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This paper presents the application of Neutrosophic Set Theory (NST) in solving Generalized Assig... more This paper presents the application of Neutrosophic Set Theory (NST) in solving Generalized Assignment Problem (GAP). GAP has been solved earlier under fuzzy environment. NST is a generalization of the concept of classical set, fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set. Elements of Neutrosophic set are characterized by a truth-membership function, falsity and also indeterminacy which is a more realistic way of expressing the parameters in real life problem. Here the elements of the cost matrix for the GAP are considered as neutrosophic elements which have not been considered earlier by any other author.
Assignment Problem (AP) is a very well-known and also useful decision making problem in real life... more Assignment Problem (AP) is a very well-known and also useful decision making problem in real life situations. It becomes more effective when different criteria are added. To solve Multi-Criteria Assignment Problem (MCAP), the different criteria have been considered as neutrosophic elements because Neutrosophic Set Theory (NST) is a generalization of the classical sets, conventional fuzzy sets, Intuitionistic Fuzzy Sets (IFS) and Interval Valued Fuzzy Sets (IVFS). In this paper two different methods have been proposed for solving MCAP.
To solve the problems of Engineering and Management Science Generalized Assignment Problem (GAP) ... more To solve the problems of Engineering and Management Science Generalized Assignment Problem (GAP) plays a very important role. The GAP is a classical example of a difficult combinatorial optimization problem that has received considerable attention over the years due to its widespread applications. In many instances it appears as a substructure in more complicated models, including routing problems, facility location models, knapsack problems, computer networking applications etc. Recently, Fuzzy Generalized Assignment Problem (FGAP) became very popular because in real life, data may not be known with certainty. So, to consider uncertainty in real life situations fuzzy data instead of crisp data is more advantageous. In this paper, cost for assigning the j-th job to the i-th person is taken as triangular fuzzy numbers. Further we have put a restriction on the total available cost which makes the problem more realistic and general. The problem is solved by modified Fuzzy Extremum Diff...
International Journal of Mathematics in Operational Research, 2019
Journal of Intelligent & Fuzzy Systems, 2017
The paper presents the solution of a multi objective multi-index generalized assignment problem u... more The paper presents the solution of a multi objective multi-index generalized assignment problem using Fuzzy Programming Technique which is a new concept. It emphasizes on minimization of the job cost and time at different sites where the jobs are being performed using different machines (medium). Multi objective assignment problem or multi objective generalized assignment problem have been solved in different ways by different mathematicians. But they have considered only two indices (jobs and alternatives). Here we have considered more than two indices and so it becomes a multi-index generalized assignment problem which makes it superior to the previous methods. This type of problem has not been solved earlier by our proposed method. Moreover in this paper Fuzzy Programming Technique has been used considering linear, exponential and hyperbolic (non-linear) membership functions for getting optimal solutions. Finally a real life application has been presented.
OPSEARCH, 2014
As a generalization of fuzzy set, Hesitant Fuzzy Set (HFS) is very useful to express people's hes... more As a generalization of fuzzy set, Hesitant Fuzzy Set (HFS) is very useful to express people's hesitancy in daily life. But there are some disadvantages in traditional HFS, as it expresses the membership degrees of an element to a given set only by several crisp numbers. In this paper, we extend the traditional HFS to Triangular Fuzzy Hesitant Fuzzy Set (TFHFS) in which the membership degree of an element to a given set is represented by several possible triangular fuzzy numbers. We have applied this TFHFS on solving Hesitant Fuzzy Generalized Assignment Problem (HFGAP). For this, we formulate the mathematical model of Generalized Assignment Problem (GAP) based on Triangular Fuzzy Hesitant Fuzzy Elements (TFHFEs) and with the help of well known TOPSIS method we have found the Relative Closeness Coefficient Matrix (RCCM). Using the above matrix as the initial data for a GAP in the minimization form we have solved the problem by Extremum Difference Method (EDM). To verify the result we have transformed the problem into LPP form and solved it by LINGO 9.0.
This paper presents the application of Neutrosophic Set Theory (NST) in solving Generalized Assig... more This paper presents the application of Neutrosophic Set Theory (NST) in solving Generalized Assignment Problem (GAP). GAP has been solved earlier under fuzzy environment. NST is a generalization of the concept of classical set, fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set. Elements of Neutrosophic set are characterized by a truth-membership function, falsity and also indeterminacy which is a more realistic way of expressing the parameters in real life problem. Here the elements of the cost matrix for the GAP are considered as neutrosophic elements which have not been considered earlier by any other author.
Assignment Problem (AP) is a very well-known and also useful decision making problem in real life... more Assignment Problem (AP) is a very well-known and also useful decision making problem in real life situations. It becomes more effective when different criteria are added. To solve Multi-Criteria Assignment Problem (MCAP), the different criteria have been considered as neutrosophic elements because Neutrosophic Set Theory (NST) is a generalization of the classical sets, conventional fuzzy sets, Intuitionistic Fuzzy Sets (IFS) and Interval Valued Fuzzy Sets (IVFS). In this paper two different methods have been proposed for solving MCAP.
To solve the problems of Engineering and Management Science Generalized Assignment Problem (GAP) ... more To solve the problems of Engineering and Management Science Generalized Assignment Problem (GAP) plays a very important role. The GAP is a classical example of a difficult combinatorial optimization problem that has received considerable attention over the years due to its widespread applications. In many instances it appears as a substructure in more complicated models, including routing problems, facility location models, knapsack problems, computer networking applications etc. Recently, Fuzzy Generalized Assignment Problem (FGAP) became very popular because in real life, data may not be known with certainty. So, to consider uncertainty in real life situations fuzzy data instead of crisp data is more advantageous. In this paper, cost for assigning the j-th job to the i-th person is taken as triangular fuzzy numbers. Further we have put a restriction on the total available cost which makes the problem more realistic and general. The problem is solved by modified Fuzzy Extremum Diff...
International Journal of Mathematics in Operational Research, 2019
Journal of Intelligent & Fuzzy Systems, 2017
The paper presents the solution of a multi objective multi-index generalized assignment problem u... more The paper presents the solution of a multi objective multi-index generalized assignment problem using Fuzzy Programming Technique which is a new concept. It emphasizes on minimization of the job cost and time at different sites where the jobs are being performed using different machines (medium). Multi objective assignment problem or multi objective generalized assignment problem have been solved in different ways by different mathematicians. But they have considered only two indices (jobs and alternatives). Here we have considered more than two indices and so it becomes a multi-index generalized assignment problem which makes it superior to the previous methods. This type of problem has not been solved earlier by our proposed method. Moreover in this paper Fuzzy Programming Technique has been used considering linear, exponential and hyperbolic (non-linear) membership functions for getting optimal solutions. Finally a real life application has been presented.
OPSEARCH, 2014
As a generalization of fuzzy set, Hesitant Fuzzy Set (HFS) is very useful to express people's hes... more As a generalization of fuzzy set, Hesitant Fuzzy Set (HFS) is very useful to express people's hesitancy in daily life. But there are some disadvantages in traditional HFS, as it expresses the membership degrees of an element to a given set only by several crisp numbers. In this paper, we extend the traditional HFS to Triangular Fuzzy Hesitant Fuzzy Set (TFHFS) in which the membership degree of an element to a given set is represented by several possible triangular fuzzy numbers. We have applied this TFHFS on solving Hesitant Fuzzy Generalized Assignment Problem (HFGAP). For this, we formulate the mathematical model of Generalized Assignment Problem (GAP) based on Triangular Fuzzy Hesitant Fuzzy Elements (TFHFEs) and with the help of well known TOPSIS method we have found the Relative Closeness Coefficient Matrix (RCCM). Using the above matrix as the initial data for a GAP in the minimization form we have solved the problem by Extremum Difference Method (EDM). To verify the result we have transformed the problem into LPP form and solved it by LINGO 9.0.