A multi-objective transportation model under neutrosophic environment

The real world conditions of transportation pose new challenges for development of intelligent assistive systems for effective decision making. The ignorance of relationships among various attributes and parameters is one of the major causes of uncertainty in existing models of transportation problems. Fuzzy sets have been explored by various investigators to address the uncertainty issues due to relationships among various attributes. However fuzzy sets are not fully capable of dealing all kinds of uncertainty to provide intelligent solutions of transportation problems. A soft set is explored in this paper to model the uncertainty arising from the relationships of attributes with the parameters in a multimodal and multi objective transportation problem. The three modes of transportation incorporated in this model are road, rail and air. The real data set is prepared using the tariff, distance and time duration of transport available on websites of transport service agencies. The objectives are to minimize the cost and time duration of transportation. The proposed model evaluates multiple criteria using various combinations of different modes of transport to optimize the objectives of the problem. The model has been illustrated using the real data set using existing methods of solution. The soft set approach is found to be quite effective in dealing with the relationships of attributes with the parameters arising due to multi criteria decision making and leads to intelligent optimal solutions. The proposed model can be used as intelligent assistive system for decision making of multi objective and multimodal transportation problems.

In the present paper, a fuzzy programming model with quadratic membership functions has been developed for the solution of a Multi-Objective Transportation problem. In literature, several fuzzy programming approaches exist with various types of membership functions such as linear, exponential, hyperbolic etc. These membership functions are defined, by taking the lower and upper values of the objective functions into account. In some cases, these methods fail to obtain an integer compromise optimal solution. In the present method, two coefficients of the quadratic membership functions are determined by the lower and upper values of the objective functions. The other coefficient is taken as a variable in the fuzzy programming approach. This means that the membership curve is fixed at the two end points and set free in between. Application of the method on numerical examples proved that the approach could generate integer compromise optimal solutions.

This chapter presents solution procedures for solving unbalanced multi-objective multi-choice stochastic transportation problems in a hybrid fuzzy uncertain environment. In this chapter, various types of unbalanced multi-objective fuzzy stochastic transportation models are considered with the assumption that the parameters representing supplies of the products at the origins and demands of the products at the destinations, capacity of the conveyances, associated with the system constraints are either fuzzy numbers (FNs) or fuzzy random variables (FRVs) with some known continuous fuzzy probability distributions. The multi-choice cost parameters are considered as FNs. In this chapter, two objectives are considered: total transportation cost and total transportation time. As the transportation cost mainly depends on fuel prices and since fuel prices are highly fluctuating, the cost parameters are taken as multi-choice cost parameters with possibilistic uncertain nature. The time of transportation mainly depends on vehicle conditions, quality of roads, and road congestion. Due to these uncertain natures, the parameters representing time of transportation are also taken as fuzzy uncertain multi-choice parameters. In this transportation model, these objectives are minimized satisfying the constraints: product availability constraints, requirement of the product constraints, and capacity of the conveyance constraints. Numerical examples are provided for the sake of illustration of the methodology presented in this chapter, and also achieved solutions are compared with the solutions obtained by some existing methodologies to establish its effectiveness.

Disasters are the unfortunate suddenly occurring events which collapse a living society within a moment. Facebook, the most trending social media have initiated an active role to response the crisis developing a safety check feature to know about the demand of victims in an area. Through this feature the Facebook authority can confirm the requirement of the affected people in a specific area. This research have introduced a mathematical model for multi-objective solid transportation problem to quick delivery of the relief products to the devastating society according to the most prior demand of an area acquiring the best information through safety check feature launched by Facebook with limited resources. The two main objectives of the model are to minimize the total cost and minimize the total time so that relief can be executed under a limited budget responding quickly to the affected area. In this paper, fuzzy goal programming is adopted to solve the multi-objective solid transportation problem. To contemplate the performance of the model, a numerical example is presented in this paper. The numerical example is solved with LINGO optimization solver.

This paper is to integrate among solid transportation problem, budget constraints and carbon emission with probable maximum profit. The range of air pollution and climate change are effected by \({\text {CO}_2}\) gas emission and other greenhouse gases from myriad transportation systems. Henceforth, our target is to minimize carbon emission for pollution-free environment. Transportation system with single objective is hardly applicable to the situation with more than one criterion. Therefore multi-objective decision making is incorporated for designing real-life transportation problem. Due to time pressure, data limitation, lack of information or measurement errors in practical problems, there exist some hesitations. Based on the fact, decision maker considers indeterminacy in the designed problems. To overcome such hesitancy of occurrence and non-occurrence in fuzzy and intuitionistic fuzzy, neutrosophic set is very important and suitable to accommodate such general structure of problems. Therefore neutrosophic environment with neutrosophic linear programming, fuzzy programming and global criterion method is utilized here to find the compromise solution of the multi-objective transportation problem. Thereafter, the performance of the considered model is useful by evaluating a numerical example, and then the derived results are compared. Finally sensitivity analysis and conclusions with upcoming works of this research are stated hereafter.

Transportation problem is an integral part of this competitive world. Minimizing transportation cost of a product from sources to destinations is the main objective of traditional transportation problems. In the present context single objective transportation problem fails to meet the managerial decision making requirements which demands the multi objective transportation problems. Many real life problems can be formulated as multi objective transportation problem, and their solution requires consideration of conflicting objectives. Naturally, these problems have a number of potentially Pareto-optimal solutions. Multi-objective transportation problem refers to a special class of vector minimum linear programming problem, which usually involves multiple, conflicting, and incommensurable objective functions. Solving these complexities, the decision maker has to develop a utility function. In this paper, we develop a utility function to attain the targeted goal for a multi objective transportation problem. This utility function is developed using fuzzy membership functions considering deviations of objective function from the goal value where deviation variable has chosen as fuzzy type. Moreover, fuzzy max-min operator has been included for taking limiting value of the objective functions. Performance of the utility function to achieve proper goal is evaluated and justified by solving numerical examples using fuzzy goal programming.

The rare earth industry is a crucial strategic industry that is related to the national economy and national security. In the context of economic globalization, international competition is becoming increasingly fierce, and the rare earth industry is facing a more severe survival and development environment than ever before. Although China is the greatest world’s rare earth country in rare earth reserves, production, consumption and export volume, it is not a rare earth power. The rare earth industry has no right to speak in the international market. The comparative advantage is weakening and the security of rare earth industry appears. Therefore, studying the rare earth industry security has important theoretical and practical significance. When measuring the China’s rare earth industry security, the primary problem involves tremendous uncertainty. Neutrosophic soft set (NSS), depicted by the parameterized form of truth membership, falsity membership and indeterminacy membership, is a more serviceable pattern for capturing uncertainty. In this paper, five dimensions of rare earth industry security are identified and then prioritized against twelve different criteria relevant to structure, organization, layout, policy and ecological aspects of industry security. Then, the objective weight is computed by CRITIC (Criteria Importance Through Inter-criteria Correlation) method while the integrated weight is determined by concurrently revealing subjective weight and objective weight. Later, neutrosophic soft decision making method based CoCoSo (Combined Compromise Solution) is explored for settling the issue of low discrimination. Lastly, the feasibility and validity of the developed algorithm is verified by the issue of China’s rare earth industry security evaluation.

This paper explores the study of multi-choice multi-objective transportation problem (MCMTP) under the environment of utility function approach. MCMTP is converted to multi-objective transportation problems (MOTP) by transforming the multi-choice parameters like cost, demand, and supply to real-valued parameters. A general transformation procedure using binary variables is illustrated to reduce MCMTP into MOTP. Most of the MOTP are solved by goal programming (GP) approach. Using GP, the solution of MOTP may not be satisfied all the time by the decision maker (DM) when the proposed problem contains interval-valued aspiration level. To overcome this difficulty, here we propose the approaches of revised multi-choice goal programming (RMCGP) and utility function into the MOTP and then compared the solution between them. Finally, numerical examples are presented to show the feasibility and usefulness of our paper.

The simplified neutrosophic set (SNS) is a generalization of the fuzzy set that is designed for some incomplete, uncertain and inconsistent situations in which each element has different truth membership, indeterminacy membership and falsity membership functions.

Neutrosophic triplet structure yields a symmetric property of truth membership on the left, indeterminacy membership in the centre and false membership on the right, as do points of object, centre and image of reflection. As an extension of a neutrosophic set, the Q-neutrosophic set was introduced to handle two-dimensional uncertain and inconsistent situations. We extend the soft expert set to generalized Q-neutrosophic soft expert set by incorporating the idea of soft expert set to the concept of Q-neutrosophic set and attaching the parameter of fuzzy set while defining a Q-neutrosophic soft expert set. This pattern carries the benefits of Q-neutrosophic sets and soft sets, enabling decision makers to recognize the views of specialists with no requirement for extra lumbering tasks, thus making it exceedingly reasonable for use in decision-making issues that include imprecise, indeterminate and inconsistent two-dimensional data. Some essential operations namely subset, equal, complement, union, intersection, AND and OR operations and additionally several properties relating to the notion of generalized Q-neutrosophic soft expert set are characterized. Finally, an algorithm on generalized Q-neutrosophic soft expert set is proposed and applied to a real-life example to show the efficiency of this notion in handling such problems.

Hydro-thermal-wind scheduling employing novel ant lion optimization technique with composite ranking index

Neutrosophic numbers and matrices extend classical fuzzy set theory by incorporating three components to represent uncertainty: truth membership, indeterminacy membership, and falsity membership degrees. Real neutrosophic matrices consist of neutrosophic numbers as their entries, offering a structure to model uncertain and imprecise information across various applications. This paper investigates operations on real neutrosophic matrices, such as addition, multiplication, and scalar multiplication, and defines how these operations function within the neutrosophic framework. The paper also examines the use of LU decomposition as an efficient method for solving systems of real neutrosophic linear algebraic equations. LU decomposition is a numerical technique that breaks down a matrix into lower and upper triangular matrices, enabling the solution of linear systems through forward and backward substitution.

The main proposal of this paper is to derive two different reduction process for a trapezoidal type-2 fuzzy number. The first reduction method is based on critical values and the second method is based on α-cut of fuzzy number. As an application a multi-objective solid transportation problem, minimizing the cost and time has been developed using trapezoidal type-2 fuzzy number as system parameters and hereby solved. Finally after solving the proposed multi-objective problem by intuitionistic fuzzy programming technique a comparison between the two proposed reduction methods are discussed briefly. The proposed models and techniques are finally illustrated by providing numerical examples at the end. Also this paper present a comparative study between the proposed method to the KM algorithm and NT method for type reduction.

In this problems is shown that the problem of allocating units of blood from the central depots of a regional blood transfusion centre to the hospital blood banks of its area, can be formulated as a multiobjective transportation problem. Various objectives can be taken into consideration such as the minimisation of the expected expiries, the minimisation of the variance of the expiries, transportation costs or distances etc.. An application of the model is examined.

In classical fractional transportation programming problem, we want to optimize the objective function in the form of one or several ratios subject to some linear constraints. If in multi-objective transportation problem, objective function is in ration of two linear function under some linear restrictions, then the problem is called multi-objective linear fractional transportation problem (MOLFTP). In this paper we propose a new method to solve multi-objective linear fractional transportation problem which is extension of Nomani et al. (Int J Manag Sci Eng Manag (2016) [9]). Two numerical problems are presented to validate the proposed algorithm.