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### Page 2196 of Mathematical Reviews Vol. , Issue 2000c [page]

2000 Mathematical Reviews
Petry and Gurdial Arora, Information measures for rough and fuzzy sets and application to uncertainty in relational databases (200-214); Robert E.  ...  fuzzy set approach (381-396); Andrzej Czyzewski and Rafal Krolikowski, Application of fuzzy logic and rough sets to audio signal enhancement (397-409); Manish Sarkar and B.  ...

### A history and introduction to the algebra of conditional events and probability logic

H.T. Nguyen, E.A. Walker
1994 IEEE Transactions on Systems, Man and Cybernetics
This article is meant to serve as an introduction to the following series of papers on various aspects of conditional event algebra and probability logic.  ...  Each rough set can of course be identi…ed with the interval [A ; A ] in the Boolean algebra of all subsets of ; where A is any member of the rough set.  ...  While algebraic logic for two-valued logic is thoroughly developed, there is no counterpart to Boolean algebras in three valued logic.  ...

### A rough set based algebraic approach to modelling complex systems

D. Sitnikov, O. Ryabov, I. Mishcheriakov, A. Kovalenko
2018 International Journal of Design & Nature and Ecodynamics
ones) and operations on them. thus, a system is considered to be complex if there is a great degree of uncertainty in the data and/or there are some serious problems with system's decomposition."  ...  All the operations designated to obtaining new knowledge or data patterns in complex systems are algebraically described from the viewpoint of algebraic systems including predicates (in particular, finite  ...  complexity. therefore, we try to consider the concept of a complex system from a logic-algebraic viewpoint, thereby considering it as a certain algebraic structure with predicates describing the available  ...

### Page 7297 of Mathematical Reviews Vol. , Issue 2003j [page]

2003 Mathematical Reviews
These properties are also used to measure the rough-fuzzy uncertainty associated with a given output class.  ...  rough uncertainty as well as the fuzzy uncertainty associated with the pattern.  ...

### A Modal Characterization of Indiscernibility and Similarity Relations in Pawlak's Information Systems [chapter]

Dimiter Vakarelov
2005 Lecture Notes in Computer Science
Approximation Spaces Piotr Wasilewski 114 Rough Sets over the Boolean Algebras Gui-Long Liu 124 Algebraic Approach to Generalized Rough Sets Michiro Kondo 132 Logic for Rough Sets with Rough  ...  Petry, Roy Ladner 275 Rough-Probabilistic Approaches Probabilistic Rough Sets Wojciech Ziarko 283 Variable Precision Bayesian Rough Set Model and Its Application to Human Evaluation Data Tatsuo  ...

### Uncertainty measures for rough formulae in rough logic: An axiomatic approach

Yanhong She, Xiaoli He
2012 Computers and Mathematics with Applications
To solve such a problem, a framework of uncertainty measure for formulae in rough logic is presented in this paper.  ...  However, a few of these uncertainty measures are explored from the viewpoint of formal rough set theory, which, however, help to develop a kind of graded reasoning model in the framework of rough logic  ...  By using these proposed uncertainty measures, we will develop a kind of approximate reasoning model in the framework of rough logic later. Definition 2.3 ([8-10]).  ...

### Page 7911 of Mathematical Reviews Vol. , Issue 99k [page]

1999 Mathematical Reviews
These transformations are based on a well-justified measure of uncertainty in the Dempster-Shafer theory.  ...  to approximation spaces (209-232); Eric SanJuan and Luisa Iturrioz, Duality and informational representability of some information algebras (233-247); Jaroslaw Stepaniuk, Rough re- lations and logics  ...

### A logic for rough sets

Ivo Düntsch
1997 Theoretical Computer Science
Using the representation theorem for these algebras by Katri%k (1974), we present such a logic for rough sets and its algebraic semantics in the spirit of Andrtka and NCmeti (1994).  ...  The appropriate class of algebras for classical propositional logic are Boolean algebras, and it is reasonable to assume that regular double Stone algebras are a class of algebras appropriate for a logic  ...  Acknowledgements I thank the referees for their constructive remarks and the pointers to earlier literature, Hajnal Andrkka for providing the information regarding the history of the algebraic semantics  ...

### A NUMERICAL APPROACH TO UNCERTAINTY IN ROUGH LOGIC

YAN-HONG SHE, XIAO-LI HE
2013 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems
More precisely, we propose the notions of accuracy degree and roughness degree for each formula in rough logic with the intension of measuring the extent to which any formula is accurate and rough, respectively  ...  For this purpose, we introduce a kind of numerical approach to the study of rough logic in this paper.  ...  Acknowledgements We would like to thank the anonymous referees for their valuable comments and suggestions for improving this paper.  ...

### Survey of Rough and Fuzzy Hybridization

Pawan Lingras, Richard Jensen
2007 IEEE International Fuzzy Systems conference proceedings
This paper provides a broad overview of logical and black box approaches to fuzzy and rough hybridization.  ...  However, continuing developments of rough and fuzzy extensions to clustering, neurocomputing, and genetic algorithms make hybrid approaches in these areas a potentially rewarding research opportunity as  ...  Fuzzy-rough ownership is used to measure the average ruggedness of data for time series in [60] .  ...

### Page 4686 of Mathematical Reviews Vol. , Issue 97H [page]

1997 Mathematical Reviews
that every P- consistent mapping is extendible to a possibility measure taking values in the second complete lattice.”  ...  Summary: “This article is devoted to constructing the proposi- tional axiomatic system Kg with fuzzy modalities over an arbi- trary complete Heyting algebra 2.  ...

### A class of multiobjective linear programming models with random rough coefficients

Jiuping Xu, Liming Yao
2009 Mathematical and computer modelling
Finally, illustrative examples are given in order to show the application of the proposed models and algorithms.  ...  In addition, the technique of random rough simulation is applied to deal with general random rough objective functions and random rough constraints which are usually hard to convert into their crisp equivalents  ...  Preliminaries People have used algebraic, topological, logical and constructive methods to study rough sets and try to formulate axiomatic systems for classical rough sets from different viewpoints [5  ...

### The uncertainty: A history in Mathematics

M K M Nasution
2018 Journal of Physics, Conference Series
Therefore, in mathematics continuously developed several paradigms to understand it.  ...  Naturally every phenomenon consists possible has the same concept but has a different character: certainty and uncertainty.  ...  In classical logic, an inference associated with logical implication to define basically something it is exist [24] . Definition 1.  ...

### Page 7602 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews
From this study, we develop two original contributions that can enhance the application of fuzzy rough set techniques to data that may be affected by several sources of uncertainty.  ...  By tracing these models back to the underlying lattice that they are defined on, on one hand we keep up with an important tradition of using algebraic structures for developing logical cal- culi (e.g.  ...

### Page 762 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews
Applications to concise func- tion representation and simple function implementation are also presented with examples.  ...  Horizontal @-additivity is a weaker condition with respect to comonotonicity: it is suitable to comparison with the associated fuzzy measure.  ...
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