Fuzzy sets in approximate reasoning, Part 2: logical approaches

1991 ◽  
Vol 40 (1) ◽  
pp. 203-244 ◽  
Author(s):  
Didier Dubois ◽  
Jérôme Lang ◽  
Henri Prade
Keyword(s):  
Fuzzy Sets ◽  
Approximate Reasoning

Rough Sets and Approximate Reasoning

2014 ◽  
pp. 180-228 ◽  
Author(s):  
B. K. Tripathy
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Point Of View ◽  
Approximate Reasoning ◽  
Human Reasoning ◽  
Intuitionistic Fuzzy ◽  
Application Point ◽  
Future Work

Several models have been introduced to capture impreciseness in data. Fuzzy sets introduced by Zadeh and Rough sets introduced by Pawlak are two of the most popular such models. In addition, the notion of intuitionistic fuzzy sets introduced by Atanassov and the hybrid models obtained thereof have been very fruitful from the application point of view. The introduction of fuzzy logic and the approximate reasoning obtained through it are more realistic as they are closer to human reasoning. Equality of sets in crisp mathematics is too restricted from the application point of view. Therefore, extending these concepts, three types of approximate equalities were introduced by Novotny and Pawlak using rough sets. These notions were found to be restrictive in the sense that they again boil down to equality of sets and also the lower approximate equality is artificial. Keeping these points in view, three other types of approximate equalities were introduced by Tripathy in several papers. These approximate equalities were further generalised to cover the approximate equalities of fuzzy sets and intuitionistic fuzzy sets by him. In addition, considering the generalisations of basic rough sets like the covering-based rough sets and multigranular rough sets, the study has been carried out further. In this chapter, the authors provide a comprehensive study of all these forms of approximate equalities and illustrate their applicability through several examples. In addition, they provide some problems for future work.

Granular Computing and Human-Centricity in Computational Intelligence

2012 ◽  
pp. 13-27
Author(s):  
Witold Pedrycz
Keyword(s):  
Fuzzy Sets ◽  
Granular Computing ◽  
Knowledge Generation ◽  
Qualitative Assessment ◽  
Information Granules ◽  
Knowledge Based ◽  
Performance Indexes ◽  
Numeric Data ◽  
Type Information

Information granules and ensuing Granular Computing offer interesting opportunities to endow processing with an important facet of human-centricity. This facet implies that the underlying processing supports non-numeric data inherently associated with the variable perception of humans. Systems that commonly become distributed and hierarchical, managing granular information in hierarchical and distributed architectures, is of growing interest, especially when invoking mechanisms of knowledge generation and knowledge sharing. The outstanding feature of human centricity of Granular Computing along with essential fuzzy set-based constructs constitutes the crux of this study. The author elaborates on some new directions of knowledge elicitation and quantification realized in the setting of fuzzy sets. With this regard, the paper concentrates on knowledge-based clustering. It is also emphasized that collaboration and reconciliation of locally available knowledge give rise to the concept of higher type information granules. Other interesting directions enhancing human centricity of computing with fuzzy sets deals with non-numeric semi-qualitative characterization of information granules, as well as inherent evolving capabilities of associated human-centric systems. The author discusses a suite of algorithms facilitating a qualitative assessment of fuzzy sets, formulates a series of associated optimization tasks guided by well-formulated performance indexes, and discusses the underlying essence of resulting solutions.

Piecewise linear reliability data analysis with fuzzy sets

2001 ◽  
Vol 215 (9) ◽  
pp. 1075-1082 ◽  
Author(s):  
J Harris
Keyword(s):  
Data Analysis ◽  
Fuzzy Sets ◽  
Piecewise Linear ◽  
Reliability Function ◽  
Graphical Analysis ◽  
Reliability Data ◽  
Knowledge Based ◽  
Form Part ◽  
Rate Functions ◽  
Insight Into

The Weibull three-parameter model is widely used in the analysis of reliability data, since it provides a good fit to many, but not all, data cases. In this work an analysis is presented in which locally constant hazard rate functions are applied in the analysis. By defining concomitant fuzzy reliability functions as overlapping fuzzy sets, the limited ranges may be conjoined to provide an extensive continuous reliability function. The efficacy of this treatment is tested with three different typical cases of published physical data that were previously the subjects of Weibull graphical analysis. It is found that in each case the treatment is effective. Different phases of the failure pattern of each case are identified and characterized by ‘time’ constants. The treatment is not limited to three parameters, as in the Weibull case, and it is therefore more flexible. It provides a deeper insight into the underlying failure mechanisms and may be expected to provide a wider range of applications, both within reliability data analysis and in other fields, and can form part of a knowledge-based system.

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