Advances in Intelligent Systems and Computing
Over the last 50 years in different areas such as decision theory, information processing, and data mining, the interest to extend probability theory and statistics has grown. The common feature of those attempts is to widen frameworks for representing different kinds of uncertainty: randomness, imprecision, vagueness, and ignorance. The scope is to develop more flexible methods to analyze data and extract knowledge from them. The extension of classical methods consists in “softening” them by means of new approaches involving fuzzy set theory, possibility theory, rough sets, or having their origin in probability theory itself, like imprecise probabilities, belief functions, and fuzzy random variables. Data science aims at developing automated methods to analyze massive amounts of data and extract knowledge from them. In the recent years the production of data is dramatically increasing. Every day a huge amount of data coming from everywhere is collected: mobile sensors, sophisticated instruments, transactions, Web logs, and so forth. This trend is expected to accelerate in the near future. Data science employs various programming techniques and methods of data wrangling, data visualization, machine learning, and probability and statistics. The soft methods proposed in this volume represent a suit of tools in these fields that can also be useful for data science. The volume contains 65 selected contributions devoted to the foundation of uncertainty theories such as probability, imprecise probability, possibility theory, soft methods for probability and statistics. Some of them are focused on robustness, non-precise data, dependence models with fuzzy sets, clustering, mathematical models for decision theory and finance.
This paper is dedicated to the research of the dynamics of development and interactions among several scientific communities in the field of fuzzy logic and soft computing. This analysis was performed with the help of the following characteristics: conferences participants’ renewal, the level of cooperation in scientific communities, participation of one community’s key players in activities of the other ones, comparative number of most active participants in each community, uniformity of key players’ participation in different conferences.
The qualitative characteristics of the combining evidence with the help of Dempster’s rule with discounting is studied in this paper in the framework of Dempster-Shafer theory. The discount coefficient (discounting rate) characterizes the reliability of information source. The conflict between evidence and change of ignorance after applying combining rule are considered in this paper as important characteristics of quality of combining. The quantity of ignorance is estimated with the help of linear imprecision index. The set of crisp and fuzzy discounting rates for which the value of ignorance after combining does not increases is described.
In the paper we continue investigations started in the paper presented at ISIPTA’15, where the notions of lower and upper generalized credal sets has been introduced. Generalized credal sets are models of imprecise probabilities, where it is possible to describe contradiction in information, when the avoiding sure loss condition is not satisfied. The paper contains the basic principles of approximate reasoning: models of uncertainty based on upper previsions and generalized credal sets, natural extension, and coherence principles.