3 research outputs found
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
Lexicographic Methods for Fuzzy Linear Programming
Fuzzy Linear Programming (FLP) has addressed the increasing complexity of real-world
decision-making problems that arise in uncertain and ever-changing environments since its
introduction in the 1970s. Built upon the Fuzzy Sets theory and classical Linear Programming
(LP) theory, FLP encompasses an extensive area of theoretical research and algorithmic development.
Unlike classical LP, there is not a unique model for the FLP problem, since fuzziness can
appear in the model components in different ways. Hence, despite fifty years of research,
new formulations of FLP problems and solution methods are still being proposed. Among the
existing formulations, those using fuzzy numbers (FNs) as parameters and/or decision variables
for handling inexactness and vagueness in data have experienced a remarkable development in
recent years. Here, a long-standing issue has been how to deal with FN-valued objective functions
and with constraints whose left- and right-hand sides are FNs. The main objective of this paper is
to present an updated review of advances in this particular area. Consequently, the paper briefly
examines well-known models and methods for FLP, and expands on methods for fuzzy single- and
multi-objective LP that use lexicographic criteria for ranking FNs. A lexicographic approach to the
fuzzy linear assignment (FLA) problem is discussed in detail due to the theoretical and practical
relevance. For this case, computer codes are provided that can be used to reproduce results presented
in the paper and for practical applications. The paper demonstrates that FLP that is focused on
lexicographic methods is an active area with promising research lines and practical implications.Spanish Ministry of Economy and CompetitivenessEuropean Union (EU)
TIN2017-86647-
A Critical Analysis of a Tourist Trip Design Problem with Time-Dependent Recommendation Factors and Waiting Times
Data Availability Statement: Publicly available datasets were analyzed in this study. This data can
be found here: http://github.com/cporrasn/TTDP_TDRF_WT_NWT.git.Acknowledgments: C.P. has been supported by a scholarship from AUIP Association coordinated
with the Universidad de Granada. B.P.-C. was supported by the Erasmus+ programme of the
European Union. The authors are grateful to the editors and the anonymous reviewers for their
constructive comments and suggestions.The tourist trip design problem (TTDP) is a well-known extension of the orienteering
problem, where the objective is to obtain an itinerary of points of interest for a tourist that maximizes
his/her level of interest. In several situations, the interest of a point depends on when the point
is visited, and the tourist may delay the arrival to a point in order to get a higher interest. In this
paper, we present and discuss two variants of the TTDP with time-dependent recommendation
factors (TTDP-TDRF), which may or may not take into account waiting times in order to have a better
recommendation value. Using a mixed-integer linear programming solver, we provide solutions
to 27 real-world instances. Although reasonable at first sight, we observed that including waiting
times is not justified: in both cases (allowing or not waiting times) the quality of the solutions is
almost the same, and the use of waiting times led to a model with higher solving times. This fact
highlights the need to properly evaluate the benefits of making the problem model more complex
than is actually needed.Projects PID2020-112754GB-I0, MCIN/AEI/10.13039/501100011033FEDER/Junta de Andalucía, Consejería de Transformación Económica, Industria, Conocimiento
y Universidades/ Proyecto (B-TIC-640-UGR20