Theoretical Advances on Interval Entropy Concept Addressing a New Methodology to Multi-criteria Decision-making Problems

Abstract

This work focuses on entropy measurements in the context of fuzzy set theory and their corresponding multi-valued logic, as it is a metric capable of quantifying not only the uncer tainty of experts in data analysis but also the lack of information in systems of reasoning to which it is applied. In this research we consider the intersection of Atanassov Intuitionist Fuzzy Logic (A-IFL) and Interval-valued Fuzzy Logic (IvFL), supporting Atanassov’s Interval-valued Intuitionistic Fuzzy Logic (A-IvIFL), in view of the characteristic inherent to this approach of enabling work with indeterminate and imprecise information. In this sense, we study the concept of Atanassov’s Generalized Intuition Fuzzy Index (A-GIFIx), including its constructive methodology based on negation operators and automorphisms. And, from that, we built the interval version, preserving its main properties. The methodology for obtaining Entropy in A-IvIFL via aggregation of Generalized Atanassov’s Interval-valued Intuitionistic Fuzzy Index (A-GIvIFIx) contributes to the analysis of decision-making systems based on multiple criteria. In the conception of the interval entropy ωA-IvE, the notion of preservation of the interval diameters is respected, considering for its obtaining interval-valued fuzzy connectives that also have this characteristic. We use the concept of admissible orders to compare interval data. This study also contributes with a new admissible order, defined by only one injective and increasing function. This order is illustrated by a Decimal Digit Interleaving (DDI) function. Merge order promotes various method expressions for ωA-IvE, described by compositions between negations with equilibrium functions, aggregation as means, and constrained equivalence functions. Finally, as a practical contribution, we apply the proposed methods in a decision-making problem related to video streaming traffic classification. Entropy analyzes the set of attributes, explaining the input-output relationship of data that model the FuzzyNetClass. In this computational approach for classifying traffic related to streaming video, which integrates fuzzy inference systems and machine learning algorithms, the results obtained by ωA-IvE show promise and indicate the continuity of studies and research efforts in the area.