Differential and integral calculus based on arithmetic of interactive fuzzy numbers

• Grant number: 16/26040-7
• Support Opportunities: Regular Research Grants
• Start date: July 01, 2017
• End date: June 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computational Mathematics
• Principal Investigator: Estevão Esmi Laureano
• Grantee: Estevão Esmi Laureano
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Fuzzy set theory is a mathematical field designed to analysing and processing sets (concepts) with uncertain boundaries. Recently, researchers have investigated solutions of dynamic systems in which their parameters and/or variables have values into the class of fuzzy numbers (R_F). In this project, we will develop a new theory of fuzzy differential and integral calculus for dealing with functions from R to R_F where the values of their range may have a special type of relationship called interactivity. To this end, we will employ the sup-J extension principle that consists in a method to extend any classic operator for dealing with interactive or non-interactive fuzzy numbers. Finally, we will apply this calculus theory to investigate analytically and numerically solutions of dynamic systems given by fuzzy differential and integral equations. In particular, we will focus on problems of biomathematics such as population and epidemiological dynamics. (AU)

Scientific publications

(33)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

EDUARDO SANCHEZ, DANIEL; ESMI, ESTEVAO; DE BARROS, LAECIO CARVALHO; MIEBACH, ALESSANDRO DONADIO; CECCONELLO, MOISEIS DOS SANTOS. Goodwin economic cycle via p -fuzzy system. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, v. 38, n. 4, SI, p. 4079-4090, 2020. (16/26040-7, 18/10946-2)

D. SÁNCHEZ; L.T. BASSANI; L.C. BARROS; E. ESMI. Adapted Fuzzy Integral: An Application in the Finite Element Method. TEMA (São Carlos), v. 19, n. 1, p. 147-160, 2018-01-00. (16/26040-7)

WASQUES, VINICIUS F.; PINTO, NILMARA J. B.; ESMI, ESTEVAO; DE BARROS, LAECIO CARVALHO; BEDE, B; CEBERIO, M; DECOCK, M; KREINOVICH, V. Consistence of Interactive Fuzzy Initial Conditions. FUZZY INFORMATION PROCESSING 2020, v. 1337, p. 13-pg., 2022-01-01. (16/26040-7)

BISCAIA PINTO, NILMARA DE JESUS; ESMI, ESTEVAO; DE BARROS, LAECIO CARVALHO; BEDE, B; CEBERIO, M; DECOCK, M; KREINOVICH, V. Carbon Emissions Trading as a Constraint in a Fuzzy Optimization Problem. FUZZY INFORMATION PROCESSING 2020, v. 1337, p. 12-pg., 2022-01-01. (16/26040-7)

WASQUES, VINICIUS F.; ESMI, ESTEVAO; BARROS, LAECIO C.; SUSSNER, PETER. Numerical Solution for Fuzzy Initial Value Problems via Interactive Arithmetic: Application to Chemical Reactions. INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS, v. 13, n. 1, p. 1517-1529, 2020. (16/26040-7, 18/13657-1)

WASQUES, VINICIUS FRANCISCO; LAUREANO, ESTEVAO ESMI; DE BARROS, LAECIO CARVALHO; PEDRO, FRANCIELLE SANTO; SUSSNER, PETER; IEEE. Higher Order Initial Value Problem with Interactive Fuzzy Conditions. 2018 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE), v. N/A, p. 8-pg., 2018-01-01. (16/26040-7)

SALGADO, S. A. B.; BARROS, L. C.; ESMI, E.; LIU, J; LU, J; XU, Y; MARTINEZ, L; KERRE, EE. Solution of a fuzzy differential equation with interactivity via fuzzy Laplace transform. DATA SCIENCE AND KNOWLEDGE ENGINEERING FOR SENSING DECISION SUPPORT, v. 11, p. 6-pg., 2018-01-01. (16/26040-7)

WASQUES, VINICIUS FRANCISCO; ESMI, ESTEVAO; BARROS, LAECIO C.; BEDE, BARNABAS; KEARFOTT, RB; BATYRSHIN, I; REFORMAT, M; CEBERIO, M; KREINOVICH, V. Comparison Between Numerical Solutions of Fuzzy Initial-Value Problems via Interactive and Standard Arithmetics. FUZZY TECHNIQUES: THEORY AND APPLICATIONS, v. 1000, p. 12-pg., 2019-01-01. (16/26040-7)

LAIATE, BEATRIZ; JAFELICE, ROSANA M.; ESMI, ESTEVAO; BARROS, LAECIO C.; KEARFOTT, RB; BATYRSHIN, I; REFORMAT, M; CEBERIO, M; KREINOVICH, V. An Interpretation of the Fuzzy Measure Associated with Choquet Calculus for a HIV Transference Model. FUZZY TECHNIQUES: THEORY AND APPLICATIONS, v. 1000, p. 12-pg., 2019-01-01. (16/26040-7)

WASQUES, VINICIUS F.; ESMI, ESTEVAO; BARROS, LAECIO C.; SUSSNER, P.; NOVAK, V; MARIK, V; STEPNICKA, M; NAVARA, M; HURTIK, P. Numerical Solution for Lotka-Volterra Model of Oscillating Chemical Reactions with Interactive Fuzzy Initial Conditions. PROCEEDINGS OF THE 11TH CONFERENCE OF THE EUROPEAN SOCIETY FOR FUZZY LOGIC AND TECHNOLOGY (EUSFLAT 2019), v. 1, p. 6-pg., 2019-01-01. (18/13657-1, 16/26040-7)

LONGO, FELIPE; LAIATE, BEATRIZ; SANTO PEDRO, FRANCIELLE; ESMI, ESTEVAO; BARROS, LAECIO C.; MEYER, JOAO F. C. A.; RAYZ, J; RASKIN, V; DICK, S; KREINOVICH, V. A-Cross Product for Autocorrelated Fuzzy Processes: The Hutchinson Equation. EXPLAINABLE AI AND OTHER APPLICATIONS OF FUZZY TECHNIQUES, NAFIPS 2021, v. 258, p. 12-pg., 2022-01-01. (16/26040-7)

LAIATE, BEATRIZ; ESMI, ESTEVAO; SANTO PEDRO, FRANCIELLE; BARROS, LAECIO C.; RAYZ, J; RASKIN, V; DICK, S; KREINOVICH, V. Solutions of Systems of Linear Fuzzy Differential Equations for a Special Class of Fuzzy Processes. EXPLAINABLE AI AND OTHER APPLICATIONS OF FUZZY TECHNIQUES, NAFIPS 2021, v. 258, p. 12-pg., 2022-01-01. (16/26040-7)

ESMI, ESTEVAO; DE BARROS, LAECIO CARVALHO; SANTO PEDRO, FRANCIELLE; LAIATE, BEATRIZ. Banach spaces generated by strongly linearly independent fuzzy numbers. FUZZY SETS AND SYSTEMS, v. 417, p. 20-pg., 2021-06-01. (16/26040-7)

DE BARROS, LAECIO CARVALHO; EDUARDO SANCHEZ, DANIEL; LOBO, RODOLFO ANIBAL; ESMI, ESTEVAO; NOVAK, V; MARIK, V; STEPNICKA, M; NAVARA, M; HURTIK, P. Free Mechanical Vibrations Models via p-fuzzy Systems. PROCEEDINGS OF THE 11TH CONFERENCE OF THE EUROPEAN SOCIETY FOR FUZZY LOGIC AND TECHNOLOGY (EUSFLAT 2019), v. 1, p. 7-pg., 2019-01-01. (18/10946-2, 16/26040-7)

WASQUES, VINICIUS F.; ESMI, ESTEVAO; BARROS, LAECIO C.; SUSSNER, PETER. The generalized fuzzy derivative is interactive. INFORMATION SCIENCES, v. 519, p. 93-109, MAY 2020. (18/13657-1, 16/26040-7)

PEDRO, FRANCIELLE SANTO; DE BARROS, LAECIO CARVALHO; ESMI, ESTEVAO. Population growth model via interactive fuzzy differential equation. INFORMATION SCIENCES, v. 481, p. 160-173, MAY 2019. (16/26040-7)

ESMI, ESTEVAO; PEDRO, FRANCIELLE SANTO; DE BARROS, LAECIO CARVALHO; LODWICK, WELDON. Frechet derivative for linearly correlated fuzzy function. INFORMATION SCIENCES, v. 435, p. 150-160, APR 2018. (16/26040-7)

PINTO, NILMARA J. B.; WASQUES, VINICIUS F.; ESMI, ESTEVAO; BARROS, LAECIO C.; BARRETO, GA; COELHO, R. Least Squares Method with Interactive Fuzzy Coefficient: Application on Longitudinal Data. FUZZY INFORMATION PROCESSING, NAFIPS 2018, v. 831, p. 12-pg., 2018-01-01. (16/26040-7)

SANCHEZ, DANIEL EDUARDO; ESMI, ESTEVAO; DE BARROS, LAECIO CARVALHO; KEARFOTT, RB; BATYRSHIN, I; REFORMAT, M; CEBERIO, M; KREINOVICH, V. Discrete and Continuous Logistic p-Fuzzy Models. FUZZY TECHNIQUES: THEORY AND APPLICATIONS, v. 1000, p. 11-pg., 2019-01-01. (16/26040-7, 18/10946-2)

WASQUES, VINICIUS F.; ESMI, ESTEVAO; DE BARROS, LAECIO CARVALHO; SANTO PEDRO, FRANCIELLE; BEDE, B; CEBERIO, M; DECOCK, M; KREINOVICH, V. Numerical Solution for Reversible Chemical Reaction Models with Interactive Fuzzy Initial Conditions. FUZZY INFORMATION PROCESSING 2020, v. 1337, p. 12-pg., 2022-01-01. (16/26040-7)

ESMI, ESTEVAO; DE BARROS, LAECIO CARVALHO; SANTO PEDRO, FRANCIELLE; LAIATE, BEATRIZ. Banach spaces generated by strongly linearly independent fuzzy numbers. FUZZY SETS AND SYSTEMS, v. 417, n. SI, p. 110-129, AUG 1 2021. (16/26040-7)

SANCHEZ IBANEZ, DANIEL; ESMI, ESTEVAO; BARROS, LAECIO C.; IEEE. Linear Ordinary Differential Equations with Linearly Correlated Boundary Values. 2018 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE), v. N/A, p. 6-pg., 2018-01-01. (16/26040-7)

SANCHEZ, D.; BARROS, L. C.; ESMI, E.; MIEBACH, A. D.; LIU, J; LU, J; XU, Y; MARTINEZ, L; KERRE, EE. Goodwin model via p-fuzzy system. DATA SCIENCE AND KNOWLEDGE ENGINEERING FOR SENSING DECISION SUPPORT, v. 11, p. 8-pg., 2018-01-01. (16/26040-7)

SUSSNER, PETER; ESMI, ESTEVAO; JARDIM, LUIS GUSTAVO; KEARFOTT, RB; BATYRSHIN, I; REFORMAT, M; CEBERIO, M; KREINOVICH, V. A Subsethod Interval Associative Memory with Competitive Learning. FUZZY TECHNIQUES: THEORY AND APPLICATIONS, v. 1000, p. 12-pg., 2019-01-01. (18/13657-1, 16/26040-7)

ESMI, ESTEVAO; DE BARROS, LAECIO CARVALHO; WASQUES, VINICIUS FRANCISCO; KEARFOTT, RB; BATYRSHIN, I; REFORMAT, M; CEBERIO, M; KREINOVICH, V. Some Notes on the Addition of Interactive Fuzzy Numbers. FUZZY TECHNIQUES: THEORY AND APPLICATIONS, v. 1000, p. 12-pg., 2019-01-01. (16/26040-7)

PEDRO, FRANCIELLE SANTO; ESMI, ESTEVAO; DE BARROS, LAECIO CARVALHO. Calculus for linearly correlated fuzzy function using Frechet derivative and Riemann integral. INFORMATION SCIENCES, v. 512, p. 219-237, FEB 2020. (16/26040-7)

BARROS, LAECIO C.; PINTO, NILMARA J. B.; ESMI, ESTEVAO; KEARFOTT, RB; BATYRSHIN, I; REFORMAT, M; CEBERIO, M; KREINOVICH, V. On Fuzzy Optimization Foundation. FUZZY TECHNIQUES: THEORY AND APPLICATIONS, v. 1000, p. 9-pg., 2019-01-01. (16/26040-7)

ESMI, ESTEVAO; SANCHEZ, DANIEL EDUARDO; WASQUES, VINICIUS FRANCISCO; DE BARROS, LAECIO CARVALHO. Solutions of higher order linear fuzzy differential equations with interactive fuzzy values. FUZZY SETS AND SYSTEMS, v. 419, n. SI, p. 122-140, AUG 30 2021. (16/26040-7)

EDUARDO SANCHEZ, DANIEL; ESMI, ESTEVAO; DE BARROS, LAECIO CARVALHO; MIEBACH, ALESSANDRO DONADIO; CECCONELLO, MOISEIS DOS SANTOS. Goodwin economic cycle via p-fuzzy system. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, v. 38, n. 4, p. 12-pg., 2020-01-01. (16/26040-7, 18/10946-2)

ESMI, E.; FLORINDO, J. B.; PEREZ, F.; BARBEITOS, M.; LIU, J; LU, J; XU, Y; MARTINEZ, L; KERRE, EE. An approach to recognize coral species on the coast of Brazil using image analysis and fuzzy associative memories based on equivalent measures. DATA SCIENCE AND KNOWLEDGE ENGINEERING FOR SENSING DECISION SUPPORT, v. 11, p. 8-pg., 2018-01-01. (16/26040-7, 16/16060-0)

SANCHEZ, DANIEL EDUARDO; DE BARROS, LAECIO CARVALHO; ESMI, ESTEVAO. On interactive fuzzy boundary value problems. FUZZY SETS AND SYSTEMS, v. 358, p. 84-96, MAR 1 2019. (16/26040-7)

BUENO SALGADO, SILVIO ANTONIO; DE BARROS, LAECIO CARVALHO; ESMI, ESTEVAO; EDUARDO SANCHEZ, DANIEL. Solution of a fuzzy differential equation with interactivity via Laplace transform. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, v. 37, n. 2, p. 2495-2501, 2019. (16/26040-7, 18/10946-2)

BISCAIA PINTO, NILMARA J.; ESMI, ESTEVAO; WASQUES, VINICIUS FRANCISCO; BARROS, LAECIO C.; KEARFOTT, RB; BATYRSHIN, I; REFORMAT, M; CEBERIO, M; KREINOVICH, V. Least Square Method with Quasi Linearly Interactive Fuzzy Data: Fitting an HIV Dataset. FUZZY TECHNIQUES: THEORY AND APPLICATIONS, v. 1000, p. 13-pg., 2019-01-01. (16/26040-7)