The general α-decomposition problem of fuzzy relations

Yan, Yang; Wang, Xueping

doi:10.1016/j.ins.2007.06.019

Cited by 6 publications

(3 citation statements)

References 26 publications

(32 reference statements)

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“…Di Nola et al (1985e) further discussed the minimal and maximal solutions of the decomposition problem. Vrba (1993) and Yang and Wang (2007) considered the general decomposition of fuzzy relations. Sanchez (1996Sanchez ( , 2004 investigated another type of decomposition problem of fuzzy relations.…”

Section: Miscellaneamentioning

confidence: 99%

A survey on fuzzy relational equations, part I: classification and solvability

Fang

2009

Fuzzy Optim Decis Making

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Fuzzy relational equations play an important role in fuzzy set theory and fuzzy logic systems, from both of the theoretical and practical viewpoints. The notion of fuzzy relational equations is associated with the concept of "composition of binary relations." In this survey paper, fuzzy relational equations are studied in a general lattice-theoretic framework and classified into two basic categories according to the duality between the involved composite operations. Necessary and sufficient conditions for the solvability of fuzzy relational equations are discussed and solution sets are characterized by means of a root or crown system under some specific assumptions.

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Section: Miscellaneamentioning

confidence: 99%

A survey on fuzzy relational equations, part I: classification and solvability

Fang

2009

Fuzzy Optim Decis Making

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“…This depends on the way the data are given and of the use we want to make of them [5,16,17]. The three most common ways are calculating the T-transitive closure of a reflexive and symmetric fuzzy relation, using the Representation Theorem and calculating a decomposable operator from a pair of fuzzy subsets [7,9,13,15].…”

Section: Introductionmentioning

confidence: 99%

The structure of decomposable indistinguishability operators

Recasens

2008

Information Sciences

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“…Fuzzy relations are commonly used, as well as known in many areas where fuzzy sets play a prominent role, cf. [2][3] [5][6] [9]. Specific examples include applications to databases, fuzzy controllers, fuzzy models, classifiers, formation of associations in data mining, and alike.…”

Section: Introductionmentioning

confidence: 99%

Structural expansion of fuzzy relations and its role in interactive system modeling

Pedrycz

Dong

Hirota

2008

2008 IEEE International Conference on Systems, Man and Cybernetics

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This study is concerned with a concept of structural expansion of fuzzy relations. Roughly speaking, when dealing with a finite family of highly dimensional fuzzy relations R i , i = 1,2,…c, the intent is to provide a way of expressing them as Cartesian products of some fuzzy sets and "reduced" fuzzy relations of lower dimensionality. More descriptively, this expansion is regarded as a vehicle to isolate fuzzy sets which are easy to interpret and retain some relational "remainder" which is far less interpretable yet still effective in terms of processing. The expansion process can be performed stepwise by moving toward isolation of more fuzzy sets. We formulate the problem as a certain optimization task where the fuzzy sets obtained in the expansion process minimize an underlying performance index. Two main strategies of structural expansion are discussed. We distinguish between expansion relying on the use of individual variables and collections of variables. While the concept of structural expansion is of a substantial level of generality, in this study, we assume that fuzzy relations are formed through fuzzy clustering (Fuzzy C-Means, FCM to be brief) so that prototypes of the clusters can be directly used in the optimization procedure. Further refinement of fuzzy sets obtained as the result of the expansion is carried out through some logic transformation realized by means of uninorms. The links of structural expansion with rule-based computing with the related issue of interpretability and effectiveness of processing are discussed as well.

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The general α-decomposition problem of fuzzy relations

Cited by 6 publications

References 26 publications

A survey on fuzzy relational equations, part I: classification and solvability

A survey on fuzzy relational equations, part I: classification and solvability

The structure of decomposable indistinguishability operators

Structural expansion of fuzzy relations and its role in interactive system modeling

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