Approximate solutions of fuzzy relational equations

Witold Pedrycz

doi:10.1016/0165-0114(88)90199-6

Approximate solutions of fuzzy relational equations

Witold Pedrycz

Department of Measurements and Control Systems (RAU/RAU2)

R and D Center for Electronic Medical Instr.

Research output: Contribution to journal › Article › peer-review

49 Citations (Scopus)

Abstract

A problem is studied of solving a system of fuzzy relational equations A_i{ring operator}R = B_i for known fuzzy sets A_i and B_i. It is pointed out that this is closely related to a task of discovering a structure of the data set (A_i, B_i), i = 1, 2,..., N, which plays an important role with respect to the solvability and identifiability property of the system of equations. Two main algorithms are proposed: their background is discussed with respect to solvablility of the system of equations. The relevant technical details are clarified in depth.

Original language	English
Pages (from-to)	183-202
Number of pages	20
Journal	Fuzzy Sets and Systems
Volume	28
Issue number	2
DOIs	https://doi.org/10.1016/0165-0114(88)90199-6
Publication status	Published - Nov 1988

Keywords

Decoupling fuzzy sets
Hierarchical clustering
Identifiability
Solvability
Systems of fuzzy relational equations

ASJC Scopus subject areas

Logic
Artificial Intelligence

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10.1016/0165-0114(88)90199-6

Cite this

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AB - A problem is studied of solving a system of fuzzy relational equations Ai{ring operator}R = Bi for known fuzzy sets Ai and Bi. It is pointed out that this is closely related to a task of discovering a structure of the data set (Ai, Bi), i = 1, 2,..., N, which plays an important role with respect to the solvability and identifiability property of the system of equations. Two main algorithms are proposed: their background is discussed with respect to solvablility of the system of equations. The relevant technical details are clarified in depth.

KW - Decoupling fuzzy sets

KW - Hierarchical clustering

KW - Identifiability

KW - Solvability

KW - Systems of fuzzy relational equations

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JF - Fuzzy Sets and Systems

IS - 2

ER -

Approximate solutions of fuzzy relational equations

Abstract

Keywords

ASJC Scopus subject areas

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