  Citation: Pap, E. Pseudo-Analysis as a Tool of Information Processing. Proceedings 2022, 81, 116. https:// doi.org/10.3390/proceedings2022081116 Academic Editor: Mark Burgin Published: 7 April 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). proceedings Proceeding Paper Pseudo-Analysis as a Tool of Information Processing † Endre Pap University Singidunum, 11000 Belgrade, Serbia; epap@singidunum.ac.rs † Presented at the Conference on Theoretical and Foundational Problems in Information Studies, IS4SI Summit 2021, online, 12–19 September 2021. Abstract: The theory of the pseudo-analysis is based on a special real semiring (called also tropical semiring). This theory enables a unified approach to three important problems as nonlinearity, uncertainty and optimization, with many applications. There are presented applications in fuzzy logics and fuzzy sets, utility theory, Cumulative Prospect theory of partial differential equations. Keywords: pseudo-analysis; utility theory; fuzzy logics; fuzzy sets; cumulative prospect theory 1. Introduction The first traces of the pseudo-analysis goes to Grossman and Katz [1] and Burgin [2] (what today is called g-calculus, see [3]), then Maslov [4] (what today is called idempotent analysis). These previous results were a starting point to develope a complete unified theory under the name pseudo-analysis [5–11], and as a special case the g-calculus [3]. This theory enables a unified approach to three important problems as nonlinearity, uncertainty and optimization, with many applications. Then corresponding pseudo additive measures and corresponding integrals were introduced. The usefulness of the pseudo-analysis is shown with some important applications in the theory of nonlinear equations, decision theory, fuzzy logics and fuzzy sets, information theory, option pricing, large deviation principle, cumulative prospect theory, physics of the universe, see [4,7–21]. 2. Pseudo-Analysis The theory of the pseudo-analysis is based on the idea to introduce a special real semiring instead of the usual field of real numbers, with new operations so-called pseudo- addition and pseudo-multiplication, see [5–9]. These operations are related to aggregation functions (operators), see [17–19]. Aggregation of the information in an intelligent system is the basic problem, and its use is increasing in more complex systems, e.g., applied mathematics with probability, statistics, decision theory, computer sciences with artificial intelligence, operations research, as well as many applied fields as economy and finance, pattern recognition and image processing, data fusion, multi-criteria decision aid, auto- mated reasoning, robotics, a fusion of images, integration of different kinds of knowledge, see [17–19]. It is considered an ordered semiring ([a, b], ⊕,⊗) on an interval [a, b] in [-∞,+∞], the operation ⊕ is called pseudo-addition and ⊗ is called pseudo-multiplication. Important special cases are: (i) ⊕ = max, ⊗ = +; (ii) ⊕ and ⊗ are generated with a monotone function g; (iii) ⊕ = max, ⊗ = min, see [7–9,11]. Special important pseudo-operations on the unit interval are triangular norms T, triangular conorms S, and uninorms, see [18]. Basic continuous t-norms are TL(x, y) = max(0, x + y - 1), TP(x, y)= xy, TM(x, y) = min(x, y), and corresponding dual t-conorms SL(x, y) = min(1, x + y), SP(x, y)= x + y - xy, SM(x; y) = max(x, y). Proceedings 2022, 81, 116. https://doi.org/10.3390/proceedings2022081116 https://www.mdpi.com/journal/proceedings