On the possibility of IF structures

Abstract

In this paper we investigate the idea of IF pseudo-intuitionistic sets. We combine two possible approaches to the problem of division of the initial universe of discourse into three mutually disjoint parts.

First, we use ideals to model "small" (possibly empty) intersection between the ranges of accepted and rejected objects. In this way we generalize Çoker's intuitionistic sets (implementing the same algebraic operations of union, intersection and complement).

Second, we use filters to describe the fact that the union of both components is "big" (but not necessarily identical with the whole universe). Thus, our structures consist of a non-empty universe $X$ together with some fixed ideal and fixed filter (on $X$). In this setting, we introduce our IF pseudo-intuitionistic sets and we analyze their algebraic properties. We implement the notion of point and we propose several possible directions of future research.

1. Introduction

We introduced possibly paraconsistent sets in [1]. We showed that they are isomorphic with so-called intuitionistic sets (in the sense of coker) and weak rough sets (known as double or flou sets too). Hence, they form an appropriate description of the situation in which our initial universe of discourse is divided into three mutually disjoint parts.

This page shows an excerpt of the introduction. The full text is available in the PDF.

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Witczak, T. (2026). On the possibility of IF structures. Asia Mathematika, 10(1), 1–11. https://doi.org/10.5281/zenodo.20982168

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