Fuzzy Similarity Measure, Measure of Fuzziness, and Entropy

2017 ◽  
pp. 47-60
Keyword(s):  
Similarity Measure ◽  
Fuzzy Similarity

Handling Fuzzy Similarity for Data Classification

2011 ◽  
pp. 796-802 ◽  
Author(s):  
Roy Gelbard ◽  
Avichai Meged
Keyword(s):  
Data Mining ◽  
Similarity Measure ◽  
Data Representation ◽  
Classification Algorithms ◽  
Binary Representation ◽  
Fuzzy Data ◽  
Problem Domain ◽  
Data Types ◽  
Fuzzy Similarity ◽  
Set Up

Representing and consequently processing fuzzy data in standard and binary databases is problematic. The problem is further amplified in binary databases where continuous data is represented by means of discrete ‘1’ and ‘0’ bits. As regards classification, the problem becomes even more acute. In these cases, we may want to group objects based on some fuzzy attributes, but unfortunately, an appropriate fuzzy similarity measure is not always easy to find. The current paper proposes a novel model and measure for representing fuzzy data, which lends itself to both classification and data mining. Classification algorithms and data mining attempt to set up hypotheses regarding the assigning of different objects to groups and classes on the basis of the similarity/distance between them (Estivill-Castro & Yang, 2004) (Lim, Loh & Shih, 2000) (Zhang & Srihari, 2004). Classification algorithms and data mining are widely used in numerous fields including: social sciences, where observations and questionnaires are used in learning mechanisms of social behavior; marketing, for segmentation and customer profiling; finance, for fraud detection; computer science, for image processing and expert systems applications; medicine, for diagnostics; and many other fields. Classification algorithms and data mining methodologies are based on a procedure that calculates a similarity matrix based on similarity index between objects and on a grouping technique. Researches proved that a similarity measure based upon binary data representation yields better results than regular similarity indexes (Erlich, Gelbard & Spiegler, 2002) (Gelbard, Goldman & Spiegler, 2007). However, binary representation is currently limited to nominal discrete attributes suitable for attributes such as: gender, marital status, etc., (Zhang & Srihari, 2003). This makes the binary approach for data representation unattractive for widespread data types. The current research describes a novel approach to binary representation, referred to as Fuzzy Binary Representation. This new approach is suitable for all data types - nominal, ordinal and as continuous. We propose that there is meaning not only to the actual explicit attribute value, but also to its implicit similarity to other possible attribute values. These similarities can either be determined by a problem domain expert or automatically by analyzing fuzzy functions that represent the problem domain. The added new fuzzy similarity yields improved classification and data mining results. More generally, Fuzzy Binary Representation and related similarity measures exemplify that a refined and carefully designed handling of data, including eliciting of domain expertise regarding similarity, may add both value and knowledge to existing databases.

scholarly journals M-CFIS-R: Mamdani Complex Fuzzy Inference System with Rule Reduction Using Complex Fuzzy Measures in Granular Computing

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 707 ◽  
Author(s):  
Tran Manh Tuan ◽  
Luong Thi Hong Lan ◽  
Shuo-Yan Chou ◽  
Tran Thi Ngan ◽  
Le Hoang Son ◽  
...  
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Fuzzy Inference System ◽  
Granular Computing ◽  
Fuzzy Inference ◽  
Fuzzy Theory ◽  
Rule Base ◽  
Inference System ◽  
Fuzzy Measures ◽  
Fuzzy Similarity

Complex fuzzy theory has strong practical background in many important applications, especially in decision-making support systems. Recently, the Mamdani Complex Fuzzy Inference System (M-CFIS) has been introduced as an effective tool for handling events that are not restricted to only values of a given time point but also include all values within certain time intervals (i.e., the phase term). In such decision-making problems, the complex fuzzy theory allows us to observe both the amplitude and phase values of an event, thus resulting in better performance. However, one of the limitations of the existing M-CFIS is the rule base that may be redundant to a specific dataset. In order to handle the problem, we propose a new Mamdani Complex Fuzzy Inference System with Rule Reduction Using Complex Fuzzy Measures in Granular Computing called M-CFIS-R. Several fuzzy similarity measures such as Complex Fuzzy Cosine Similarity Measure (CFCSM), Complex Fuzzy Dice Similarity Measure (CFDSM), and Complex Fuzzy Jaccard Similarity Measure (CFJSM) together with their weighted versions are proposed. Those measures are integrated into the M-CFIS-R system by the idea of granular computing such that only important and dominant rules are being kept in the system. The difference and advantage of M-CFIS-R against M-CFIS is the usage of the training process in which the rule base is repeatedly changed toward the original base set until the performance is better. By doing so, the new rule base in M-CFIS-R would improve the performance of the whole system. Experiments on various decision-making datasets demonstrate that the proposed M-CFIS-R performs better than M-CFIS.

Spectral clustering with fuzzy similarity measure

2011 ◽  
Vol 21 (6) ◽  
pp. 701-709 ◽  
Author(s):  
Feng Zhao ◽  
Hanqiang Liu ◽  
Licheng Jiao
Keyword(s):  
Similarity Measure ◽  
Spectral Clustering ◽  
Fuzzy Similarity
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