• Honam Mathematical Journal
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• v.27 no.4
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• pp.543-550
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• 2005

Some properties of a transitive fuzzy matrix are examined and the canonical form of the transitive fuzzy matrix is given using the properties. As a special case an open problem concerning idempotent matrices is solved. Thus we have the same result in a intuitionistic fuzzy matrix theory. In our results a nilpotent intuitionistic matrix and a symmetric intuitionistic matrix play an important role. We decompose a transitive intuitionistic fuzzy matrix into sum of a nilpotent intuitionistic matrix and a symmetric intuitionistic matrix. Then we obtain a canonical form of the transitive intuitionistic fuzzy matrix.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.207-220
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• 2004

Necessary and sufficient conditions are given for the regularity of block triangular fuzzy matrices. This leads to characterization of idem-potency of a class of triangular Toeplitz matrices. As an application, the existence of group inverse of a block triangular fuzzy matrix is discussed. Equivalent conditions for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived. Further, fuzzy relational equations consistency is studied.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.301-310
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• 2011

In this paper, we construct the sets of fuzzy matrix pairs. These sets are naturally occurred at the extreme cases for the zero-term rank inequalities derived from the multiplication of fuzzy matrix pairs. We characterize the linear operators that preserve these extreme sets of fuzzy matrix pairs.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.401-412
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• 2003

Using the idea of "intuitionistic fuzzy set" [l, 2, 3], we defined the concept of intuitionistic fuzzy matrices as a natural generalization of fuzzy matrices. And we introduced and studied the determinant of square intuitionistic fuzzy matrices [4]. In this paper, we investigate the adjoint of square intuitionistic fuzzy matrices.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.473-486
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• 2008

In this paper we generate a fuzzy dynamical matrix Lyapunov system and obtain a sufficient condition for the observability of this system.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.615-624
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• 2014

We study special types of matrices. The involutary fuzzy matrices are important in various applications and have many interesting properties. Using the graphical method, we have the zero patterns of involutary fuzzy matrix, that is, involutary Boolean matrices. And we give the construction of all involutary fuzzy matrices for some dimensions and suggest the canonical form of involutary fuzzy matrix.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.3
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• pp.155-162
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• 2012

This study proposes an integrated approach that uses both a fuzzy service FMEA (failure mode and effect analysis) and HOQ (house of quality) matrix algebra in designing and improving a service system. The fuzzy service FMEA methodology applies the customer satisfaction to the fuzzy RPN model. We fuzzify only the service satisfaction that consist in two failure factors, intangible service and tangible service, to more effectively assess the customer satisfactions on service encounters. Proposed fuzzy service satisfactions with triangle membership function are defuzzified by using the Fuzzy Inference System, and these are eventually identified the ranks on the potential fail points. HOQ matrices are constructed from cause-effect relationships. It is possible for these relationship matrix to find a linear approximation solution on the engineering attributes. Thus, in order to demonstrate how the proposed methods work, practical sample of the A/S part in S Electronic Co. provides for the ranking of the engineering attributes which has been successfully implemented.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1133-1136
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• 1993

Fuzzy algorithm is essentially nondeterministic, but to guarantee the stable control the fuzzy control program should be deterministic in practice. Fuzzy controllers with matrix representation is very simple in construction and very fast in computation. The value of the matrix is not adequate at the first place, but can be modified by using the neural networks. We apply the simple heuristic techniques to modify the matrix successfully.

• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.3
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• pp.218-227
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• 2000

In this paper, we present a new fuzzy information retrieval method based on thesaurus. In the proposed method th thesaurus is represented by a fuzzy linguistic matrix, where the elements in fuzzy linguistic matrix represent a qualitative linguistic values between terms. In the fuzzy linguistic matrix, there are three kinds of fuzzy relationships between terms, i.e., similar relation, hierarchical relation, and associative relation. The implicit fuzzy relationships between terms are inferred by the transitive closure of the fuzzy linguistic matrix based on fuzzy theory. And the proposed method has the capability to deal with a qualitative linguistic weights in a query and in indexing of information items to reflect qualitative measure of human based on vague and uncertain decisions rather than a quantitiative measure. Therefore the proposed method is more flexible than the ones presented in papers[1-3]. Moreover our method is more effectual of time than the ones presented in papers[1-3] because we use a fuzzy linguistic matrix and AON (Associate Ordinary Number) values in query evaluation process. As a result, the proposed method allows the users to perform fuzzy queries in a more flexible and more intelligent manner.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.187-198
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• 2014

The fuzzy idempotent matrices are important in various applications and have many interesting properties. Using the upper diagonal completion process, we have the zero patterns of fuzzy idempotent matrix, that is, Boolean idempotent matrices. And we give the construction of all fuzzy idempotent matrices for some dimention.