A fascinating extension of Pawlak rough set theory to handle uncertainty is multigranulation roug... more A fascinating extension of Pawlak rough set theory to handle uncertainty is multigranulation roughness, which has been researched by several researchers over dual universes. In light of this, we proposed a novel optimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes and established two types of approximations of a fuzzy set with respect to forsets and aftersets of the finite number of soft binary relations in this article. We obtain two sets of fuzzy soft sets in this way, referred to as the lower approximation and upper approximation with respect to the aftersets and the foresets, respectively. Next, we look into some of the lower and higher approximations of the newly multigranulation rough set model's algebraic properties. Both the roughness and accuracy measurements were defined. In order to show our suggested model, we first develop a decision-making algorithm. Then, we give an example from a variety of applications.
The rough set model for dual universes and multi granulation over dual universes is an interestin... more The rough set model for dual universes and multi granulation over dual universes is an interesting generalization of the Pawlak rough set model. In this paper, we present a pessimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes. Firstly, we approximate fuzzy set w.r.t aftersets and foresets of the finite number of soft binary relations. As a result, we obtained two sets of fuzzy soft sets known as the pessimistic lower approximation of a fuzzy set and the pessimistic upper approximation of a fuzzy set—the w.r.t aftersets and the w.r.t foresets. The pessimistic lower and pessimistic upper approximations of the newly proposed multigranulation rough set model are then investigated for several interesting properties. This article also addresses accuracy measures and measures of roughness. Finally, we give a decision-making algorithm as well as examples from the perspective of application.
Introduction/purpose: The paper presents the DIBR-FMARCOS model of multi-criteria decision-making... more Introduction/purpose: The paper presents the DIBR-FMARCOS model of multi-criteria decision-making for defining a location for placing a bridge over an obstacle using a heavy mechanized bridge (TMM-3). After the application of the proposed model, the sensitivity analysis of the output results was performed and it was concluded that the model is stable, i.e. that the model gives consistent results and that its application is possible in real situations. Methods: The DIBR method was used to determine the weight coefficients of the criteria, while the ranking of alternatives was performed by the FuzzyMARCOS method. Results: The application of this model has led to the selection of the location for placing a bridge from the TMM-3 set, based on the defined criteria. After applying the proposed model, the sensitivity analysis of the output results was performed and the consistency of the output results of the method was proven. Conclusion: Finally, it was concluded that the proposed model ...
The original rough set model, developed by Pawlak depends on a single equivalence relation. Qian ... more The original rough set model, developed by Pawlak depends on a single equivalence relation. Qian et al, extended this model and defined multigranulation rough sets by using finite number of equivalence relations. This model provide new direction to the research. Recently, Shabir et al. proposed a rough set model which depends on a soft relation from an universe V to an universe W . In this paper we are present multigranulation roughness based on soft relations. Firstly we approximate a non-empty subset with respect to aftersets and foresets of finite number of soft binary relations. In this way we get two sets of soft sets called the lower approximation and upper approximation with respect to aftersets and with respect to foresets. Then we investigate some properties of lower and upper approximations of the new multigranulation rough set model. It can be found that the Pawlak rough set model, Qian et al. multigranulation rough set model, Shabir et al. rough set model are special cas...
A multigranulation rough set over two universes delivers a unique perspective on the combination ... more A multigranulation rough set over two universes delivers a unique perspective on the combination of multigranulation information. This paper presents the pessimistic multignualtion rough set over dual universes based on soft binary relations. Firstly, a new pessimistic multigranualtion rough set over dual universes based on two soft binary relations has been developed, and their properties are derived. Then we extend this idea and present pessimistic multigranulation roughness over dual universes based on the finite number of soft binary relations. Finally, we present an example to illustrate our proposed multigranualtion rough set model.
A fascinating extension of Pawlak rough set theory to handle uncertainty is multigranulation roug... more A fascinating extension of Pawlak rough set theory to handle uncertainty is multigranulation roughness, which has been researched by several researchers over dual universes. In light of this, we proposed a novel optimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes and established two types of approximations of a fuzzy set with respect to forsets and aftersets of the finite number of soft binary relations in this article. We obtain two sets of fuzzy soft sets in this way, referred to as the lower approximation and upper approximation with respect to the aftersets and the foresets, respectively. Next, we look into some of the lower and higher approximations of the newly multigranulation rough set model's algebraic properties. Both the roughness and accuracy measurements were defined. In order to show our suggested model, we first develop a decision-making algorithm. Then, we give an example from a variety of applications.
The rough set model for dual universes and multi granulation over dual universes is an interestin... more The rough set model for dual universes and multi granulation over dual universes is an interesting generalization of the Pawlak rough set model. In this paper, we present a pessimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes. Firstly, we approximate fuzzy set w.r.t aftersets and foresets of the finite number of soft binary relations. As a result, we obtained two sets of fuzzy soft sets known as the pessimistic lower approximation of a fuzzy set and the pessimistic upper approximation of a fuzzy set—the w.r.t aftersets and the w.r.t foresets. The pessimistic lower and pessimistic upper approximations of the newly proposed multigranulation rough set model are then investigated for several interesting properties. This article also addresses accuracy measures and measures of roughness. Finally, we give a decision-making algorithm as well as examples from the perspective of application.
Introduction/purpose: The paper presents the DIBR-FMARCOS model of multi-criteria decision-making... more Introduction/purpose: The paper presents the DIBR-FMARCOS model of multi-criteria decision-making for defining a location for placing a bridge over an obstacle using a heavy mechanized bridge (TMM-3). After the application of the proposed model, the sensitivity analysis of the output results was performed and it was concluded that the model is stable, i.e. that the model gives consistent results and that its application is possible in real situations. Methods: The DIBR method was used to determine the weight coefficients of the criteria, while the ranking of alternatives was performed by the FuzzyMARCOS method. Results: The application of this model has led to the selection of the location for placing a bridge from the TMM-3 set, based on the defined criteria. After applying the proposed model, the sensitivity analysis of the output results was performed and the consistency of the output results of the method was proven. Conclusion: Finally, it was concluded that the proposed model ...
The original rough set model, developed by Pawlak depends on a single equivalence relation. Qian ... more The original rough set model, developed by Pawlak depends on a single equivalence relation. Qian et al, extended this model and defined multigranulation rough sets by using finite number of equivalence relations. This model provide new direction to the research. Recently, Shabir et al. proposed a rough set model which depends on a soft relation from an universe V to an universe W . In this paper we are present multigranulation roughness based on soft relations. Firstly we approximate a non-empty subset with respect to aftersets and foresets of finite number of soft binary relations. In this way we get two sets of soft sets called the lower approximation and upper approximation with respect to aftersets and with respect to foresets. Then we investigate some properties of lower and upper approximations of the new multigranulation rough set model. It can be found that the Pawlak rough set model, Qian et al. multigranulation rough set model, Shabir et al. rough set model are special cas...
A multigranulation rough set over two universes delivers a unique perspective on the combination ... more A multigranulation rough set over two universes delivers a unique perspective on the combination of multigranulation information. This paper presents the pessimistic multignualtion rough set over dual universes based on soft binary relations. Firstly, a new pessimistic multigranualtion rough set over dual universes based on two soft binary relations has been developed, and their properties are derived. Then we extend this idea and present pessimistic multigranulation roughness over dual universes based on the finite number of soft binary relations. Finally, we present an example to illustrate our proposed multigranualtion rough set model.
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