Grafos fuzzy intervalares n-dimensionais

Abstract

A fuzzy graph, roughly speaking, is a fuzzy relation between the elements of a nonempty set. They are ideal for modeling uncertain data about these sets. There are several extensions of fuzzy graph for different fuzzy logics, such as: intervals fuzzy graphs, hesitant fuzzy graphs and intuitionistic fuzzy graphs. The applications of these concepts are vast: cluster analysis, pattern classification, database theory, social science, neural networks, decision analysis, among others. On the other hand, originally admissible orders were introduced in the context of interval-valued fuzzy sets by H. Bustince et al. and since then they have been widely investigated. Recently, this notion has been studied in other types of fuzzy sets, such as interval-valued intuitionistic fuzzy sets, typical hesitant fuzzy sets, multidimensional fuzzy sets and n-dimensional fuzzy sets. In this context, this work proposes to extend the fuzzy graph of Rosenfeld to interval-valued n-dimensional fuzzy graphs, based on n-dimensional fuzzy sets, as well as, for the admissible interval-valued n-dimensional fuzzy graphs, that we equip with an admissible ordered semi-vector space. We present some methods to generate admissible orders in the n-dimensional fuzzy set and the concept of n-dimensional aggregation functions with respect to an admissible order. We extend the concept of ordered semi-vector space in a semi-field of non-negative real numbers to an arbitrary weak semi-field. We define in a set of admissible interval n-dimensional fuzzy graphs the concept of ordered semi-vector space, whit this, we introduced in this set the concept of admissible interval n-dimensional fuzzy graphs aggregation function. Several properties of these concepts were investigated, in addition to presenting some applications in problems of: energy efficiency, determining the best path between two cities and people traffic.