Role of Distance Metric in Goal Geometric Programming Problem (G^2 P^2) Under Imprecise Environment

The objective of this article is to tie a knot between distance measure and fuzzy and intuitionistic fuzzy optimization through goal programming. Firstly, a distance measure for an intuitionistic fuzzy number is developed, and then it is implemented into an intuitionistic fuzzy nonlinear goal programming. Then using some conditions, the distance measure of intuitionistic fuzzy number is converted into distance measure of fuzzy number and a comparative study using a numerical example is shown for highest applicability of distance measure based intuitionistic fuzzy goal programming than distance measure based fuzzy goal programming.

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Fuzzy Goal Programming with an Imprecise Intuitionistic Fuzzy Preference Relations

Symmetry ◽

10.3390/sym12091548 ◽

2020 ◽

Vol 12 (9) ◽

pp. 1548

Author(s):

Abdul Razzaq Abdul Ghaffar ◽

Md. Gulzarul Hasan ◽

Zubair Ashraf ◽

Mohammad Faisal Khan

Keyword(s):

Goal Programming ◽

Distance Measure ◽

Optimization Problems ◽

Fuzzy Goal Programming ◽

Preference Relations ◽

Intuitionistic Fuzzy ◽

Fuzzy Preference Relations ◽

Fuzzy Goals ◽

Fuzzy Goal ◽

Fuzzy Preference

Fuzzy goal programming (FGP) is applied to solve fuzzy multi-objective optimization problems. In FGP, the weights are associated with fuzzy goals for the preference among them. However, the hierarchy within the fuzzy goals depends on several uncertain criteria, decided by experts, so the preference relations are not always easy to associate with weight. Therefore, the preference relations are provided by the decision-makers in terms of linguistic relationships, i.e., goal A is slightly or moderately or significantly more important than goal B. Due to the vagueness and ambiguity associated with the linguistic preference relations, intuitionistic fuzzy sets (IFSs) are most efficient and suitable to handle them. Thus, in this paper, a new fuzzy goal programming with intuitionistic fuzzy preference relations (FGP-IFPR) approach is proposed. In the proposed FGP-IFPR model, an achievement function has been developed via the convex combination of the sum of individual grades of fuzzy objectives and amount of the score function of IFPRs among the fuzzy goals. As an extension, we presented the linear and non-linear, namely, exponential and hyperbolic functions for the intuitionistic fuzzy preference relations (IFPRs). A study has been made to compare and analyze the three FGP-IFPR models with intuitionistic fuzzy linear, exponential, and hyperbolic membership and non-membership functions. For solving all three FGP-IFPR models, the solution approach is developed that established the corresponding crisp formulations, and the optimal solution are obtained. The validations of the proposed FGP-IFPR models have been presented with an experimental investigation of a numerical problem and a banking financial statement problem. A newly developed distance measure is applied to compare the efficiency of proposed models. The minimum value of the distance function represents a better and efficient model. Finally, it has been found that for the first illustrative problem considered, the exponential FGP-IFPR model performs best, whereas for the second problem, the hyperbolic FGP-IFPR model performs best and the linear FGP-IFPR model shows worst in both cases.

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Optimasi Kebutuhan Kendaraan Pengangkut Sampah Menggunakan Model Fuzzy Goal Programming

Jurnal Matematika ◽

10.24843/jmat.2017.v07.i02.p92 ◽

2018 ◽

Vol 7 (2) ◽

pp. 119

Author(s):

Eka Susanti ◽

Oki Dwipurwani ◽

Evy Yuliza

Keyword(s):

Goal Programming ◽

Fuzzy Number ◽

Triangular Fuzzy Number ◽

Fuzzy Goal Programming ◽

Dump Truck ◽

Fuzzy Goal

Penelitian ini bertujuan untuk menentukan jumlah optimal kendaraan pengangkut sampah menggunakan model goal programming (GP) dengan pendekatan fuzzy. Jumlah minimum sisa sampah yang tidak terangkut dan muatan kosong kendaraan sebagai goal. Jumlah sampah yang harus diangkut, jumlah ketersediaan kendaraan pengangkut, dan jumlah area layanan dinyatakan dalam bentuk Triangular Fuzzy Number (TFN) dan merupakan kendala pada model fuzzy goal programming (FGP). Model FGP diubah ke bentuk deterministik menggunakan teknik program fuzzy. Dipertimbangkan dua jenis kendaraaan yaitu dumb truck dan armroll. Diberikan contoh perhitungan untuk kecamatan Kalidoni kota Palembang. TFN jumlah sampah adalah (58100, 58150, 58300), TFN jumlah dump truck (190,190,193), TFN jumlah armroll (21,21,22), TFN jumlah minimal wilayah layanan (4,5,5). Diperoleh solusi optimal dengan derajat keanggotaan 0,8 untuk mengangkut sampah sebanyak 58150 kg diperlukan kendaraan jenis dump truck sebanyak 1 kendaraan dan jenis armroll sebanyak 18 kendaraan. Terdapat sisa sampah yang tidak terangkut sebanyak 140 kg.

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