In this paper, the concept of intension is used to introduce two types of ordering relations base... more In this paper, the concept of intension is used to introduce two types of ordering relations based on information that generates a cover for the universal set. These types of ordering relations are distinct from the well-known ordering relation based on set inclusion. For these ordering relations, we consider the algebraic structures that arise in various types of covers. We
In this paper, the counterparts of generalized open (g-open) and generalized closed (g-closed) se... more In this paper, the counterparts of generalized open (g-open) and generalized closed (g-closed) sets for ditopological texture spaces are introduced and some of their characterizations are obtained. Some characterizations are presented for generalized bicontinuous difunctions. Also, we introduce new notions of compactness and stability in ditopological texture spaces based on the notion of g-open and g-closed sets. Finally, as an application of g-open and g-closed sets, we generalize the subsystem based denition of rough set theory by using new subsystem, called generalized open sets to dene new types of lower and upper approximation operators, called g-lower and g-upper approximations. These decrease the upper approximation and increase the lower approximation and hence increase the accuracy. Properties of these approximations are studied. An example of multi-valued information systems are given
Background: In this work, we recall the concepts of multiset and multi topology. Then, we will in... more Background: In this work, we recall the concepts of multiset and multi topology. Then, we will introduce separatedness and connectedness on multi topological spaces and give basic definitions and theorems about it. Also, by using - open mset we study the concept of -separated msets. With this concept, we study the notion of -connected multiset and we give some properties of such concepts. Some characterizations of generalized connectedness are given. As an application, we generalize some results of m- topological spaces.
Fatimah et al. introduced the notion of N-soft set that is the extension of soft set introduced b... more Fatimah et al. introduced the notion of N-soft set that is the extension of soft set introduced by Molodtsov. Shabir et al. studied the bipolarity of data within the soft set by defining the notion of bipolar soft set. During this paper, we have a tendency to encourage and introduce the concept of N-bipolar soft set as an extension of bipolar soft set and N-soft set. Some helpful algebraical definitions and properties are presented. Our concept is illustrated with real life examples, which have uncertainties in knowledge that may be properly captured by this structure. Also, we tend to introduce the notion of N-bipolar soft topology and its specific structures including N-bipolar soft neighborhood, N-bipolar soft interior, N-bipolar soft closure, and N-bipolar soft basis. Moreover, potential applications of N-bipolar soft sets in decision making are presented with algorithms. Finally, we present multi criteria group decision making (MCGDM) methods by utilizing N-bipolar soft set and...
In this paper, the concept of intension is used to introduce two types of ordering relations base... more In this paper, the concept of intension is used to introduce two types of ordering relations based on information that generates a cover for the universal set. These types of ordering relations are distinct from the well-known ordering relation based on set inclusion. For these ordering relations, we consider the algebraic structures that arise in various types of covers. We
In this paper, the counterparts of generalized open (g-open) and generalized closed (g-closed) se... more In this paper, the counterparts of generalized open (g-open) and generalized closed (g-closed) sets for ditopological texture spaces are introduced and some of their characterizations are obtained. Some characterizations are presented for generalized bicontinuous difunctions. Also, we introduce new notions of compactness and stability in ditopological texture spaces based on the notion of g-open and g-closed sets. Finally, as an application of g-open and g-closed sets, we generalize the subsystem based denition of rough set theory by using new subsystem, called generalized open sets to dene new types of lower and upper approximation operators, called g-lower and g-upper approximations. These decrease the upper approximation and increase the lower approximation and hence increase the accuracy. Properties of these approximations are studied. An example of multi-valued information systems are given
Background: In this work, we recall the concepts of multiset and multi topology. Then, we will in... more Background: In this work, we recall the concepts of multiset and multi topology. Then, we will introduce separatedness and connectedness on multi topological spaces and give basic definitions and theorems about it. Also, by using - open mset we study the concept of -separated msets. With this concept, we study the notion of -connected multiset and we give some properties of such concepts. Some characterizations of generalized connectedness are given. As an application, we generalize some results of m- topological spaces.
Fatimah et al. introduced the notion of N-soft set that is the extension of soft set introduced b... more Fatimah et al. introduced the notion of N-soft set that is the extension of soft set introduced by Molodtsov. Shabir et al. studied the bipolarity of data within the soft set by defining the notion of bipolar soft set. During this paper, we have a tendency to encourage and introduce the concept of N-bipolar soft set as an extension of bipolar soft set and N-soft set. Some helpful algebraical definitions and properties are presented. Our concept is illustrated with real life examples, which have uncertainties in knowledge that may be properly captured by this structure. Also, we tend to introduce the notion of N-bipolar soft topology and its specific structures including N-bipolar soft neighborhood, N-bipolar soft interior, N-bipolar soft closure, and N-bipolar soft basis. Moreover, potential applications of N-bipolar soft sets in decision making are presented with algorithms. Finally, we present multi criteria group decision making (MCGDM) methods by utilizing N-bipolar soft set and...
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