scholarly journals Logics with lower and upper probability operators

2017 ◽  
Vol 88 ◽  
pp. 148-168 ◽  
Author(s):  
Nenad Savić ◽  
Dragan Doder ◽  
Zoran Ognjanović
Keyword(s):  
Probability Operators ◽  
Upper Probability ◽  
Lower And Upper Probability

INCLUSIVENESS MEASUREMENT OF RANDOM EVENTS USING ROUGH SET THEORY

2007 ◽  
Vol 15 (04) ◽  
pp. 483-491
Author(s):  
H. TORABI ◽  
B. DAVVAZ ◽  
J. BEHBOODIAN
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Probability Model ◽  
Complete Information ◽  
Random Events ◽  
Arbitrary Event ◽  
Upper Probability ◽  
Lower And Upper Probability

In some probabilistic problems, complete information about the probability model may not exist. In this article, we obtain a lower and upper probability for an arbitrary event by using rough set theory and then a measurement for inclusiveness of events is introduced.

Some New Probability Operators

2020 ◽  
pp. 143-163
Author(s):  
Zoran Marković ◽  
Miodrag Rašković
Keyword(s):  
Probability Operators

Probability Operators

2010 ◽  
Vol 5 (11) ◽  
pp. 916-937 ◽  
Author(s):  
Seth Yalcin
Keyword(s):  
Probability Operators

scholarly journals Triangular Surface Patch Based on Bivariate Meyer-König-Zeller Operator

2019 ◽  
Vol 17 (1) ◽  
pp. 282-296 ◽  
Author(s):  
Guorong Zhou ◽  
Qing-Bo Cai
Keyword(s):  
Convex Hull ◽  
Curve Surface ◽  
Surface Modeling ◽  
Modeling Method ◽  
Basis Functions ◽  
Surface Patch ◽  
Affine Invariance ◽  
Triangular Domain ◽  
Probability Operators ◽  
The Relationship

Abstract Based on the relationship between probability operators and curve/surface modeling, a new kind of surface modeling method is introduced in this paper. According to a kind of bivariate Meyer-König-Zeller operator, we study the corresponding basis functions called triangular Meyer-König-Zeller basis functions which are defined over a triangular domain. The main properties of the basis functions are studied, which guarantee that the basis functions are suitable for surface modeling. Then, the corresponding triangular surface patch called a triangular Meyer-König-Zeller surface patch is constructed. We prove that the new surface patch has the important properties of surface modeling, such as affine invariance, convex hull property and so on. Finally, based on given control vertices, whose number is finite, a truncated triangular Meyer-König-Zeller surface and a redistributed triangular Meyer-König-Zeller surface are constructed and studied.

scholarly journals Weighted Regret-Based Likelihood: A New Approach to Describing Uncertainty

2015 ◽  
Vol 54 ◽  
pp. 471-492
Author(s):  
Joseph Y. Halpern
Keyword(s):  
Axiomatic Characterization ◽  
Lower Probability ◽  
Probability Measures ◽  
New Approach ◽  
Upper Probability ◽  
Weighted Probability ◽  
Natural Way

Recently, Halpern and Leung suggested representing uncertainty by a set of weighted probability measures, and suggested a way of making decisions based on this representation of uncertainty: maximizing weighted regret. Their paper does not answer an apparently simpler question: what it means, according to this representation of uncertainty, for an event E to be more likely than an event E'. In this paper, a notion of comparative likelihood when uncertainty is represented by a set of weighted probability measures is defined. It generalizes the ordering defined by probability (and by lower probability) in a natural way; a generalization of upper probability can also be defined. A complete axiomatic characterization of this notion of regret-based likelihood is given.

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