Renata Reiser

On interval fuzzy S-implications

This paper presents an analysis of interval-valued S-implications and interval-valued automorphisms, showing a way to obtain an interval-valued S-implication from two S-implications, such that the resulting interval-valued S-implication is said to be obtainable. Some consequences of that are: (1) the resulting interval-valued S-implication satisfies the correctness property, and (2) some important properties of usual S-implications are preserved by such interval representations. A relation between S-implications and interval-valued S-implications is outlined, showing that the action of an interval-valued automorphism on an interval-valued S-implication produces another interval-valued S-implication.

Interval additive generators of interval t-norms and interval t-conorms

Abstract The aim of this paper is to introduce the concepts of interval additive generators of interval t-norms and interval t-conorms, as interval representations of additive generators of t-norms and t-conorms, respectively, considering both the correctness and the optimality criteria. The formalization of interval fuzzy connectives in terms of their interval additive generators provides a more systematic methodology for the selection of interval t-norms and interval t-conorms in the various applications of fuzzy systems. We also prove that interval additive generators satisfy the main properties of additive generators discussed in the literature.

Interval valued QL-implications

The aim of this work is to analyze the interval canonical representation for fuzzy QL-implications and automorphisms. Intervals have been used to model the uncertainty of a specialists information related to truth values in the fuzzy propositional calculus: the basic systems are based on interval fuzzy connectives. Thus, using subsets of the real unit interval as the standard sets of truth degrees and applying continuous t-norms, t-conorms and negation as standard truth interval functions, the standard truth interval function of an QL-implication can be obtained. Interesting results on the analysis of interval canonical representation for fuzzy QL-implications and automorphisms are presented. In addition, commutative diagrams are used in order to understand how an interval automorphism acts on interval QL-implications, generating other interval fuzzy QL-implications.

Typical Hesitant Fuzzy Negations

Since the seminal paper of fuzzy set theory by Zadeh in 1965, many extensions have been proposed to overcome the difficulty for assigning the membership degrees. In recent years, a new extension, the hesitant fuzzy sets, has attracted a lot of interest due to its usefulness to handle those problems in which it is difficult to provide accurately a single membership value; since for hesitant sets, membership values are given by a whole set of values. On the other hand, since fuzzy negations have an important role in applications as well as in the theoretical approach to of fuzzy logics, it is important to study an extension of the concept of fuzzy negation for hesitant fuzzy degrees (elements). In this paper, we propose such a definition and we study some of the main properties of this new concept.

Interval-valued intuitionistic fuzzy implications – Construction, properties and representability

Abstract Firstly, this work studies the class of representable (co)implications obtained by idempotent aggregations and pair of dual interval functions, namely fuzzy implications and coimplications. Following the same construction, as the main contribution in the context of the interval-valued intuitionistic fuzzy logic, which is conceived by Atanassov, the class of representable Atanassov’s intuitionistic fuzzy implications is obtained by composition of idempotent interval aggregations and dual pairs of representable fuzzy implications and coimplications. Additionally, the conditions under which relevant properties of fuzzy implications and Atanassov’s intuitionistic fuzzy implications are preserved by such constructions are investigated. Furthermore, taking into account the projection functions and related (interval-valued) Atanassov’s intuitionistic fuzzy implications, it also shows that representable (interval-valued) Atanassov’s intuitionistic fuzzy implications preserve (degenerate) diagonal elements.

Interval Additive Generators of Interval T-Norms

The aim of this paper is to introduce the notion of interval additive generators of interval t-norms as interval representations of additive generators of t-norms, considering both the correctness and the optimality criteria, in order to provide a more systematic methodology for the selection of interval t-norms in the various applications. We prove that interval additive generators satisfy the main properties of punctual additive generators discussed in the literature.

(S,N)-implications on bounded lattices

Since the birth of the fuzzy sets theory several extensions have been proposed. For these extensions, different sets of membership functions were considered. Since fuzzy connectives, such as conjunctions, negations and implications, play an important role in the theory and applications of fuzzy logics, these connectives have also been extended. An extension of fuzzy logic, which generalizes the ones considered up to the present, was proposed by Joseph Goguen in 1967. In this extension, the membership values are drawn from arbitrary bounded lattices. The simplest and best studied class of fuzzy implications is the class of (S,N)-implications, and in this chapter we provide an extension of (S,N)-implications in the context of bounded lattice valued fuzzy logic, and we show that several properties of this class are preserved in this more general framework.

Interval-valued fuzzy coimplications and related dual interval-valued conjugate functions

The aim of this paper is to introduce the dual notion of interval conjugate implications, the interval coimplications, as interval representations of corresponding conjugate fuzzy coimplications. Using the canonical representation, this paper considers both the correctness and the optimality criteria, in order to provide interpretation for fuzzy coimplications as the non-truth degree of conditional rule in expert systems and study the action of interval automorphisms on such interval fuzzy connectives. It is proved that interval automorphisms acting on N-dual interval coimplications preserve the main properties of interval implications discussed in the literature including the duality principle. Lastly, the action of interval automorphisms on interval classes of border, model and S-coimplications are considered, summarized in commutative diagrams.

High-Performance Quantum Computing Simulation for the Quantum Geometric Machine Model

Due to the unavailability of quantum computers, simulation of quantum algorithms using classical computers is still the most affordable option for research of algorithms and models for quantum computing. As such simulation requires high computing power and memory resources, and computations are regular and data-intensive, GPUs become a suitable solution for accelerating the simulation of quantum algorithms. This work introduces an extension of the execution library for the VPE-qGM environment to support GPU acceleration. Hadamard gates with up to 20 quantum bits were simulated, and speedups of up to approximately 540× over a sequential simulation and of approximately 85× over a 8-core distributed simulation in the VirD-GM environment were achieved.

Robustness of N -Dual Fuzzy Connectives

The main contribution of this paper is concerned with the robustness of N-dual connectives in fuzzy reasoning. Starting with an evaluation of the sensitivity in n-order function on [0,1], we apply the results in the D-coimplication classes. The paper formally states that the robustness of pairs of mutual dual n-order functions can be compared, preserving properties and the ordered relation of their arguments.