Approximate Nonnegative Symmetric Solution of Fully Fuzzy Systems Using Median Interval Defuzzification
We propose an approach for computing an approximate nonnegative symmetric solution of some fully fuzzy linear system of equations, where the components of the coefficient matrix and the right hand side vector are nonnegative fuzzy numbers, considering equality of the median intervals of the left and...
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doaj-fff65c6eb0444428aaf2fa8c73c0a3292020-11-24T21:35:54ZengTaylor & Francis GroupFuzzy Information and Engineering1616-86582014-09-016333135810.1016/j.fiae.2014.12.005Approximate Nonnegative Symmetric Solution of Fully Fuzzy Systems Using Median Interval DefuzzificationR. Ezzati0S. Khezerloo1N. Mahdavi-Amiri2Z. Valizadeh3Department of Mathematics, College of Basic Sciences, Karaj Branch, Islamic Azad University, Alborz, IranDepartment of Mathematics, Islamic Azad University -South Tehran Branch, Tehran, IranFaculty of Mathematical Sciences, Sharif University of Technology, 1458-889694, Tehran, IranDepartment of Mathematics, Faculty of Basic Sciences, Roudehen Islamic Azad University, 189 Roudehen, Tehran, IranWe propose an approach for computing an approximate nonnegative symmetric solution of some fully fuzzy linear system of equations, where the components of the coefficient matrix and the right hand side vector are nonnegative fuzzy numbers, considering equality of the median intervals of the left and right hand sides of the system. We convert the m×n fully fuzzy linear system to two m×n real linear systems, one being related to the cores and the other being concerned with spreads of the solution. We propose an approach for solving the real systems using the modified Huang method of the Abaffy-Broyden-Spedicato (ABS) class of algorithms. An appropriate constrained least squares problem is solved when the solution does not satisfy nonnegative fuzziness conditions, that is, when the obtained solution vector for the core system includes a negative component, or the solution of the spread system has at least one negative component, or there exists an index for which the component of the spread is greater than the corresponding component of the core. As a special case, we discuss fuzzy systems with the components of the coefficient matrix as real crisp numbers. We finally present two computational algorithms and illustrate their effectiveness by solving some randomly generated consistent as well as inconsistent systems.http://www.sciencedirect.com/science/article/pii/S1616865814000442Fully fuzzy systemsFuzzy numbersABS algorithmsMedian interval defuzzification |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
R. Ezzati S. Khezerloo N. Mahdavi-Amiri Z. Valizadeh |
spellingShingle |
R. Ezzati S. Khezerloo N. Mahdavi-Amiri Z. Valizadeh Approximate Nonnegative Symmetric Solution of Fully Fuzzy Systems Using Median Interval Defuzzification Fuzzy Information and Engineering Fully fuzzy systems Fuzzy numbers ABS algorithms Median interval defuzzification |
author_facet |
R. Ezzati S. Khezerloo N. Mahdavi-Amiri Z. Valizadeh |
author_sort |
R. Ezzati |
title |
Approximate Nonnegative Symmetric Solution of Fully Fuzzy Systems Using Median Interval Defuzzification |
title_short |
Approximate Nonnegative Symmetric Solution of Fully Fuzzy Systems Using Median Interval Defuzzification |
title_full |
Approximate Nonnegative Symmetric Solution of Fully Fuzzy Systems Using Median Interval Defuzzification |
title_fullStr |
Approximate Nonnegative Symmetric Solution of Fully Fuzzy Systems Using Median Interval Defuzzification |
title_full_unstemmed |
Approximate Nonnegative Symmetric Solution of Fully Fuzzy Systems Using Median Interval Defuzzification |
title_sort |
approximate nonnegative symmetric solution of fully fuzzy systems using median interval defuzzification |
publisher |
Taylor & Francis Group |
series |
Fuzzy Information and Engineering |
issn |
1616-8658 |
publishDate |
2014-09-01 |
description |
We propose an approach for computing an approximate nonnegative symmetric solution of some fully fuzzy linear system of equations, where the components of the coefficient matrix and the right hand side vector are nonnegative fuzzy numbers, considering equality of the median intervals of the left and right hand sides of the system. We convert the m×n fully fuzzy linear system to two m×n real linear systems, one being related to the cores and the other being concerned with spreads of the solution. We propose an approach for solving the real systems using the modified Huang method of the Abaffy-Broyden-Spedicato (ABS) class of algorithms. An appropriate constrained least squares problem is solved when the solution does not satisfy nonnegative fuzziness conditions, that is, when the obtained solution vector for the core system includes a negative component, or the solution of the spread system has at least one negative component, or there exists an index for which the component of the spread is greater than the corresponding component of the core. As a special case, we discuss fuzzy systems with the components of the coefficient matrix as real crisp numbers. We finally present two computational algorithms and illustrate their effectiveness by solving some randomly generated consistent as well as inconsistent systems. |
topic |
Fully fuzzy systems Fuzzy numbers ABS algorithms Median interval defuzzification |
url |
http://www.sciencedirect.com/science/article/pii/S1616865814000442 |
work_keys_str_mv |
AT rezzati approximatenonnegativesymmetricsolutionoffullyfuzzysystemsusingmedianintervaldefuzzification AT skhezerloo approximatenonnegativesymmetricsolutionoffullyfuzzysystemsusingmedianintervaldefuzzification AT nmahdaviamiri approximatenonnegativesymmetricsolutionoffullyfuzzysystemsusingmedianintervaldefuzzification AT zvalizadeh approximatenonnegativesymmetricsolutionoffullyfuzzysystemsusingmedianintervaldefuzzification |
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1725943442683461632 |