. We investigated the stability set of the first kind (SSFK) corresponding to the solution by extending the Kuhn-Tucker optimality conditions of multi-objective programming problems. An algorithm to crystalize the progressing SSFK for PIF-MOFTP as well as an illustrative numerical example is presented.

Intuitionistic fuzzy sustainable multi-objective multi-item multi-choice step fixed-charge solid transportation problem

Intuitionistic fuzzy sustainable multi-objective multi-item multi-choice step fixed-charge solid transportation problem

From fuzzy transportation problem to non-linear intuitionistic fuzzy multi-objective transportation problem: A literature review

ABSTRACT To deal with the unpredictability of certain parameters of the transportation problem like fuel charges, climatic conditions, supply and demand of the product, etc., the concept of fuzzy transportation problem came into the limelight. It has been proved to be an efficient approach and extended in literature by various scholars. In the given paper, the existing methods to obtain the solution of different types of fuzzy transportation problem and its extensions are critically reviewed. Intuitionistic fuzzy transportation problems having single and multiple objectives have been focused upon. A review of the past ten years has been done to know the recent advancement. Tabular and graphical comparisons of different approaches are incorporated to understand their benefits and drawbacks.

Least-looping stepping-stone-based ASM approach for transportation and triangular intuitionistic fuzzy transportation problems

Transportation problem (TP) is a popular branch of Linear Programming Problem in the field of Transportation engineering. Over the years, attempts have been made in finding improved approaches to solve the TPs. Recently, in Quddoos et al. (Int J Comput Sci Eng (IJCSE) 4(7): 1271–1274, 2012), an efficient approach, namely ASM, is proposed for solving crisp TPs. However, it is found that ASM fails to provide better optimal solution in some cases. Therefore, a new and efficient ASM appoach is proposed in this paper to enhance the inherent mechanism of the existing ASM method to solve both crisp TPs and Triangular Intuitionistic Fuzzy Transportation Problems (TIFTPs). A least-looping stepping-stone method has been employed as one of the key factors to improve the solution quality, which is an improved version of the existing stepping-stone method (Roy and Hossain in, Operation research Titus Publication, 2015). Unlike stepping stone method, least-looping stepping-stone method only deals with few selected non-basic cells under some prescribed conditions and hence minimizes the computational burden. Therefore, the framework of the proposed method (namely LS-ASM) is a combination of ASM (Quddoos et al. 2012) and least-looping stepping-stone approach. To validate the performance of LS-ASM, a set of six case studies and a real-world problem (those include both crisp TPs and TIFTPs) have been solved. The statistical results obtained by LS-ASM have been well compared with the existing popular modified distribution (MODI) method and the original ASM method, as well. The statistical results confirm the superiority of the LS-ASM over other compared algorithms with a less computationl effort.

An unknown Transit technique for Solving Generalized Trapezoidal Intuitionistic Fuzzy Transportation Problems using Centroid of Centroids

In the present day by day life circumstances TP we habitually face the circumstance of unreliability in addition to unwillingness due to various unmanageable segments. To deal with unreliability and unwillingness multiple researchers have recommended the intuitionistic fuzzy (IF) delineation for material. This paper proposes the approach used by generalized trapezoidal intuitionistic fuzzy number to solve these transport problem, i.e. capacity and demand are considered as real numbers and charge of transport from origin to destination is considered as generalized trapezoidal intuitionistic fuzzy numbers as charge of product per unit. The generalized trapezoidal intuitionistic fuzzy numbers ranking function is used on the basis of IFN'S centroid of centroids. Through the traditional optimization process, we generate primary basic feasible solution and foremost solution. The numerical illustration shows efficacy of technique being suggested. A fresh technique is implemented to seek foremost solution using ranking function of a fuzzy TP of generalized trapezoidal intuitionistic fuzzy number. Without finding a IBFS, this approach explicitly provides optimal solution for GTrIFTP. Finally, for ranking function we apply a proposed GTrIFTP method illustrated Numerical example.

Pareto-optimal solution for fixed-charge solid transportation problem under intuitionistic fuzzy environment

An intuitionistic fuzzy transportation problem considers both membership as well as non-membership functions. It may be linear or non-linear. In the literature, a lot of work is done in the case of linear membership and non-membership functions, but not in non-linear functions. The presented paper defines the non-membership functions of hyperbolic and exponential functions. The novelty lies in suggesting a unique approach of obtaining pareto-optimal solution of multi-objective fixed-charge solid transportation problem by using intuitionistic fuzzy programming approach with linear, hyperbolic, and exponential membership as well as non-membership functions. A real-life numerical illustration is solved, which exhibits the suitability of the proposed methodology as well as the functionality of all the membership and non-membership functions considered here.

Multi-objective fully intuitionistic fuzzy fixed-charge solid transportation problem

During past few decades, fuzzy decision is an important attention in the areas of science, engineering, economic system, business, etc. To solve day-to-day problem, researchers use fuzzy data in transportation problem for presenting the uncontrollable factors; and most of multi-objective transportation problems are solved using goal programming. However, when the problem contains interval-valued data, then the obtained solution was provided by goal programming may not satisfy by all decision-makers. In such condition, we consider a fixed-charge solid transportation problem in multi-objective environment where all the data are intuitionistic fuzzy numbers with membership and non-membership function. The intuitionistic fuzzy transportation problem transforms into interval-valued problem using (alpha ,beta )-cut, and thereafter, it reduces into a deterministic problem using accuracy function. Also the optimum value of alternative corresponds to the optimum value of accuracy function. A numerical example is included to illustrate the usefulness of our proposed model. Finally, conclusions and future works with the study are described.

Value- and Ambiguity-Based Approach for Solving Intuitionistic Fuzzy Transportation Problem with Total Quantity Discounts and Incremental Quantity Discounts

The cost of goods per unit transported from the source to the destination is considered to be fixed regardless of the number of units transported. But, in reality, the cost is often not fixed. Quantity discount is often allowed for large shipments. Furthermore, the transportation cost and the price break quantities are not deterministic. In this study, we introduce the concept of Value- and Ambiguity-based approach for solving the intuitionistic fuzzy transportation problem with total quantity discounts and incremental quantity discounts. Here, the cost and quantity price breakpoints are represented by trapezoidal intuitionistic fuzzy numbers. The Values and Ambiguities are defined as the degree of acceptance and rejection for trapezoidal intuitionistic fuzzy numbers. The trapezoidal intuitionistic fuzzy transportation problem is converted to a parametric transportation problem based on their Value indices and Ambiguity indices. Then, for different Values of the parameter, the transformed problem is reduced to the linear programming problem. Then, the linear programming problem is solved by using the classical methods. The proposed method is demonstrated with a numerical example. In conclusion, the intuitionistic fuzzy transportation problem with total quantity discounts is compared with the intuitionistic fuzzy transportation problem with incremental quantity discounts.

A novel Approach for Fully Intuitionistic Fuzzy Multi-Objective Fractional Transportation Problem

This paper exhibits a novel approach for solving fully intuitionistic fuzzy multi-objective fractional transportation problem (FIF-MOFTP). Because of the change of market policies, we expect that the transportation cost, the shipped quantity, the source, and the destination parameters are not generally exact. In this paper, a theorem which demonstrate that FIF-MOFTP is ever solvable was presented. In our approach, the problem is converted into a linear one based on some transformations. Then the linearized model is reduced to a crisp multi-objective transportation problem utilizing the accuracy function for each objective. Moreover, various theorems that set up the relation among the FIF-MOFTP and its equivalent crisp model using linear, hyperbolic, and parabolic membership functions are also proofed. To approve the proposed approach, a numerical example is incorporated. Deductions and future exploration of this paper are depicted at end.

Approximate Membership Function Shapes of Solutions to Intuitionistic Fuzzy Transportation Problems

In this paper, proposing a mathematical model with disjunctive constraint system, and providing approximate membership function shapes to the optimal values of the decision variables, we improve the solution approach to transportation problems with trapezoidal fuzzy parameters. We further extend the approach to solving transportation problems with intuitionistic fuzzy parameters; and compare the membership function shapes of the fuzzy solutions obtained by our approach to the fuzzy solutions to full fuzzy transportation problems yielded by approaches found in the literature.

Intuitionistic fuzzy multi-stage multi-objective fixed-charge solid transportation problem in a green supply chain

This research mainly focuses on presenting an innovative study of a multi-stage multi-objective fixed-charge solid transportation problem (MMFSTP) with a green supply chain network system under an intuitionistic fuzzy environment. The most controversial issue in recent years is that greenhouse gas emissions such as carbon dioxide, methane, etc. induce air pollution and global warming, thus motivating us to formulate the proposed research. In real-world situations the parameters of MMFSTP via a green supply chain network system usually have unknown quantities, and thus we assume trapezoidal intuitionistic fuzzy numbers to accommodate them and then employ the expected value operator to convert intuitionistic fuzzy MMFSTP into deterministic MMFSTP. Next, the methodologies are constructed to solve the deterministic MMFSTP by weighted Tchebycheff metrics programming and min-max goal programming, which provide Pareto-optimal solutions. A comparison is then drawn between the Pareto-optimal solutions that are extracted from the programming, and thereafter a procedure is performed to analyze the sensitivity analysis of the target values in the min–max goal programming. Finally, we incorporate an application example connected with a real-life industrial problem to display the feasibility and potentiality of the proposed model. Conclusions about the findings and future study directions are also offered.

Zero-Point Maximum Allocation Method for Solving Intuitionistic Fuzzy Transportation problem

Transportation problems (TP) can be solved by various methods when the parameters are in crisp nature. But when the parameters are vague in nature or have imperfect knowledge or have partial information then we have to use the fuzzy optimization. Sujatha et al. [Solving fuzzy transportation problem (FTP) using zero point maximum allocation method] proposed the procedure for fuzzy transportation problem (FTP) with parameters are in the form of trapezoidal fuzzy numbers. But fuzzy logic is not adequate to describe all the characteristics of the system. To describe all the properties of the system, we have to consider the membership as well as the non-membership including the hesitation part. In the present research paper, we have proposed the solution of the transportation problem (TP) in the form of intuitionistic fuzzy logic by using zero point maximum allocation method. By using this technique, we can observe that the method applied to solve the fuzzy transportation problem (FTP) gives the most suitable optimal solution. A numerical example has also been given to elaborate this technique to solve the intuitionistic fuzzy transportation problem (IFTP).

Solving unbalanced intuitionistic fuzzy transportation problem

In this paper, we find the optimal solution for an unbalanced intuitionistic fuzzy transportation problem by using monalisha’s approximation method. The main aim of this method is to avoid large number of iterations. To illustrate this method a numerical example Triangular intuitionistic fuzzy number, unbalanced intuitionistic fuzzy transportation problem, accuracy function.is given.