Negotiation sets: a general framework

TL;DR

This paper introduces a unified framework called negotiation sets, combining concepts from double and intuitionistic sets, and explores their applications in logic, data clustering, and decision making.

Contribution

It proposes a novel integration of double and intuitionistic set operations, highlighting advantages, limitations, and practical interpretations.

Findings

Unified structure for multiple participants' requirements

Applications in logic, clustering, and decision making

Insights into compatibility of set theories

Abstract

It is well-known fact that there exists 1-1 correspondence between so-called double (or flou) sets and intuitionistic sets (also known as orthopairs). At first glance, these two concepts seem to be irreconcilable. However, one must remember that algebraic operations in these two classes are also defined differently. Hence, the expected compatibility is possible. Contrary to this approach, we combine standard definition of double set with operations which are typical for intuitionistic sets. We show certain advantages and limitations of this viewpoint. Moreover, we suggest an interpretation of our sets and operations in terms of logic, data clustering and multi-criteria decision making. As a result, we obtain a structure of discussion between several participants who propose their "necessary" and "allowable" requirements or propositions.