Open Access
A method for inference in approximate reasoning based on normal intuitionistic fuzzy sets
(Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1995) Bustince Sola, Humberto; Burillo López, Pedro; Mohedano Salillas, Victoria; Automática y Computación; Automatika eta Konputazioa
This paper introduces a method of approximate inference which operates with nornal intuitionistic fuzzy. We give a definition of degree of compatibility between intuitionistic fuzzy sets and we present a method for the construction of these sets. Lastly we present the method of inference in approximate reasoning with normal intuitionistic fuzzy sets and we study its most immediate properties.
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From type-(2,k) grouping indices to type-(2,k) Jaccard indices
(Elsevier, 2025-02-01) Roldán López de Hierro, Antonio Francisco; Roldán, Concepción; Guerra Errea, Carlos; Fernández Fernández, Francisco Javier; Cruz, Anderson; Moraes, Ronei Marcos de; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In this work, we introduce the notion of grouping index for type-2 fuzzy sets as a measure of how far the union of two type-2 fuzzy sets over the same universe is from the total universe. We also show how we can extend the notion of the Jaccard index to the type-2 setting by means of type-2 grouping and overlap indexes.
Open Access
On the notion of fuzzy dispersion measure and its application to triangular fuzzy numbers
(Elsevier, 2023) Roldán López de Hierro, Antonio Francisco; Bustince Sola, Humberto; Rueda, María del Mar; Roldán, Concepción; Miguel Turullols, Laura de; Guerra Errea, Carlos; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In this paper, based on the analysis of the most widely used dispersion measure in the real context (namely, the variance), we introduce the notion of fuzzy dispersion measure associated to a finite set of data given by fuzzy numbers. This measure is implemented as a fuzzy number, so there is no loss of information caused by any defuzzification. The proposed concept satisfies the usual properties in a genuinely fuzzy sense and it avoids limitations in terms of its geometric shape or its analytical properties: under this conception, it could have a piece of its support in the negative part of the real line. This novel notion can be interpreted as a way of fusing the information included in a fuzzy data set in order to make a decision based on its dispersion. To illustrate the main characteristics of this approach, we present an example of a fuzzy dispersion measure that allows to conclude that this new way to deal this problem is coherent, at least, from the point of view of human intuition.
Open Access
Handling multicriteria fuzzy decision-making problems based on intuitionistic fuzzy sets
(Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1995) Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa
In this paper we present a new technique for handling multicriteria decision making problems based on intuitionistic fuzzy sets. In this new technique we use the degree of reliability and of non-reliability of each criterion in relation to a set of alternatives. We also present a new score function in order to evaluate the degree of suitability of the choice of a certain alternative.
Open Access
A theorem for constructing interval-valued intuitionistic fuzzy sets from intuitionistic fuzzy sets
(Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1995) Bustince Sola, Humberto; Burillo López, Pedro; Automática y Computación; Automatika eta Konputazioa
In this paper we present a theorem that allows us to construct interval-valued intuitionistic fuzzy sets from intuitionistic fuzzy sets. We also study the way of recovering intuitionistic fuzzy sets used in the construction of the interval-valued intuitionistic fuzzy set from different operators. We analise the numerical measures of information of the internal-valued intuitionistic fuzzy set constructed in function with the numerical measures of information of the intuitionistic fuzzy sets used in its construction. We review the most important properties of intuitionistic fuzzy sets and of internal-valued intuitionistic fuzzy sets and we analise three operators among these sets along with their properties.