Related papers: Probability theory and its models
This paper mainly focuses on (1) a generalized treatment of fuzzy sets of type $n$, where $n$ is an integer larger than or equal to $1$, with an example, mathematical discussions, and real-life interpretation of the given mathematical…
In a series of papers, a many-minds interpretation of quantum theory has been developed. The aim in these papers is to present an explicit mathematical formalism which constitutes a complete theory compatible with relativistic quantum field…
This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…
In this paper, we present betting strategy of a football game using probability theory. We know all betting houses offer slightly unfair odds towards the player. Here we discuss a simple way to figure out which betting house is offering…
The basic concepts of category theory are developed and examples of them are presented to illustrate them using measurement theory and probability theory tools. Motivated by Perrone's workarXiv:1912.10642 where notes on category theory are…
Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…
Measurement theory is the cornerstone of science, but no equivalent theory underpins the huge volumes of non-numerical data now being generated. In this study, we show that replacing numbers with alternative mathematical models, such as…
Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the…
Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief…
A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between…
Every scientific endeavour consists of (at least) two components: A hypothesis on the one hand and data on the other. There is always a more or less abstract level - some theory, a set of concepts, certain relations of ideas - and a…
Hypercomputational formal theories will, clearly, be both structurally and foundationally different from the formal theories underpinning computational theories. However, many of the maps that might guide us into this strange realm have…
In this paper, we introduce a fundamental framework to create a bridge between Probability Theory and Fuzzy Logic. Indeed, our theory formulates a random experiment of selecting crisp elements with the criterion of having a certain fuzzy…
People who by training end up dealing with probabilities ("statisticians") roughly fall into one of two camps. One is either a frequentist or a Bayesian. To a scientist, who needs to use probabilities to make sense of the real world, this…
The purpose of this paper is to give an introduction to the field of Schema Theory written by a mathematician and for mathematicians. In particular, we endeavor to to highlight areas of the field which might be of interest to a…
We describe the fundamental difference between the nature of problems in traditional physics and that of many problems arising today in systems biology and other complex settings. The difference hinges on the much larger number of a priori…
Recently, topic modeling has been widely used to discover the abstract topics in text corpora. Most of the existing topic models are based on the assumption of three-layer hierarchical Bayesian structure, i.e. each document is modeled as a…
Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's…
Statistical thermodynamics has a universal appeal that extends beyond molecular systems, and yet, as its tools are being transplanted to fields outside physics, the fundamental question, \textit{what is thermodynamics?}, has remained…
This paper introduces epistemic graphs as a generalization of the epistemic approach to probabilistic argumentation. In these graphs, an argument can be believed or disbelieved up to a given degree, thus providing a more fine--grained…