Solving P - Norm Intuitionistic Fuzzy Programming Problem

In this paper, notion of p - norm generalized trapezoidal intuitionistic fuzzy numbers is introduced. A new ranking method is introduced for p - norm generalized trapezoidal intuitionistic fuzzy numbers. Also we consider linear programming problem in intuitionistic fuzzy environment. In this problem, all the coefficients and variables are represented by p - norm generalized trapezoidal intuitionistic fuzzy numbers. To overcome the limitations of the existing methods, a new method is proposed to compute the intuitionistic fuzzy optimal solution for intuitionistic fuzzy linear programming problem. An illustrative numerical example is solved to demonstrate the efficiency of the proposed approach.Comment: some erro

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 epsilon-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.MCIN/AEI PID2020-112754GB-I00FEDER/Junta de Andalucia-Consejeria de Transformacion Economica, Industria, Conocimiento y Universidades/Proyecto B-TIC-640-UGR2

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

A New Approach to Solve Intuitionistic Fuzzy Linear Programming Problems with Symmetric Trapezoidal Intuitionistic Fuzzy Numbers

Parvathi & Malathi (Intuitionistic fuzzy simplex method, International Journal of Computer Applications, 48, 39-48, 2012) proposed an intuitionistic fuzzy simplex algorithm to solve Intuitionistic Fuzzy Linear Programming Problems (IFLPPs) with Symmetric Trapezoidal Intuitionistic Fuzzy Numbers (STIFNs) by using a special ranking function and used the linearity property to obtain the desired results. In this paper, it is proved that the linearity property, used by authors, is not satisfied for given ranking function. So, to overcome this drawback, a new method is proposed to solve the same type of intuitionistic fuzzy linear programming problems. Keywords: Intuitionistic fuzzy linear programming problems, Symmetric trapezoidal intuitionistic fuzzy numbers, Ranking function

Sustainability performance assessment with intuitionistic fuzzy composite metrics and its application to the motor industry

The performance assessment of companies in terms of sustainability requires to find a balance between multiple and possibly conflicting criteria. We here rely on composite metrics to rank a set of companies within an industry considering environmental, social and corporate governance criteria. To this end, we connect intuitionistic fuzzy sets and composite programming to propose novel composite metrics. These metrics allow to integrate important environmental, social and governance principles with the gradual membership functions of fuzzy set theory. The main result of this paper is a sustainability assessment method to rank companies within a given industry. In addition to consider multiple objectives, this method integrates two important social principles such as maximum utility and fairness. A real-world example is provided to describe the application of our sustainability assessment method within the motor industry. A further contribution of this paper is a multicriteria generalization of the concept of magnitude of a fuzzy number

Arithmetic Operations on Intuitionistic Hexagonal Fuzzy Numbers Using ? Cut

Presently, the fuzzy set theory has been also developed in a large extent and different variations and simplification. This paper focuses on alpha cuts in intuitionistic hexagonal fuzzy numbers by assuming different alpha values without affecting its originality. We have proposed a new arithmetic operation on alpha - cuts of hexagonal intuitionistic fuzzy numbers. Numerical examples are done to show the e?ciency of the study

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