Fuzzy goal programming model: an overview of the current state‐of‐the art

Abstract

The standard Goal Programming (GP) model considers the aspiration levels (goals) as precise and deterministic. However, in practice, there are many decision-making situations where the decision-maker is not able to establish the goal values precisely. The goals fuzziness is more related to the nature of the objectives involved in the decisionmaking situation. The Fuzzy Goal Programming (FGP) Model has been developed in the earliest of the 80s to deal with such situations. The concept of membership functions, based on fuzzy sets theory, has been used for modelling the goals fuzziness in the GP. The aim of this paper is to give an overview of the current state-of-the art regarding the FGP model.

A model for solving incompatible fuzzy goal programming: an application to portfolio selection

“…Each one of the fuzzy goals (or constraints) of an FGP model can be represented by a fuzzy set whose membership function provides the drop in satisfaction from a situation of total satisfaction, which could be the aspiration level (where the membership function takes the value 1), to a state of total dissatisfaction, which could be the tolerance threshold or (where the membership function takes the value 0) (Delgado et al., ). One of the most common assumptions in theory (Zimmermann, ; Narasimhan, ; Hannan, ; Aouni et al., ) and applications (Rommelfanger, ; Arenas‐Parra et al., ; Mekidiche et al., ; Aouni et al., ) is that this drop can be represented by a linear function. As Verdegay () states: “It was shown that possible further changes of those membership functions do not affect the former optimal solution, … This sensitivity analysis … shows the convenience of using linear functions instead of other more complicated ones.” Therefore, for the sake of simplicity and due to the relevance of the linear case in the literature (see Jiménez et al., ; Chang, ; Huang, , among others), we focus our approach on this type of membership functions.…”

“…GP has become one of the most popular techniques within the field of multiple criteria decision making (Caballero et al., ; Tamiz et al. ; Jones and Tamiz, , ; Aouni et al., ) and is one of the most widely used methods due to its applicability to real problems (see, e.g., Blancas et al., ; Marcenaro‐Gutiérrez et al., ; Voces et al., ; Buyukozkan and Berkol, ; Bilbao‐Terol et al., ; Zopounidis and Doumpos, ; Díaz‐Balteiro and Romero, ). GP is based on the satisficing solution concept, introduced by the Nobel Prize in Economics, Herbert Simon ().…”

“…GP has become one of the most popular techniques within the field of multiple criteria decision making (Caballero et al, 1997;Tamiz et al 1998;Tamiz, 2002, 2010;Aouni et al, 2009) and is one of the most widely used methods due to its applicability to real problems (see, e.g., Blancas et al, 2010;Marcenaro-Gutiérrez et al, 2010;Voces et al, 2010;Buyukozkan and Berkol, 2011;Bilbao-Terol et al, 2012;Zopounidis and Doumpos, 2013;Díaz-Balteiro and Romero, 2016 is based on the satisficing solution concept, introduced by the Nobel Prize in Economics, Herbert Simon (1955). Simon conjectured that in complex decisional problems with conflicting objectives where the decision maker (DM) is unable to optimize all objectives simultaneously, more interest exists for reaching aspiration levels.…”

Solving a bi-objective vehicle routing problem under uncertainty by a revised multi-choice goal programming approach

“…The aspiration level of each goal is determined by the DMs. The comprehensive review of the GP method can be found in Aouni et al (2009). The linear and non-linear GP can be solved using well-developed software, such as LINGO software or meta-heuristics methods (e.g.…”

Multi-criteria decision analysis with goal programming in engineering, management and social sciences: a state-of-the art review

“…, Aouni et al (2009) and Li (2012) present details on FGP and its variants. For detailed mathematical treatment and solution we refer the readers to several interesting books and papers on GP models by Saber and Ravindran (1993), Schniederjans (1995), Jones and Tamiz, (2010) and review articles by Lin (1980), Zanakis and Gupta (1985), Romero (1986), Tamiz et.al., (1995Tamiz et.al., ( , 1998, Aouni and Kettani (2001), Jones and Tamiz (2002), Aouni et al, (2009aAouni et al, ( , 2009b.…”