Integration in Possibility Theory
نویسنده
چکیده
The paper discusses integration in possibility theory, both in an ordinal and in a numerical (behavioral) context. It is shown that in an ordinal context, the fuzzy integral has an important part in at least three areas: the extension of possibility measures to larger domains, the construction of product measures from marginals and the definition of conditional possibilities. In a numerical (behavioral) context, integration can be used to extend upper probabilities to upper previsions. It is argued that the role of the fuzzy integral in this context is limited, as it can only be used to define a coherent upper prevision if the associated upper probability is 0 − 1-valued, in which case it moreover coincides with the Choquet integral. These results are valid for arbitrary coherent upper probabilities, and therefore also relevant for possibility theory. It follows from the discussion that in a numerical context, the Choquet integral is better suited than the fuzzy integral for producing coherent upper previsions starting from possibility measures. At the same time, alternative expressions for the Choquet integral associated with a possibility measure are derived.
منابع مشابه
Integration and Reduction of Microarray Gene Expressions Using an Information Theory Approach
The DNA microarray is an important technique that allows researchers to analyze many gene expression data in parallel. Although the data can be more significant if they come out of separate experiments, one of the most challenging phases in the microarray context is the integration of separate expression level datasets that have gathered through different techniques. In this paper, we prese...
متن کاملFuzzy relations, Possibility theory, Measures of uncertainty, Mathematical modeling.
A central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. In this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. The main stages of the modeling process are represented as fuzz...
متن کاملIdentity Integration of Afghan Immigrants in Iran: A Grounded Theory Study
Introduction: Iran has hosted foreign immigrants, mostly Afghans and Iraqis, for the past four decades. The number of Afghan refugees registered by the UN Refugee Agency in 2021, shows that among different countries, Iran is the second destination of Afghan refugees after Pakistan. One of the key aspects of immigrants' lives that changes in the context of life and residence in the host communit...
متن کاملIdentity Integration of Afghan Immigrants in Iran: A Grounded Theory Study
Introduction: Iran has hosted foreign immigrants, mostly Afghans and Iraqis, for the past four decades. The number of Afghan refugees registered by the UN Refugee Agency in 2021, shows that among different countries, Iran is the second destination of Afghan refugees after Pakistan. One of the key aspects of immigrants' lives that changes in the context of life and residence in the host communit...
متن کاملThe Formal Analogy between Possibility and Probability Theory
It is well known that the theory of probability can be treated and developed in a consistent and uniform way using the classical theory of measure and integration. Indeed, the Russian scientist Kolmogorov identified probability with normalized classical measures and used the Lebesgue theory of integration to give a logically consistent and unifying account of probability theory. In this paper, ...
متن کامل