Fuzzy optimal solution of fully fuzzy linear programming problems using ranking function

Kumar, Amit; Kaur, Jagdeep

doi:10.3233/ifs-120742

Cited by 31 publications

(5 citation statements)

References 25 publications

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“…Khan et al [22] studied a fully FLPP where parameters and decision variables were taken to be triangular FNs and proposed a method by making use of some ranking function. Ozkok et al [8] extended the method of Kumar and Kaur [3] to solve fully FLPP with all types of constraints having parameters as unrestricted and decision variables as non-negative triangular FNs.…”

Section: Literature Review 21 Fuzzy Lppmentioning

confidence: 99%

Developing solution algorithm for LR-type fully interval-valued intuitionistic fuzzy linear programming problems using lexicographic-ranking method

Malik¹,

Gupta²

2022

Preprint

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In this article, a new concept of -type interval-valued intuitionistic fuzzy numbers ( -type IV-IFN) has been introduced. The theory has also been enriched by demonstrating diagrammatic representations of -type IVIFNs and establishing arithmetic operations among these fuzzy numbers. The total order properties of lexicographic criteria have been used for ranking -type IVIFNs. Further, a linear programming problem having both equality as well as inequality type constraints with all the parameters as -type IVIFNs and unrestricted decision variables has been formulated. An algorithm to find a unique optimal solution to the problem using the lexicographic ranking method has been developed. In the proposed methodology, the given linear programming problem is converted to an equivalent mixed 0 -1 lexicographic non-linear programming problem. Various theorems have been proved to show the equivalence of the proposed problem and its different constructions. The model formulation, algorithm and discussed results have not only developed a new idea but also generalized various well-known related works existing in the literature. A numerical problem has also been exemplified to show the steps involved in the approach. Finally, a practical application in production planning is framed, solved and analyzed to establish the applicability of the study.

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Section: Literature Review 21 Fuzzy Lppmentioning

confidence: 99%

Developing solution algorithm for LR-type fully interval-valued intuitionistic fuzzy linear programming problems using lexicographic-ranking method

Malik¹,

Gupta²

2022

Preprint

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“…An example of this case is obtained from the journal "Solution of Fuzzy Transportation Problems with Triangular Fuzzy Numbers using Rangking Function"(source: Internasional Journal of Pure and Applied Mathematics tahun 2018 ) [7]. and the fuzzy request available at the destination are (25, 30, 35), (10,15,20), (5,15,20), (10,15,25).…”

Section: Case Example With Balanced Triangular Membershipmentioning

confidence: 99%

Analysis on ASM Method Perfomance in Solving Fuzzy Transportation Problems

Anggraini,

Sawaluddin

2022

J. of Maths Tech and Edu

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This study aims to show the performance of the ASM method on transportation problem. The transportation problem relates to the distribution of a product from several sources, with limited supply, to several destinations, with a certain demand, in order to obtain the minimum transportation costs. However, the amount of supply and demand cannot always be known with certainty and may change from time to time. In this paper, the coefficient of supply and demand uses fuzzy numbers and uses the ASM method to determine the optimal solution both to minimize costs and maximize profits. The result is that with the ASM method, the balanced transportation problem is always optimal, while the unbalanced transportation problem is not always optimal.

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“…In particular, fully fuzzy linear programming (FFLP) problems with triangular, trapezoidal and hexagonal fuzzy numbers have been considered by several authors. For instance, Kumar and Kaur [8] FFLP and Das et al [9] considered the trapezoidal FFLP. Recently, Tuffaha and Alrefaei [10] presented a polygonal FFLP which is a generalization of all the above FFLP.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy linear programming with the intuitionistic polygonal fuzzy numbers

Alrefaei,

Tuffaha

2024

IJECE

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In real world applications, data are subject to ambiguity due to several factors; fuzzy sets and fuzzy numbers propose a great tool to model such ambiguity. In case of hesitation, the complement of a membership value in fuzzy numbers can be different from the non-membership value, in which case we can model using intuitionistic fuzzy numbers as they provide flexibility by defining both a membership and a non-membership functions. In this article, we consider the intuitionistic fuzzy linear programming problem with intuitionistic polygonal fuzzy numbers, which is a generalization of the previous polygonal fuzzy numbers found in the literature. We present a modification of the simplex method that can be used to solve any general intuitionistic fuzzy linear programming problem after approximating the problem by an intuitionistic polygonal fuzzy number with n edges. This method is given in a simple tableau formulation, and then applied on numerical examples for clarity.

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Fuzzy optimal solution of fully fuzzy linear programming problems using ranking function

Cited by 31 publications

References 25 publications

Developing solution algorithm for LR-type fully interval-valued intuitionistic fuzzy linear programming problems using lexicographic-ranking method

Developing solution algorithm for LR-type fully interval-valued intuitionistic fuzzy linear programming problems using lexicographic-ranking method

Analysis on ASM Method Perfomance in Solving Fuzzy Transportation Problems

Fuzzy linear programming with the intuitionistic polygonal fuzzy numbers

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