Standard goal programming with fuzzy hierarchies: a sequential approach

Arenas-Parra, Mar; Bilbao-Terol, Amelia; Jiménez, Mariano

doi:10.1007/s00500-015-1644-2

Cited by 8 publications

(20 citation statements)

References 27 publications

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“…Before moving to the GP, we first go through the formulation of normalized function and membership functions of preference relations for linear as well as exponential case. To avoid biasedness towards goals with high and low aspiration levels, Arenas-Parra et al [35] used a normalized function corresponding to each objective. Let us assume that f k and f * k , k = 1, .…”

Section: Goal Programming Formulationmentioning

confidence: 99%

“…The preference relations are of asymmetric nature in importance of goals. After Aköz and Petrovic [16], the fuzzy preference relation was applied and extended by many authors, e.g., Cheng [19], Petrovic and Aköz [28], Torabi and Moghaddam [29], Khalili-Damghani and Sadi-Nezhad [30], Díaz-Madroñero et al [31], Sheikhalishahi and Torabi [32], Bilbao-Terol et al [33], Bilbao-Terol et al [34], Arenas-Parra et al [35] Hasan et al [36], and Hashmi et al [37]. Khalili-Damghani and Sadi-Nezhad [30], Khalili-Damghani et al [38] extended the work of Aköz and Petrovic [16]; they extended the linear membership function for three linguistic preference terms to ten statements.…”

Section: Introductionmentioning

confidence: 99%

“…Here, "FuzzyHierMax" denotes the fuzzy hierarchical maximization for achieving the satisfactory solution considering the preferences among the objectives. The proposed GP models are the extensions to existing models of Aköz and Petrovic [16], Arenas-Parra et al [35]. The preferences among the goals {…”

Section: Introductionmentioning

confidence: 99%

“…As per our knowledge, in existing literature, there is no GP model with proposed exponential membership function for relative preferences between the goals. In the proposed GP model, we take account of maximization of the minimum and the sum of achievements of goals using approaches from Arenas-Parra et al [35], Torabi and Hassini [47]. Hence, this work address the research gap, and helps the decision maker to plan more realistically by introducing exponential type preference relations.…”

Section: Introductionmentioning

confidence: 99%

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Goal Programming Models with Linear and Exponential Fuzzy Preference Relations

et al. 2020

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Goal programming (GP) is a powerful method to solve multi-objective programming problems. In GP the preferential weights are incorporated in different ways into the achievement function. The problem becomes more complicated if the preferences are imprecise in nature, for example ‘Goal A is slightly or moderately or significantly important than Goal B’. Considering such type of problems, this paper proposes standard goal programming models for multi-objective decision-making, where fuzzy linguistic preference relations are incorporated to model the relative importance of the goals. In the existing literature, only methods with linear preference relations are available. As per our knowledge, nonlinearity was not considered previously in preference relations. We formulated fuzzy preference relations as exponential membership functions. The grades or achievement function is described as an exponential membership function and is used for grading levels of preference toward uncertainty. A nonlinear membership function may lead to a better representation of the achievement level than a linear one. Our proposed models can be a useful tool for different types of real life applications, where exponential nonlinearity in goal preferences exists. Finally, a numerical example is presented and analyzed through multiple cases to validate and compare the proposed models. A distance measure function is also developed and used to compare proposed models. It is found that, for the numerical example, models with exponential membership functions perform better than models with linear membership functions. The proposed models will help decision makers analyze and plan real life problems more realistically.

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Section: Goal Programming Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Goal Programming Models with Linear and Exponential Fuzzy Preference Relations

et al. 2020

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“…The problem of fuzzy goal programming when the importance relation between the fuzzy goals is vague has initially been investigated by Aköz and Petrovic [1] and followed by Li and Hu [2] and Cheng [3]. A suggested sequential approach in fuzzy goal programming, when the importance hierarchy of the goals is imprecise, has been presented by Arenas-Parra et al [4]. In their article, the model of goal programming with fuzzy hierarchy (GPFH) is given as ( )…”

Section: Introductionmentioning

confidence: 99%

A Note on Standard Goal Programming with Fuzzy Hierarchies: A Sequential Approach

Iskander¹

2016

AJOR

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In the paper [Standard goal programming with fuzzy hierarchies: a sequential approach, Soft Computing, First online: 22 March 2015], it was assumed that the normalized deviations should lie between zero and one. In some cases, this assumption may not be valid. Therefore, additional constraints must be incorporated into the model to ensure that the normalized deviations should not exceed one. This modification is illustrated by the given numerical example.

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