Use of Fuzzy Relation Equations for Evaluating Mathematical Modelling Skills

In the present paper a new assessment approach is developed involving the use of fuzzy relation equations, which are associated with the composition of binary fuzzy relations, for evaluating student mathematical modelling skills. A classroom application and other examples are also presented illustrating our results, and useful conclusions are obtained.

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FUZZY RELATION CALCULUS IN THE COMPRESSION AND DECOMPRESSION OF FUZZY RELATIONS

International Journal of Image and Graphics ◽

10.1142/s0219467802000871 ◽

2002 ◽

Vol 02 (04) ◽

pp. 617-631 ◽

Cited By ~ 10

Author(s):

VINCENZO LOIA ◽

WITOLD PEDRYCZ ◽

SALVATORE SESSA

Keyword(s):

Lossy Compression ◽

Fuzzy Relation ◽

Fuzzy Relations ◽

Triangular Norm ◽

Fuzzy Matrix ◽

Fuzzy Relation Equations

We firstly review some fundamentals of fuzzy relation calculus and, by recalling some known results, we improve the mathematical contents of our previous papers by using the properties of a triangular norm over [0,1]. We make wide use of the theory of fuzzy relation equations for getting lossy compression and decompression of images interpreted as two-argument fuzzy matrices.The same scope is achieved by decomposing a fuzzy matrix using the concept of Schein rank. We illustrate two algorithms with a few examples.

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The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic Systems

Journal of Applied Mathematics ◽

10.1155/2014/459508 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Shan Zhao ◽

Hongxing Li

Keyword(s):

Fuzzy Logic ◽

Fuzzy Reasoning ◽

Fuzzy Relation ◽

Fuzzy Relations ◽

Fuzzy Logic Systems ◽

Fuzzy Relation Equations ◽

Logic Systems ◽

Special Case

Type-2 fuzzy reasoning relations are the type-2 fuzzy relations obtained from a group of type-2 fuzzy reasonings by using extended t-(co)norm, which are essential for implementing type-2 fuzzy logic systems. In this paper an algorithm is provided for constructing type-2 fuzzy reasoning relations of SISO type-2 fuzzy logic systems. First, we give some properties of extended t-(co)norm and simplify the expression of type-2 fuzzy reasoning relations in accordance with different input subdomains under certain conditions. And then different techniques are discussed to solve the simplified expressions on the input subdomains by using the related methods on solving fuzzy relation equations. Besides, it is pointed out that the computation amount level of the proposed algorithm is the same as that of polynomials and the possibility of applying the proposed algorithm in the construction of type-2 fuzzy reasoning relations is illustrated on several examples. Finally, the calculation of an arbitrary extended continuous t-norm can be obtained as the special case of the proposed algorithm.

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