Granular Computing Based on m-Polar Fuzzy Hypergraphs

2020 ◽  
pp. 339-364
Author(s):  
Muhammad Akram ◽  
Anam Luqman
Keyword(s):  
Granular Computing ◽  
Fuzzy Hypergraphs

Hesitant fuzzy graphs, hesitant fuzzy hypergraphs and fuzzy graph decisions1

2021 ◽  
Vol 40 (1) ◽  
pp. 865-875
Author(s):  
Zengtai Gong ◽  
Junhu Wang
Keyword(s):  
Decision Making ◽  
Granular Computing ◽  
Formal Concept ◽  
Fuzzy Graph ◽  
Hypergraph Model ◽  
Multi Attribute Decision Making ◽  
The Difference ◽  
Fuzzy Hypergraphs ◽  
Fuzzy Formal Concept ◽  
Fuzzy Formal Concept Analysis

Up to now, there have been a lot of research results about multi-attribute decision making problems by fuzzy graph theory. However, there are few investigations about multi-attribute decision making problems under the background of indecisiveness. The main reason is that the difference of cognition and the complexity of thinking by decision makers, for the same question have different opinions. In this paper, we proposed a hesitant fuzzy hypergraph model based on hesitant fuzzy sets and fuzzy hypergraphs. At the same time, some basic graph operations of hesitant fuzzy hypergraphs are investigated and several equivalence relationship between hesitant fuzzy hypergraphs, hesitant fuzzy formal concept analysis and hesitant fuzzy information systems are discussed. Since granular computing can deal with multi-attribute decision-making problems well, we considered the hesitant fuzzy hypergraph model of granular computing, and established an algorithm of multi-attribute decision-making problem based on hesitant fuzzy hypergraph model. Finally an example is given to illustrate the effectiveness of the algorithm.

scholarly journals An m-Polar Fuzzy Hypergraph Model of Granular Computing

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 483 ◽  
Author(s):  
Anam Luqman ◽  
Muhammad Akram ◽  
Ali Koam
Keyword(s):  
Real World ◽  
Granular Computing ◽  
Fuzzy Model ◽  
Vital Role ◽  
Information Granules ◽  
Fuzzy Models ◽  
Hypergraph Model ◽  
Real World Problem ◽  
Processing Information ◽  
Fuzzy Hypergraphs

An m-polar fuzzy model plays a vital role in modeling of real-world problems that involve multi-attribute, multi-polar information and uncertainty. The m-polar fuzzy models give increasing precision and flexibility to the system as compared to the fuzzy and bipolar fuzzy models. An m-polar fuzzy set assigns the membership degree to an object belonging to [ 0 , 1 ] m describing the m distinct attributes of that element. Granular computing deals with representing and processing information in the form of information granules. These information granules are collections of elements combined together due to their similarity and functional/physical adjacency. In this paper, we illustrate the formation of granular structures using m-polar fuzzy hypergraphs and level hypergraphs. Further, we define m-polar fuzzy hierarchical quotient space structures. The mappings between the m-polar fuzzy hypergraphs depict the relationships among granules occurring at different levels. The consequences reveal that the representation of the partition of a universal set is more efficient through m-polar fuzzy hypergraphs as compared to crisp hypergraphs. We also present some examples and a real-world problem to signify the validity of our proposed model.

Conversion-based aggregation algorithms for linear ordinal rankings combined with granular computing

2021 ◽  
Vol 219 ◽  
pp. 106880
Author(s):  
Nana Liu ◽  
Zeshui Xu ◽  
Hangyao Wu ◽  
Peijia Ren
Keyword(s):  
Granular Computing

Certain models of granular computing based on rough fuzzy approximations

2020 ◽  
Vol 39 (3) ◽  
pp. 2797-2816
Author(s):  
Muhammad Akram ◽  
Anam Luqman ◽  
Ahmad N. Al-Kenani
Keyword(s):  
Social Networks ◽  
Social Network ◽  
Problem Solving ◽  
Granular Computing ◽  
Research Study ◽  
Network Models ◽  
Mathematical Framework ◽  
Human Reasoning ◽  
Accuracy Measures ◽  
Lower And Upper Approximations

An extraction of granular structures using graphs is a powerful mathematical framework in human reasoning and problem solving. The visual representation of a graph and the merits of multilevel or multiview of granular structures suggest the more effective and advantageous techniques of problem solving. In this research study, we apply the combinative theories of rough fuzzy sets and rough fuzzy digraphs to extract granular structures. We discuss the accuracy measures of rough fuzzy approximations and measure the distance between lower and upper approximations. Moreover, we consider the adjacency matrix of a rough fuzzy digraph as an information table and determine certain indiscernible relations. We also discuss some general geometric properties of these indiscernible relations. Further, we discuss the granulation of certain social network models using rough fuzzy digraphs. Finally, we develop and implement some algorithms of our proposed models to granulate these social networks.

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