General Mathematics

2311 Submissions

[3] viXra:2311.0012 [pdf] submitted on 2023-11-04 00:33:34

Development of Some New Hybrid Structures of Hypersoft Set with Possibility-degree Settings

Authors: Atiqe Ur Rahman, Florentin Smarandache, Muhammad Saeed, Khuram Ali Khan
Comments: 32 Pages.

The concept of a hypersoft membership function is introduced in the extension of a soft set known as a hypersoft set, permitting it to handle complicated and uncertain information in a more powerful and flexible manner. Many academics have already become fascinated with this new area of study, leading to the development of a number of hybrid structures. This chapter develops some new hybrid hypersoft set structures by taking into account multiple fuzzy set-like settings and possibility degree-based settings collectively. Additionally, numerical examples are included to clarify the concept of these structures. Researchers can utilize this work to better understand and apply a variety of mathematical ideas.
Category: General Mathematics

[2] viXra:2311.0011 [pdf] submitted on 2023-11-03 14:16:53

Improvement of Proportional Conflict Redistribution Rules of Combination of Basic Belief Assignments

Authors: Théo Dezert, Jean Dezert, Florentin Smarandache
Comments: 27 Pages.

This paper discusses and analyzes the behaviors of the Propor tional Conflict Redistribution rules no. 5 (PCR5) and no. 6 (PCR6) to combine several distinct sources of evidence characterized by their basic belief assignments defined over the same frame of discernment. After a brief review of these rules, the paper shows through simple examples why their behaviors can sometimes increase the uncertainty more than necessary,which is detrimental to decision-making support drawn from the result of the combination.We present a theoretical improvement of these rules, and establish new PCR5+ and PCR6+ rules of combination.These new rules overcome the weakness of PCR5 and PCR6 rules by computing binary-keeping indexes that allow to keep only focal elements that play an effective role in the partial conflict redistribution. PCR5+ and PCR6+ rules are not associative but they preserve the neutrality of the vacuous belief assignment contrary to the PCR5 and PCR6 rules, and they make a more precise redistribution which does not increase improperly the mass of partial uncertainties.
Category: General Mathematics

[1] viXra:2311.0007 [pdf] replaced on 2023-11-12 08:06:05

A Proof for a Generalization of the Inequality from the 42nd International Mathematical Olympiad

Authors: Youming Zhao
Comments: 3 pages, fixed two notational typos

In this paper, we present a proof for a generalization of the inequality from the 42nd International Mathematical Olympiad. The proved inequality relates to a sum involving square roots of fractions. It has various applications in mathematical analysis, optimization, or statistics. In the field of mathematical analysis, it can be used in the study of convergence. In terms of optimization, it may help establish bounds or relationships between the variables involved.
Category: General Mathematics