scholarly journals A Lattice-Theoretic Approach to Multigranulation Approximation Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xiaoli He ◽  
Yanhong She
Keyword(s):  
Distributive Lattice ◽  
Mathematical Structure ◽  
Galois Connection ◽  
Theoretic Approach ◽  
Approximation Space ◽  
Approximation Spaces ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Definable Sets

In this paper, we mainly investigate the equivalence between multigranulation approximation space and single-granulation approximation space from the lattice-theoretic viewpoint. It is proved that multigranulation approximation space is equivalent to single-granulation approximation space if and only if the pair of multigranulation rough approximation operators(Σi=1nRi¯,Σi=1nRi_)forms an order-preserving Galois connection, if and only if the collection of lower (resp., upper) definable sets forms an (resp., union) intersection structure, if and only if the collection of multigranulation upper (lower) definable sets forms a distributive lattice whenn=2, and if and only if∀X⊆U,  Σi=1nRi_(X)=∩i=1nRi_(X). The obtained results help us gain more insights into the mathematical structure of multigranulation approximation spaces.

scholarly journals A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Tianyu Xue ◽  
Zhan’ao Xue ◽  
Huiru Cheng ◽  
Jie Liu ◽  
Tailong Zhu
Keyword(s):  
Rough Sets ◽  
Rough Set Theory ◽  
Binary Relations ◽  
Approximation Space ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Fuzzy Binary Relation ◽  
Novel Method ◽  
Interval Valued

Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators.

N-soft rough sets and its applications

2021 ◽  
Vol 40 (1) ◽  
pp. 565-573
Author(s):  
Di Zhang ◽  
Pi-Yu Li ◽  
Shuang An
Keyword(s):  
Decision Making ◽  
Hybrid Model ◽  
Rough Sets ◽  
Real Life ◽  
Decision Problems ◽  
Multi Criteria Decision Making ◽  
Approximation Space ◽  
Soft Sets ◽  
Approximation Operators ◽  
Rough Approximation

In this paper, we propose a new hybrid model called N-soft rough sets, which can be seen as a combination of rough sets and N-soft sets. Moreover, approximation operators and some useful properties with respect to N-soft rough approximation space are introduced. Furthermore, we propose decision making procedures for N-soft rough sets, the approximation sets are utilized to handle problems involving multi-criteria decision-making(MCDM), aiming at electing the optional objects and the possible optional objects based on their attribute set. The algorithm addresses some limitations of the extended rough sets models in dealing with inconsistent decision problems. Finally, an application of N-soft rough sets in multi-criteria decision making is illustrated with a real life example.

scholarly journals A New Single-Valued Neutrosophic Rough Sets and Related Topology

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Qiu Jin ◽  
Kai Hu ◽  
Chunxin Bo ◽  
Lingqiang Li
Keyword(s):  
Rough Sets ◽  
Topological Spaces ◽  
Approximation Operator ◽  
Approximation Space ◽  
Fuzzy Rough Sets ◽  
Approximation Spaces ◽  
Lower Approximation ◽  
Basic Properties ◽  
Approximation Operators ◽  
New Type

(Fuzzy) rough sets are closely related to (fuzzy) topologies. Neutrosophic rough sets and neutrosophic topologies are extensions of (fuzzy) rough sets and (fuzzy) topologies, respectively. In this paper, a new type of neutrosophic rough sets is presented, and the basic properties and the relationships to neutrosophic topology are discussed. The main results include the following: (1) For a single-valued neutrosophic approximation space U , R , a pair of approximation operators called the upper and lower ordinary single-valued neutrosophic approximation operators are defined and their properties are discussed. Then the further properties of the proposed approximation operators corresponding to reflexive (transitive) single-valued neutrosophic approximation space are explored. (2) It is verified that the single-valued neutrosophic approximation spaces and the ordinary single-valued neutrosophic topological spaces can be interrelated to each other through our defined lower approximation operator. Particularly, there is a one-to-one correspondence between reflexive, transitive single-valued neutrosophic approximation spaces and quasidiscrete ordinary single-valued neutrosophic topological spaces.

scholarly journals Axiomatic Characterizations of IVF Rough Approximation Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Guangji Yu
Keyword(s):  
Approximation Spaces ◽  
Axiomatic Characterizations ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Different Types

This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.

scholarly journals Rough Approximation Operators on a Complete Orthomodular Lattice

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 164
Author(s):  
Songsong Dai
Keyword(s):  
Boolean Algebra ◽  
Orthomodular Lattice ◽  
Orthomodular Lattices ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Distributive Law ◽  
Complete Orthomodular Lattice ◽  
The Relationship

This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the distributive law. Furthermore, we study the relationship among the distributive law, rough approximation and orthomodular lattice-valued relation.

scholarly journals Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 417 ◽  
Author(s):  
Hu Zhao ◽  
Hong-Ying Zhang
Keyword(s):  
Algebraic Structure ◽  
Rough Sets ◽  
Lattice Structure ◽  
Single Domain ◽  
One Dimensional ◽  
Basic Properties ◽  
Approximation Operators ◽  
Rough Approximation ◽  
The One ◽  
Comprehensive Study

As a generalization of single value neutrosophic rough sets, the concept of multi-granulation neutrosophic rough sets was proposed by Bo et al., and some basic properties of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators were studied. However, they did not do a comprehensive study on the algebraic structure of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators. In the present paper, we will provide the lattice structure of the pessimistic multigranulation neutrosophic rough approximation operators. In particular, in the one-dimensional case, for special neutrosophic relations, the completely lattice isomorphic relationship between upper neutrosophic rough approximation operators and lower neutrosophic rough approximation operators is proved.

scholarly journals A Category Theoretic Approach to Metaphor Comprehension: Theory of Indeterminate Natural Transformation

2020 ◽  
Author(s):  
Miho Fuyama ◽  
Hayato Saigo ◽  
Tatsuji Takahashi
Keyword(s):  
Category Theory ◽  
Natural Transformation ◽  
Mathematical Structure ◽  
Theoretic Approach ◽  
Metaphor Comprehension ◽  
Central Notion ◽  
Meaning Creation ◽  
Natural Transformations ◽  
Categories And Functors ◽  
The Relationship

We propose the theory of indeterminate natural transformation (TINT) to investigate the dynamical creation of meaning as an association relationship between images, focusing on metaphor comprehension as an example. TINT models meaning creation as a type of stochastic process based on mathematical structure and defined by association relationships, such as morphisms in category theory, to represent the indeterminate nature of structure-structure interactions between the systems of image meanings. Such interactions are formulated in terms of the so-called coslice categories and functors as structure-preserving correspondences between them. The relationship between such functors is “indeterminate natural transformation”, the central notion in TINT, which models the creation of meanings in a precise manner. For instance, metaphor comprehension is modeled by the construction of indeterminate natural transformations from a canonically defined functor, which we call the base-of-metaphor functor.

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