A flexible programming approach based on intuitionistic fuzzy optimization and geometric programming for solving multi-objective nonlinear programming problems

Jafarian, Ehsan; Razmi, Jafar; Baki, Mohammed Fazle

doi:10.1016/j.eswa.2017.10.030

Cited by 39 publications

(29 citation statements)

References 32 publications

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“…In their study, coefficients of objectives and constraints of the problem are assumed to be left and right-type intuitionistic fuzzy numbers (IFN) and reference functions are used to describe the levels of satisfaction and dissatisfaction. Recently Jafarian et al [9] proposed an effective solution algorithm for multi-objective nonlinear programming problems in an IFE resolving the limitations of the existing methods. Their model integrated IFS, interactive optimization and geometric programming to find a compromise solution that satisfies the conditions of intuitionistic fuzzy efficiency and Pareto-optimality.…”

Section: Introductionmentioning

confidence: 99%

http://pu.edu.pk/images/journal/maths/PDF/Paper_3_53_9_2021.pdf

2021

Punjab Univ. j. math.

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Decision-making is one of the contemporary issues in this modern era due to the interaction of risk and uncertainties in every aspect of the daily lives of human beings. Accordingly, solving practical optimization problems tends to be more challenging. The fundamental reason for this investigation is to explore an effective solution technique for multi-objective optimization problems (MOOPs) in an intuitionistic fuzzy environment (IFE) addressing the issue of determining proper violation parameters and tolerances to the objectives and constraints. The other significant characteristic of this study is the consideration of the decisionmaker’s perspective, namely, optimistic, pessimistic and mixed views in the solution procedure. In the proposed method, compared to the existing study, the required number of iterations and stages are considerably reduced in solving intuitionistic fuzzy multi-objective optimization problems (IFMOOPs). Hence it has imperative advantages in solving complex real-world problems without much difficulty. One problem is solved to demonstrate the competency of the planned approach. A comparative analysis is also undertaken to ascertain the efficiency of the technique.

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Section: Introductionmentioning

confidence: 99%

http://pu.edu.pk/images/journal/maths/PDF/Paper_3_53_9_2021.pdf

2021

Punjab Univ. j. math.

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“…Rani et al [17] presented a model for solving the non‐linear optimisation model based on IFNs. Jafariana et al [18] proposed a flexible programming approach for solving multi‐objective non‐linear programming problems in intuitionistic fuzzy environment. Recently, Garai et al [19] considered the chance‐operator techniques to solve the multi‐item inventory models.…”

Section: Introductionmentioning

confidence: 99%

Multi‐objective linear fractional inventory model with possibility and necessity constraints under generalised intuitionistic fuzzy set environment

Garai¹,

Garg

2019

CAAI Transactions on Intelligence Technology

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“…After that, many authors worked on fuzzy non-linear programming and fuzzy GP problems to obtain an optimal solution with fewer errors and shortages, in line with the different types of fuzzy numbers [22][23][24]. Jafarian et al [25] proposed a novel method to support the process of solving multi-objective nonlinear programming problems, which are subjected to strict or flexible constraints. The concept of intuitionistic fuzzy sets is integrated into the solving procedure and continuously interacts with the decision maker.…”

Section: Introductionmentioning

confidence: 99%

A New Method to Optimize the Satisfaction Level of the Decision Maker in Fuzzy Geometric Programming Problems

2019

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Geometric programming problems are well-known in mathematical modeling. They are broadly used in diverse practical fields that are contemplated through an appropriate methodology. In this paper, a multi-parametric vector α is proposed for approaching the highest decision maker satisfaction. Hitherto, the simple parameter α , which has a scalar role, has been considered in the problem. The parameter α is a vector whose range is within the region of the satisfaction area. Conventionally, it is assumed that the decision maker is sure about the parameters, but, in reality, it is mostly hesitant about them, so the parameters are presented in fuzzy numbers. In this method, the decision maker can attain different satisfaction levels in each constraint, and even full satisfaction can be reached in some constraints. The goal is to find the highest satisfaction degree to maintain an optimal solution. Moreover, the objective function is turned into a constraint, i.e., one more dimension is added to n-dimensional multi-parametric α . Thus, the fuzzy geometric programming problem under this multi-parametric vector α ∈ ( 0 , 1 ] n + 1 gives a maximum satisfaction level to the decision maker. A numerical example is presented to illustrate the proposed method and the superiority of this multi-parametric α over the simple one.

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A flexible programming approach based on intuitionistic fuzzy optimization and geometric programming for solving multi-objective nonlinear programming problems

Cited by 39 publications

References 32 publications

http://pu.edu.pk/images/journal/maths/PDF/Paper_3_53_9_2021.pdf

http://pu.edu.pk/images/journal/maths/PDF/Paper_3_53_9_2021.pdf

Multi‐objective linear fractional inventory model with possibility and necessity constraints under generalised intuitionistic fuzzy set environment

A New Method to Optimize the Satisfaction Level of the Decision Maker in Fuzzy Geometric Programming Problems

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