Narrow Results

Quantum logic (QL) and fuzzy logic (FL) have been gaining attention nowadays due to its potential to be used in quantum computing and information theory. This paper aims to provide a comprehensive overview of QL models of fuzzy representations viz. fuzzy sets (FSs), interval valued fuzzy sets (IVFSs), intuitionistic fuzzy sets (IFSs) and interval valued intuitionistic fuzzy sets (IVIFSs). These QL models can be used to analyze the behavior of quantum logical systems in a fuzzy environment, which is particularly useful for dealing with uncertainty and imprecision in quantum environment. Furthermore, this paper explores the concept of effect algebras (EAs), which are algebraic structures that provide a natural framework for studying FL. Specifically, it is shown that the family of FS, IVFS, IFS and IVIFS can be organized into an EA if the Lukasiewicz operations are considered. This result is significant because EAs can be used to model a wide range of physical and mathematical systems, including quantum systems, and provide a useful tool for analyzing the properties of FL.

This paper focuses on two very important questions: “what is the future of a hybrid mathematical structure of soft set in science and social science?” and “why should we take care to use hybrid structures of soft set?”. At present, these are the most fundamental questions; which encircle a few prominent areas of mathematics of uncertainties viz. fuzzy set theory, rough set theory, vague set theory, hesitant fuzzy set theory, IVFS theory, IT2FS theory, etc. In this paper, we review connections of soft set theory and hybrid structures in a non-technical manner; so that it may be helpful for a non-mathematician to think carefully to apply hybrid structures in his research areas. Moreover, we must express that we do not have any intention to nullify contributions of fuzzy set theory or rough set theory, etc. to mankind; but our main intention is to show that we must be careful to develop any new hybrid structure with soft set. Here, we have a short discussion on needs of artificial psychology and artificial philosophy to enrich artificial intelligence.

In this paper, we propose a new fractal deformation technique. An “extended unit Iterated Shuffle Transformation (ext-unit-IST)” is a mapping that changes the order of the places of a code on a code space. When it is applied on a geometric space, it constructs a fractal-like repeated structure, named “local resemblance”. In our previously proposed fractal deformation technique, a geometric shape was deformed by applying an ext-unit-IST to displacement vectors (d-vectors) given on the shape. In the new technique proposed in this paper, the ext-unit-IST is applied to the increasing rates of the d-vectors. This allows the d-vectors to change widely without disturbing the shape and improves the deformation quality. Several examples demonstrate the performance of the newly proposed technique.