NN-soft sets: OWA aggregation operators and multi-agent decisions --- Slides in 22nd IPMC 2022 (1/3)

[EN]The 22nd International Pure Mathematics Conference 2022 (22nd IPMC 2022) on Algebra, Analysis and Geometry, was held in Islamabad (Pakistan) from August 21–23, 2022

NN-soft sets: OWA aggregation operators and multi-agent decisions --- Slides in 22nd IPMC 2022 (2/3)

[EN]The 22nd International Pure Mathematics Conference 2022 (22nd IPMC 2022) on Algebra, Analysis and Geometry, was held in Islamabad (Pakistan) from August 21–23, 2022

Notes on soft sets and aggregation operators

[EN]Under uncertainty, traditional sets may not be sufficient to represent real-world phenomena, and fuzzy sets can provide a more flexible and natural approach. The concept of fuzzy sets has been widely used in various fields, including artificial intelligence, control theory, decision-making, and pattern recognition. Fuzzy sets can also be combined with other mathematical tools, such as probability theory, to provide a more comprehensive approach to uncertainty management. In these notes, we explore the concept of fuzzy sets under uncertainty, and their applications in various fields. We discuss the fundamental concepts of fuzzy sets, including fuzzy membership functions, fuzzy operations, and fuzzy relations. We also examine different types of uncertainty, including epistemic and aleatory uncertainty, and how fuzzy sets can be used to model and manage uncertainty in these cases

2021 Research

This document includes the publications made by Dr. Santos-García in the year 2021

Research on fuzzy sets

[EN] This paper explores the advancements in soft sets and their extensions, contributing to the evolving field of soft computing. Soft sets, introduced by Molodtsov, provide a flexible framework for handling uncertainty and imprecision in decision-making processes. The research delves into various extensions of soft sets, including hybrid models with other mathematical structures, enhancing their applicability in diverse domains. Novel methodologies for parameterization and optimization within soft sets are investigated, aiming to improve their efficiency and effectiveness in real-world applications. The study emphasizes the integration of soft sets with machine learning techniques, fostering the development of intelligent systems capable of handling complex and uncertain information. The findings showcase the versatility and potential of soft sets and their extensions, opening new avenues for future research in this dynamic field

NN-soft sets: OWA aggregation operators and multi-agent decisions --- Slides in 22nd IPMC 2022 (3/3)

[EN]The 22nd International Pure Mathematics Conference 2022 (22nd IPMC 2022) on Algebra, Analysis and Geometry, was held in Islamabad (Pakistan) from August 21–23, 2022

Expanded hesitant fuzzy sets and group decision making: slides for FUZZ-IEEE 2017

[EN]We define expanded hesitant fuzzy sets, which incorporate all available information of the decision makers that provide the membership degrees that define a hesitant fuzzy set. We show how this notion relates to hesitant fuzzy set and extended hesitant fuzzy set. We define various scores for this setting, which generalize popular scores for hesitant fuzzy elements. Finally, a group decision making procedure is presented and illustrated with an example

A new criterion for soft set based decision making problems under incomplete information

[EN]We put forward a completely redesigned approach to soft set based decision making problems under incomplete information. An algorithmic solution is proposed and compared with previous approaches in the literature. The computational performance of our algorithm is critically analyzed by an experimental study

Notes on Transformation Techniques for IVIFS: Applications to Aggregation and Decision Making

We delve into the application of two operational transformation techniques that represent a single interval-valued intuitionistic fuzzy number using two intuitionistic fuzzy numbers in a constructive fashion. These techniques are employed to achieve seamless aggregation of interval-valued intuitionistic fuzzy numbers and facilitate multi-attribute decision-making within this framework. The decision-making and prioritization processes rely on comparison laws that consider the score and accuracy of an interval-valued intuitionistic fuzzy number. We illustrate how these parameters can be derived from the analogous proxies associated with the intuitionistic fuzzy numbers that represent it. To wrap up our exploration, we present a comparative study as the culmination of this research endeavor

Notes on Aggregation of IVIFS based on transformation techniques

The abundant growth of variations in intuitionistic fuzzy sets has posed a challenge in assessing the characteristics of diverse decision-making models. In this context, we will delve into the subject within the context of interval-valued intuitionistic fuzzy sets. Our work has a dual purpose. On a theoretical plane, we establish two theorems that facilitate the conversion of interval-valued intuitionistic fuzzy sets into appropriately correlated pairs of intuitionistic fuzzy sets. On a more pragmatic note, we illustrate how these findings can be harnessed to amalgamate interval-valued intuitionistic fuzzy sets and applied to the collective decision-making process within this framework