Science vs. Sophistry—A historical debate on bipolar fuzzy sets and equilibrium-based mathematics for AI&QI

Quantum Logic Automata Generate Class IV-like patterns and 1/f noise

Owing to recent advancements in brain science and AI, researchers tend to focus on the concept of self-organized criticality or the edge of chaos. On the other hand, quantum cognition, which is rooted in quantum mechanics, is promising for resolving various cognitive illusions. However, until recently, no connection between criticality and quantum mechanics was proposed. Gunji et al. (2024) recently introduced a linkage termed quantum logic automata, which encompasses not only quantum logic but also criticality characterized by power-law distributions. While quantum logic automata can be derived from various structures, only one of them has been proposed and discussed. Here, we define another type of quantum logic automata involving quantum logic and demonstrate that symmetric quantum logic automata lead to complex Class IV-like patterns and power-law distributions. Our findings support the association between criticality and quantum theory.

Topological structures on cubic bipolar fuzzy sets with linear assignment model and SIR method for healthcare

The idea of a cubic bipolar fuzzy set (CBFS) is a new hybrid extension of the cubic set (CS) and the bipolar fuzzy set (BFS). A CBFS is a strong model to deal with bipolarity and fuzziness in terms of positive membership grades (PMGs) and negative membership grades (NMGs). A positive interval and a positive numbers represent a PMG to express the degree of belongingness of a specific property, and a negative interval and a negative number represent a NMG which defines the degree of non-belongingness of the specific property (or satisfaction level of its counter property). The aim of this paper is to define the cubic bipolar fuzzy topology under P-order (CBFS P topology) as well as the cubic bipolar fuzzy topology under R-order (CBFS R topology). We investigate certain properties and results of CBFS P topology and CBFS R topology. Topological structures on CBFSs are helping in the development of new artificial intelligence (AI) techniques for healthcare domain strategies and investigating various critical diseases. Such techniques allow for the early detection and investigation of diseases, assisting clinicians in minimizing the possible risk factors. An extended linear assignment model (LAM) and superiority and inferiority ranking method (SIR method) are proposed for healthcare diagnosis based on newly developed structures. The proposed LAM and SIR method are successfully applied for investigation of critical diseases. Moreover, we discuss a comparison analysis of investigations made by suggested techniques with some existing approaches.

Connecting the free energy principle with quantum cognition

It appears that the free energy minimization principle conflicts with quantum cognition since the former adheres to a restricted view based on experience while the latter allows deviations from such a restricted view. While free energy minimization, which incorporates Bayesian inference, leads to a Boolean lattice of propositions (classical logic), quantum cognition, which seems to be very dissimilar to Bayesian inference, leads to an orthomodular lattice of propositions (quantum logic). Thus, we address this challenging issue to bridge and connect the free energy minimization principle with the theory of quantum cognition. In this work, we introduce “excess Bayesian inference” and show that this excess Bayesian inference entails an underlying orthomodular lattice, while classic Bayesian inference entails a Boolean lattice. Excess Bayesian inference is implemented by extending the key idea of Bayesian inference beyond classic Bayesian inference and its variations. It is constructed by enhancing the idea of active inference and/or embodied intelligence. The appropriate lattice structure of its logic is obtained from a binary relation transformed from a distribution of the joint probabilities of data and hypotheses by employing a rough-set lattice technique in accordance with quantum cognition logic.