IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

Aggregation operations from quantum computing

Lidiane Visintin, Adriano Maron, Renata Reiser, Владик Крейнович

Published Jul 1, 2013• 13 citations

Abstract

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.

DOI: 10.1109/fuzz-ieee.2013.6622365

Related papers

Fuzzy Computing from Quantum Computing - Case Study in Reichenbach Implication Class

Adriano Maron, Lidiane Visintin, Renata Reiser +1 more

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.

Jan 1, 20134 citations

Quantum Fuzzy Sets: Blending Fuzzy Set Theory and Quantum Computation

Mirco A. Mannucci

In this article we investigate a way in which quantum computing can be used to extend the class of fuzzy sets. The core idea is to see states of a quantum register as characteristic functions of quantum fuzzy subsets of a given set. As the real unit interval is embedded in the Bloch sphere, every fuzzy set is automatically a quantum fuzzy set. However, a generic quantum fuzzy set can be seen as a (possibly entangled) superposition of many fuzzy sets at once, offering new opportunities for modeling uncertainty. After introducing the main framework of quantum fuzzy set theory, we analyze the standard operations of fuzzification and defuzzification from our viewpoint. We conclude this preliminary paper with a list of possible applications of quantum fuzzy sets to pattern recognition, as well as future directions of pure research in quantum fuzzy set theory.

arXiv:cs/0604064Apr 16, 200613 citations

Interpretations on Quantum Fuzzy Computing: Intuitionistic Fuzzy Operations × Quantum Operators

Renata Reiser, Alexandre Lemke, Anderson Ávila +3 more

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.

Electronic Notes in Theoretical Computer ScienceSep 1, 201611 citations

IBM-Qiskit Simulations for Quantum-Fuzzy Interpretations of X(N)or-Connectives using Overlapping and Grouping Aggregations

Juliano Buss, Bruna Novack, Hélida Santos +5 more

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.

IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)Jul 6, 20251 citation

Fuzzy Inference on Quantum Annealers

Amir Pourabdollah, Colin Wilmott, Roberto Schiattarella +1 more

Quantum computers can potentially perform certain types of optimisation problems much more efficiently than classical computers, making them a promising tool for solving complex fuzzy logic problems. In two recent developments, based on solving Quadratic Unconstrained Binary Optimization (QUBO) problems on a type of quantum computers known as quantum annealers, we have introduced novel representations of a) fuzzy sets; b) implementations of some basic fuzzy logic operators (union, intersection, alpha-cut and maximum) and; c) the centroid defuzzification. In this paper, the previous works are further extended by presenting an implementation of Mamdani inference on the quantum annealer machines. We first present how the fuzzy rules can be formulated for such an implementation, then we present how to cascade different quantum-fuzzy operators in order to implement the quantum-fuzzy inference, and finally, a sample implementation of the inference on a real quantum computer is demonstrated. Having the main components of a rule-based fuzzy logic system implemented on quantum computers, this paper provides an integrated solution for implementing a whole fuzzy rule-based system on quantum computers.

IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)Aug 13, 20234 citations

Representing continuoust-norms in quantum computation with mixed states

Héctor Freytes, Giuseppe Sergioli, Antonino Salvatore Aricò

A model of quantum computation is discussed in (Aharanov et al 1997 Proc. 13th Annual ACM Symp. on Theory of Computation, STOC pp 20–30) and ( Tarasov 2002 J. Phys. A: Math. Gen. 35 5207–35 ) in which quantum gates are represented by quantum operations acting on mixed states. It allows one to use a quantum computational model in which connectives of a four-valued logic can be realized as quantum gates. In this model, we give a representation of certain functions, known as t -norms (Menger 1942 Proc. Natl Acad. Sci. USA 37 57–60), that generalize the triangle inequality for the probability distribution-valued metrics. As a consequence an interpretation of the standard operations associated with the basic fuzzy logic (Hájek 1998 Metamathematics of Fuzzy Logic ( Trends in Logic vol 4) (Dordrecht: Kluwer)) is provided in the frame of quantum computation.

Journal of Physics A Mathematical and TheoreticalNov 1, 201021 citations