Modelagem de conectivos Fuzzy intuicionistas via computação quântica

Abstract

This work introduces a methodology representing operations of Intuitionistic Fuzzy Set Theory (CFIs), as proposed by Krassemir Atanassov, making use of properties such as superposition, linearity and distributivity of the tensorial product in the state space and transformations of Quantum Computation (QC). The information regarding each intuitionistic fuzzy connective is represented by pairs of quantum registers, guaranteeing the inherent unitarity of quantum states and transformations well as the flexibility of the complementarity relation of membership and non-membership functions characterizing CFIs. The achieved results make significant contributions: (i) consolidating the qfuzz-Analyzer methodology for representing fuzzy sets via operators and states fo QC; and (ii) collaborating with the development of the qfuzz2-Analyzer methodology, extending the representation of information modelled by intuitionist fuzzy sets and their operations, both of which are defined by intuitionistic fuzzy connectors via registers and quantum transformations in the Quantum Circuits model. As the main contribution, based on the extensibility from qfuzz-Analyzer, the qfuzz2-Analyzer methodology guarantees the preservation of the representable intuitionistic fuzzy connectives. The work also considered the validation of the methodology by extending the library of intuitionistic fuzzy operators in the Visual Programming Environment for Quantum Geometric Machine Model (VPE-qGM). The simulation of quantum intuitionistic fuzzy operators via interfaces of the VPE-qGM components (simulator, memory and process editors), contributes to generation of the computations minimizing problems as the exponential increase in the quantum memory and the complexity of quantum measurement projection operations, facilitating the interpretation and analysis by applying quantum algorithms of qfyzz2-Analyzer.