The relationship between goal programming and fuzzy programming

Mohamed, Rahma

doi:10.1016/s0165-0114(96)00100-5

Cited by 193 publications

(117 citation statements)

References 7 publications

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“…The general form of a multi-objective fuzzy programming model with fuzzy both objectives and constraints can formulated as (Mohamed, 1997): …”

Section: Multi-objective Fuzzy Goal Programming (Mofgp)mentioning

confidence: 99%

“…It means that these inequalities are flexible and should be described imprecisely like "it should be basically greater than or equal to g k " or "basically smaller than or equal to", which can then be characterized by their membership functions by defining the lower or upper tolerance limits. The most popular used ( Mohamed, 1997) linear membership functions to solve (1), for each goal is as:…”

Section: Multi-objective Fuzzy Goal Programming (Mofgp)mentioning

confidence: 99%

“…The basis of this approach is the fact that the maximum value of any membership function is 1, hence maximizing any of themis equivalent to making them as close as possible to 1 by minimizing its negative deviational variable from 1 (Mohamed, 1997). In this sense, by using the definitions of u 1k (z k (X)) and u 2k (z k (X)) and applying them to the conventional GP formulation, the problem (1) is converted to the following Fuzzy Goal Programming (FGP) program:…”

Section: Multi-objective Fuzzy Goal Programming (Mofgp)mentioning

confidence: 99%

“…To this, the lower or upper tolerance limit must be defined for each one and depend on the fuzzy restriction given to a fuzzy goal of the problem (Biswas and Pal, 2005;Hu et al, 2007;Li and Hu, 2009). In addition Zimmermann (1978), Mohamed (1997) has also discussed the relationship between goal programming and fuzzy programming and introduced another approach for solving FGP problems. In this approach, the membership functions transform into membership goals by assigning the highest degree (unity) as the aspiration level and introducing under and over-deviational variables to each of them.…”

Section: Introductionmentioning

confidence: 99%

“…The larger violation (or tolerance) of the goal indicates the less important of this goal. It is provable that every fuzzy linear program has an equivalent weighted linear goal program where the weights are the reciprocals of the admissible violation constants (Mohamed, 1997). The FGP approach has been extended by Sinha et al (1988) and Pal and Moitra (2003) to agricultural and crop planning problems.…”

Section: Introductionmentioning

confidence: 99%

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Application of Fuzzy Multi-Objective Programming in Optimization of Crop Production Planning

Fasakhodi¹

2015

Asian J. of Agricultural Research

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Planning for the optimal use of productive resources in agricultural systems leads to the conservation in addition to the promotion of farmers' socio-economical conditions. Being certain or precise in any decision making in agricultural planning is impossible. Fuzzy mathematical programming techniques, developed in recent decades, are the most appropriate and applicable approaches to include the uncertainty in crop planning and productive resources management. Using the multi-objective Fuzzy Goal Programming (FGP) approach, the farming system of a rural region located in the central of Iran has investigated in this study in order to identify the optimal cropping pattern and land use planning under uncertainty. For this purpose, several objectives like maximizing the area under cultivation, net return and employment opportunities and simultaneously the land, capital, monthly water and labor force requirements and availabilities, crop rotation and a crop lower bound production constraint imprecisely considered as fuzzy goals. The needed data gathered through fieldwork operations. In multi-objective programming context, as the results revealed, the constraints of the productive resources are more determinant in land allocation than the objective functions. To illustrate the precedence of the cited FGP model, the results were quantitatively compared with the existing situation and a crisp goal programming model containing the same objectives and constraints. The precedence mainly pertained to the goals of objective functions. The crop-mix in FGP pattern change achieved considerable conservation of water and capital resources and improvement of income generation of the agricultural system, with almost no variation in the cultivation area.Key words: Rural farming system, optimal cropping, uncertainty, fuzzy multi-objective programming INTRODUCTIONMathematical Programming (MP) has been a widely used tool for studying and analyzing agricultural systems. Beginning with the well-known Linear Programming (LP) model, operations research has supplied us with a great variety of theoretically sound models (Lara and Stancu-Minasian, 1999). Optimization procedures have been receiving much attention in agricultural economic research over several decades. The LP is a single objective optimization technique and most of the farm planning problems are multi-objective in nature. Crop area planning or agricultural planning arenas involve multiple, conflicting and non-commensurable criteria and a compromise satisfying decision is looking for. Issues of risk, resources conservation and sustainability, environmental quality and social aspects of farming systems are as important as economic efficiency. It is clearly impossible to develop a single objective that satisfies all

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“…The general form of a multi-objective fuzzy programming model with fuzzy both objectives and constraints can formulated as (Mohamed, 1997): …”

Section: Multi-objective Fuzzy Goal Programming (Mofgp)mentioning

confidence: 99%

Section: Multi-objective Fuzzy Goal Programming (Mofgp)mentioning

confidence: 99%

Section: Multi-objective Fuzzy Goal Programming (Mofgp)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Application of Fuzzy Multi-Objective Programming in Optimization of Crop Production Planning

Fasakhodi¹

2015

Asian J. of Agricultural Research

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Dynamic Investment Strategy Toward Emissions Reduction and Energy Conservation of Coal Mining

2021

Innovative Approaches Towards Ecological Coal Mining and Utilization

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A fuzzy goal programming procedure for solving quadratic bilevel programming problems

Pal

Moitra

2003

Int. J. Intell. Syst.

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This article presents a fuzzy goal programming (FGP) procedure for solving quadratic bilevel programming problems (QBLPP). In the proposed approach, the membership functions for the defined fuzzy objective goals of the decision makers (DM) at both the levels are developed first. Then, a quadratic programming model is formulated by using the notion of distance function minimizing the degree of regret to satisfaction of both DMs. At the first phase of the solution process, the quadratic programming model is transformed into an equivalent nonlinear goal programming (NLGP) model to maximize the membership value of each of the fuzzy objective goals on the extent possible on the basis of their priorities in the decision context. Then, at the second phase, the concept of linear approximation technique in goal programming is introduced for measuring the degree of satisfaction of the DMs at both the levels by arriving at a compromised decision regarding the optimality of two different sets of decision variables controlled separately by each of them. A numerical example is provided to illustrate the proposed approach.

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The relationship between goal programming and fuzzy programming

Cited by 193 publications

References 7 publications

Application of Fuzzy Multi-Objective Programming in Optimization of Crop Production Planning

Application of Fuzzy Multi-Objective Programming in Optimization of Crop Production Planning

Dynamic Investment Strategy Toward Emissions Reduction and Energy Conservation of Coal Mining

A fuzzy goal programming procedure for solving quadratic bilevel programming problems

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