Intuitionistic Fuzzy Programming Technique to Solve Multi- Objective Transportation Problem

This paper presents an explanation of the multi-objective-transportation problem (MOTP) via Fuzzy programming algorithm and the goods is to be transported from origin to destination. The time and cost of transportation from origin i to destination j were recorded. Here we-have considered MOTP with-intuitionistic fuzzy numbers and completed the problem in both ways. Therefore, the optimal compromise solution will remain same both the exponential and linear membership function. For the solution the membership functions are used for such a problem. LINDO statistical-software was used in the present facts analysis and is completed in two stages

NEUTROSOPHIC MULTI-OBJECTIVE LINEAR PROGRAMMING

For modeling imprecise and indeterminate data for multi-objective decision making, two different methods: neutrosophic multi-objective linear/non-linear programming neutrosophic goal programming, which have been very recently proposed in the literatuire. In many economic problems, the well-known probabilities or fuzzy solutions procedures are not suitable because they cannot deal the situation when indeterminacy inherently involves in the problem. In this case we propose a new concept in optimization problem under uncertainty and indeterminacy. It is an extension of fuzzy and intuitionistic fuzzy optimization in which the degrees of indeterminacy and falsity (rejection) of objectives and constraints are simultaneously considered together with the degrees of truth membership (satisfaction/acceptance). The drawbacks of the existing neutrosophic optimization models have been presented and new framework of multi-objective optimization in neutrosophic environment has been proposed. The essence of the proposed approach is that it is capable of dealing with indeterminacy and falsity simultaneously

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 (α, β)-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.Portuguese Foundation for Science and Technology ("FCT-Fundacao para a Ciencia e a Tecnologia"), through the CIDMA-Center for Research and Development in Mathematics and Applications UID/MAT/ 04106/2019Spanish Ministry of Economy and Competitiveness, FEDER funds from the European Union TIN2014-55024-P TIN2017-86647-

Reverse Logistics Network Design with a 3-Phase Interactive Intuitionistic Fuzzy Goal Programming Approach: A Case Study of Covid-19 in Pathum Thani, Thailand

During outbreaks, a vast quantity of Infected Medical Waste (IMW) can be substantially generated in a short period, which poses a massive risk to medical personnel and surrounding communities. This study proposes an Intuitionistic Fuzzy Multi-Objective Multi-Period Mixed-Integer Linear Programming (IFMOMILP) model for effective IMW management in outbreaks under uncertainty, considering financial and risk factors subject to a priority from Decision Makers (DMs). The primary emphasis is on determining the optimal locations and capacity levels for temporary facilities, including temporary storage and treatment centers, as well as the optimal transportation routes. A 3-phase interactive Intuitionistic Fuzzy Goal Programming (i-IFGP) approach is developed to solve this IFMOMILP model. First, the Jiménez approach is applied to handle the uncertainties. Then, the problem is solved by Intuitionistic Fuzzy Goal Programming (IFGP). An actual case study of the COVID-19 outbreak in Pathum Thani province in Thailand was carried out to demonstrate the effectiveness of the proposed approach. The proposed approach yields solutions with varying feasibility degrees and scaling factors, providing alternatives for DMs. Then, the score function is utilized to imply DMs’ satisfaction with the outcomes, which is a concrete measure since it can reflect the intention of the DMs

An integrated model for solving production planning and production capacity problems using an improved fuzzy model for multiple linear programming according to Angelov's method

Decision making has become a part of our everyday lives. The main apprehension is that almost all decision difficulties include certain criteria, which usually can be multiple or conflicting. Certainly, the production planning and production capacity development includes several parameters uncertainty such as fuzzy resource capacity, fuzzy demand and fuzzy production rate. This situation makes decision maker challenging to describe the objective crisply and at the end the real optimum solution cannot attained correctly. The Fuzzy model for multi-objective linear programming should be an suitable approach for dealing with the production planning and production capacity (PP& PC) problems. The PP& PC problem based on the fuzzy environment becomes even more sophisticated as decision makers try to consider multi-objectives, Therefore, this study attempts to propose a novel scheme which is capable of dealing with these obstacles in PP& PC problem. Intuitionistic Fuzzy Optimization (1FO) by implementing the optimization problem in an Intuitionistic Fuzzy Set (IFS) environment and considered the degrees of rejection of objective(s) and of constraints as the complement of satisfaction degrees. The aim of the research is to propose a new method capable of dealing with these obstacles in the PP & PC problem. It takes into account uncertainty and makes trade-offs between multiple conflicting goals simultaneously. To verify the validity of the proposed method, a case study of the fuzzy multi-objective model of the PP&PC is used. This research takes into account uncertainty and makes a comparison between multiple conflicting goals at the same time. Therefore, this study attempts to propose a new scheme which is the modified Angelov’s approach

An Efficient Ranking Technique for Intuitionistic Fuzzy Numbers with Its Application in Chance Constrained Bilevel Programming

The aim of this paper is to develop a new ranking technique for intuitionistic fuzzy numbers using the method of defuzzification based on probability density function of the corresponding membership function, as well as the complement of nonmembership function. Using the proposed ranking technique a methodology for solving linear bilevel fuzzy stochastic programming problem involving normal intuitionistic fuzzy numbers is developed. In the solution process each objective is solved independently to set the individual goal value of the objectives of the decision makers and thereby constructing fuzzy membership goal of the objectives of each decision maker. Finally, a fuzzy goal programming approach is considered to achieve the highest membership degree to the extent possible of each of the membership goals of the decision makers in the decision making context. Illustrative numerical examples are provided to demonstrate the applicability of the proposed methodology and the achieved results are compared with existing techniques

Soft Computing

Soft computing is used where a complex problem is not adequately specified for the use of conventional math and computer techniques. Soft computing has numerous real-world applications in domestic, commercial and industrial situations. This book elaborates on the most recent applications in various fields of engineering

Matrix Game with Payoffs Represented by Triangular Dual Hesitant Fuzzy Numbers

Matrix Game with Payoffs RepresentedDue to the complexity of information or the inaccuracy of decision-makers’ cognition, it is difficult for experts to quantify the information accurately in the decision-making process. However, the integration of the fuzzy set and game theory provides a way to help decision makers solve the problem. This research aims to develop a methodology for solving matrix game with payoffs represented by triangular dual hesitant fuzzy numbers (TDHFNs). First, the definition of TDHFNs with their cut sets are presented. The inequality relations between two TDHFNs are also introduced. Second, the matrix game with payoffs represented by TDHFNs is investigated. Moreover, two TDHFNs programming models are transformed into two linear programming models to obtain the numerical solution of the proposed fuzzy matrix game. Furthermore, a case study is given to to illustrate the efficiency and applicability of the proposed methodology. Our results also demonstrate the advantage of the proposed concept of TDHFNs