A new effective solution method for fully intuitionistic fuzzy transportation problem

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 is applied to get the initial basic feasible solution and then intuitionistic fuzzy modified distribution method is applied to acquire the optimal solution of the fully InFTP. Also a new ordering is developed here in which the compensation, linearity and additive property is 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. From the comparative analysis, the proposed approach shows better optimal solution than existing methods.

The reliability analysis based on the generalized intuitionistic fuzzy two-parameter Pareto distribution

In this paper, the two-parameter Pareto lifetime distribution is considered with vague shape and scale parameters, where parameters are set as generalized intuitionistic fuzzy numbers. A new L-R type intuitionistic fuzzy number is introduced, and cuts of the new fuzzy set are provided. The generalized intuitionistic fuzzy reliability characteristics such as reliability, conditional reliability, hazard rate and mean time to failure functions are defined, along with the special case of the two-parameter Pareto generalized intuitionistic fuzzy reliability analysis. Furthermore, the series and parallel system reliability are evaluated by the generalized intuitionistic fuzzy sets. Finally, for certain cases of the fuzzy shape and scale parameters and cut set values, the generalized intuitionistic fuzzy reliability characteristics are provided and compared through several illustrative plots.

A new method to determine the Fermatean fuzzy optimal solution of transportation problems

 Transportation Problems (TP) have multiple applications in supply chain management to reduce costs. Efficient methods have been developed to address TP when all factors, including supply, demand, and unit transportation costs, are precisely known. However, due to uncertainty in practical applications, it is necessary to study TP in an uncertain environment. In this paper, we define the Trapezoidal Fermatean Fuzzy Number (TrFFN) and its arithmetic operations. Then we introduce a new approach to solve TP, where transportation cost, supply, and demand are treated as TrFFN, and we call it Fermatean Fuzzy TP (FFTP). We illustrate the feasibility and superiority of this method with two application examples, and compare the performance of this method with existing methods. Furthermore, the advantages of the proposed method over existing methods are described to address TP in uncertain environments.

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.

Transportation problem with interval-valued intuitionistic fuzzy sets: impact of a new ranking

To address uncertainty and hesitation of a real-life problem, interval-valued intuitionistic fuzzy sets (IVIFSs) have received increasing interest among researchers and industrialists. In this paper, we present an advanced illustration of IVIFSs using physical distancing during COVID-19 to understand the deep concept of IVIFSs. Due to special feature of an IVIFSs, it finds a better decision of a real-life problem having uncertainty and hesitation. Here some important arithmetic operations between two IVIFSs are also stated. Ranking of IVIFSs is a valuable tool and it is not easy to rank due to its ill-defined membership and non-membership degrees, and same difficulties arise in a wide variety of real-life problems. To tackle these difficulties, we introduce a new ranking function of IVIFSs, and it follows well to the law of trichotomy. And for its superiority, we compare it with some existing ranking functions by taking a suitable example. Furthermore, its applicability are tested on the basis of an IVIFSs. Further, it is very interesting to note that some unpredicted factors such as road condition, diesel prices, traffic condition and weather condition affect to the cost of transportation, and therefore, decision makers encounter uncertainty and hesitation to estimate cost of transportation. To resolve such issues, we consider transportation problem with IVIFSs parameters, and for its solution, a simple computational method is developed and illustrated.

An intuitionistic fuzzy two stage supply chain network design problem with multi-mode demand and multi-mode transportation

In this study, a typical supply chain network design problem consisting of plants, distribution centers, and customers is considered with the assumptions of multi-mode demand and multi-mode transportation. In it, the parameters of the problem are considered as a trapezoidal intuitionistic fuzzy value to handle the vagueness in the information. Based on it, a hybrid approach is proposed where the fuzzy objective function is converted to a set of crisp objective functions and the fuzzy constraints are crisped using their credibility measure. Finally, the crisp multi-objective formulation is obtained and solved it with different approaches. To evaluate the formulations and solution approaches, a case study from healthcare sector and several test problems are used. The results of computational experiments are used to compare the solution approaches, where the behavior of the proposed crisp formulation is fully discovered.

Solving the fully fuzzy multi-objective transportation problem based on the common set of weights in DEA

A transportation problem basically deals with the problem which aims to minimize the total transportation cost or maximize the total transportation profit of distributing a product from a number of sources or origins to a number of destinations. While, in general, most of the real life applications are modeled as a transportation problem (TP) with the multiple, conflicting and incommensurate objective functions. On the other hand, for some reason such as shortage of information, insufficient data or lack of evidence, the data of the mentioned problem are not always exact but can be fuzzy. This type of problem is called fuzzy multi-objective transportation problem (FMOTP). There are a few approaches to solve the FMOTPs. In this paper, a new fuzzy DEA based approach is developed to solve the Fully Fuzzy MOTPs (FFMOTPs) in which, in addition to parameters of the MOTPs, all of the variables are considered fuzzy. This approach considers each arc in a FFMOTP as a decision making unit which produces multiple fuzzy outputs using the multiple fuzzy inputs. Then, by using the concept of the common set of weights (CSW) in DEA, a unique fuzzy relative efficiency is defined for each arc. In the following, the unique fuzzy relative efficiency is considered as the only attribute for the arcs. In this way, a single objective fully fuzzy TP (FFTP) is obtained that can be solved using the existing standard algorithms for solving this kind of TPs. A numerical example is provided to illustrate the developed approach.