Flaulles Boone Bergamaschi

• PhD
• Professor (Assistant) at Southwest Bahia State University

A well-known problem in the interval analysis literature is the overestimation and loss of information. In this article, we define new interval operators, called constrained interval operators, that preserve information and mitigate overestimation. These operators are investigated in terms of correction, algebraic properties, and orders. It is show...

In this paper we proposed a concept of Agnesi quasi-fuzzy numbers based on Agnesi’s curve. Also, in the set of all Agnesi quasi-fuzzy numbers is defined an arithmetic where field properties are satisfied.

Fuzzy Mathematical Morphology extends binary morphological operators to grayscale and color images using concepts from fuzzy logic. To define the morphological operators of erosion and fuzzy dilation, the R-implications and fuzzy T-norm respectively are used. This work presents the application of the fuzzy morphological operators of Lukasiewicz, Gö...

This paper discuss on Interval Arithmetic by Moore under two main principles: inclusion isotonicity and quick computations under algebraic cost. In 1999, to overcome Moore difficulties Lodwick introduced constrained interval arithmetic. This paper discuss on Lodwick’s theory under these principles.

The impreciseness of numeric input data can be expressed by intervals. On the other hand, the normalization of numeric data is a usual process in many applications. How do we match the normalization with impreciseness on numeric data? A straightforward answer is that it is enough to apply a correct interval arithmetic, since the normalized exact va...

This paper is an investigation about primeness in quantales environment. It is proposed a new definition for prime ideal in noncommutative setting. As a consequence, fuzzy primeness can be defined in similar way to ring theory.

In this paper we propose a new concept of primeness in quantales. It is proved that this concept coincide with classical definition in commutative quantales, but no longer valid in the noncommutative setting. Also, the notions of strong and uniform strong primeness are investigated.

The main aim of this investigation is to propose the notion of uniform and strong prime- ness in fuzzy environment. First, it is proposed and investigated the concept of fuzzy strongly prime and fuzzy uniformly strongly prime ideal. As an additional tool, the concept of t/m systems for fuzzy environment gives an alternative way to deal with primene...

The main purpose of this paper is to continue the study of uniform strong primeness in fuzzy setting started in 2014. A pure fuzzy notion of this structure allows us to develop specific fuzzy results on Uniformly Strongly Prime (USP) ideals over commutative and noncommutative rings. Besides, the differences between crisp and fuzzy setting are inves...

In 2013, Bergamaschi and Santiago proposed Strongly Prime Fuzzy(SP) ideals for commutative and noncommutative rings with unity, and investigated their properties. This paper goes a step further since it provides the concept of Strongly Prime Radical of a fuzzy ideal and its properties are investigated. It is shown that Zadeh's extension preserves s...

In this paper we introduced the concept of three-dimensional triangular fuzzy number and their properties are investigated. It is shown that this set has important metrical properties, e.g convexity. The paper also provides a rotation method for such numbers based on quaternion and aggregation operator.

This paper is a step forward in the field of fuzzy algebra. Its main target is the investigation of some properties about uniformly strongly prime fuzzy ideals (USPf) based on a definition without a-cuts dependence. This approach is relevant because it is possible to find pure fuzzy results and to see clearly how the fuzzy algebra is different from...

In this paper we define the concept of uniformly strongly prime fuzzy ideal for associative rings with unity. This concept is proposed without dependence of level cuts. We show a pure fuzzy demonstration that all uniformly strongly prime fuzzy ideals are a prime fuzzy ideal according to the newest definition given by Navarro, Cortadellas and Lobill...

In this paper we build the concept of fuzzy quaternion numbers as a natural extension of fuzzy real numbers. We discuss some important concepts such as their arithmetic properties, distance, supremum, infimum and limit of sequences.

In this paper it is defined the concept of strongly prime fuzzy ideal for noncommutative rings. Also, it is proved that the Zadeh's extension preserves strongly fuzzy primeness and that every strongly prime fuzzy ideal is a prime fuzzy ideal as well as every fuzzy maximal is a strongly prime fuzzy ideal.

The main goal of this paper is to investigate the properties of fuzzy ideals of a ring R. It provides a proof that there exists an isomorphism of lattices of fuzzy ideals when ever the rings are isomorphic. Finite-valued fuzzy ideals are also described and a method is created to count the number of fuzzy ideals in finite and Artinian rings.

In this paper we explore classic-like aspects of Kripke models endowed with a fuzzy accessibility relation and a fuzzy notion of satisfaction, and prove a general completeness result concerning the fuzzy semantics of a generous class of normal modal systems enriched with multiple instances of the axiom of confluence.