This study aims to contribute to the broader dissemination of knowledge concerning quantum fuzzy computing. Combining characteristics and exploring fusion information by Fuzzy Logic and Quantum Computing, this work extends the quantum interpretation in the class of fuzzy Xor-connectives. Firstly, the X(N)or-connective is defined using aggregation functions. Additionally, the results are validated in the Qfuzzy-Analyser, a computational component providing methodologies for algebraic analysis and logical interpretation of flexible systems via quantum circuit modeling. This study considers the well-known IBM Qiskit simulator, which enables execution and graphical representations for fuzzy X(N)or-connectives, including quantum circuits and many tools to observe the evolution of flexible systems and quantum-fuzzy interpretations.
This study aims to contribute to the broader dissemination of knowledge concerning quantum fuzzy computing. Combining characteristics and exploring fusion information by Fuzzy Logic and Quantum Computing, this work extends the quantum interpretation in the class of fuzzy Xor-connectives. Firstly, the X(N)or-connective is defined using aggregation functions. Additionally, the results are validated in the Qfuzzy-Analyser, a computational component providing methodologies for algebraic analysis and logical interpretation of flexible systems via quantum circuit modeling. This study considers the well-known IBM Qiskit simulator, which enables execution and graphical representations for fuzzy X(N)or-connectives, including quantum circuits and many tools to observe the evolution of flexible systems and quantum-fuzzy interpretations.
This study is given at the intersection of three important areas: Modal Logic (ML), Fuzzy Logic (FL), and Quantum Computing (QC), leveraging from their main features. On the one hand, we have the QC ability to handle complex data more efficiently, taking advantage of the quantum mechanics concepts. On the other hand, ML and FL allow us to express uncertainties by mathematically modeling the imprecision of the natural language. Therefore, we first provide an algebraic model to interpret modal operators on fuzzy logic, and then we represent them in a quantum computing environment. Besides, we present some case studies simulating the fuzzy modal connectives in the Qiskit platform, aiming to better understand the evolution of quantum circuits.
Computer systems based on fuzzy logic are capable of generating a reliable output even when handling inaccurate input data by applying a rule based system. The main contribution of this paper is to show that quantum computing can be used to extend the class of fuzzy sets. The central idea associates the states of a quantum register to membership functions (mFs) of fuzzy subsets, and the rules for the processes of fuzzyfication are performed by unitary quantum transformations. Thus, this paper describes multi-dimensional quantum registers, associated to mFs on the unitary interval U, in order to introduce a novel interpretation of aggregations found in fuzzy set theory. In particular, t-norms and t-conorms based on quantum gates allows the modeling and interpretation of union, intersection, difference and implication among fuzzy sets, also including an expression for the class of fuzzy S-implications. Furthermore, an interpretation of the symmetric sum was achieved by considering the quantum register sum operator.
This manuscript provides a comprehensive exploration of quantum computing and communication’s foundational elements, employing Qiskit—an open-source quantum computing framework. It delves into the simulation of fundamental quantum blocks and the intricacies of two-qubit entanglement, presenting findings through graphical analyses. The discussion extends to quantum logic gates, including X, Y, Z and CNOT. This study not only examines the construction and application of quantum circuits. The simulation with Qiskit programming presents the basic quantum circuits and its outcomes after measurement.
This work introduces an innovative approach from modeling to simulations, integrating quantum fuzzy interpretations, focusing on the expression of membership degrees in quantum circuits, interpreted as a unitary quantum transformation. Our research contrasts Quantum Fuzzy Computing with Classical Computing, particularly in the context of the prisoner's dilemma and parent-child relationships. Through the Qiskit framework, we conduct simulations, demonstrating the differences in results obtained by both approaches. Well-known fuzzy connectives, such as “exclusive or” and “arithmetic means”, provide an algebraic description for the corresponding composition of quantum operators and circuit representations. Thus, such algorithms can easily extend to model multiple agents' relationships, described by multidimensional quantum registers. The Qiskit simulations provide the structure for the algorithms' computation on the actual quantum platforms, indicating a promising direction for future research in this hybrid research area.
Quantum processes provide a parallel model for fuzzy connectives. Calculations of quantum states may be simultaneously performed by the superposition of membership and non-membership degrees of each element regarding the intuitionistic fuzzy sets. This work aims to interpret Atanassov's intuitionistic fuzzy logic through quantum computing, where not only intuitionistic fuzzy sets, but also their basic operations and corresponding connectives (negation, conjuntion, disjuntion, difference, codifference, implication, and coimplication), are interpreted based on the traditional quantum circuit model.
This paper shows that quantum computing extends the class of fuzzy sets, taking advantage of properties such as quantum parallelism. The central idea associates the states of a quantum register with membership functions of fuzzy subsets, and the rules for the processes of fuzzyfication are performed by unitary quantum transformations. Besides studying the construction of logical operators, such as negation, using quantum, this paper also introduces the definition of t-norms and t-conorms based on unitary and controlled quantum gates. Such constructors allow modelling and interpreting union, intersection and difference between fuzzy sets. As the main contribution, an interpretation for the Reichenbach implication from quantum computing is obtained. An evaluation of the corresponding computation is implemented and simulated in the VPE-qGM visual programming environment.