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- 주제어 : t-norm-based addition (검색결과 7 건)
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T-sum of bell-shaped fuzzy intervals
Elsevier 2007 FUZZY SETS AND SYSTEMS Vol.158 No.7
<P><B>Abstract</B></P><P>The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm <I>T</I>. A t-norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation, if this arithmetic operation is closed for this class. It is important to know which t-norms are consistent with a particular type of fuzzy intervals. Recently, Dombi and Győrbíró proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. A result proved by Mesiar on a strict t-norm based shape preserving additions of <I>LR</I>-fuzzy intervals with unbounded support is recalled. As applications, we define a broader class of bell-shaped fuzzy intervals. Then we study t-norms which are consistent with these particular types of fuzzy intervals. Dombi and Győrbíró's results are special cases of the results described in this paper.</P>
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T-sum of sigmoid-shaped fuzzy intervals
Hong, D.H.,Hwang, C.,Kim, K.T. Elsevier science 2007 Information Sciences Vol.177 No.18
The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. A t-norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation, if this arithmetic operation is closed for this class. It is important to know which t-norms are consistent with particular types of fuzzy intervals. Recently, Dombi and Gyorbiro [J. Dombi, N. Gyorbiro, Additions of sigmoid-shaped fuzzy intervals using the Dombi operator and infinite sum theorems, Fuzzy Sets and Systems 157 (2006) 952-963] proved that addition is closed if the Dombi t-norm is used with sigmoid-shaped fuzzy intervals. In this paper, we define a broader class of sigmoid-shaped fuzzy intervals. Then, we study t-norms that are consistent with these particular types of fuzzy intervals. Dombi and Gyorbiro's results are special cases of the results described in this paper.
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Shape preserving additions of LR-fuzzy intervals with unbounded support
홍덕헌 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
Continuous t−norm based shape preserving additions of LR− fuzzy intervals with unbounded support is studied. The case for bounded support, which was a conjecture suggested by Mesiar in 1997, was proved by the author in 2002 and 2008. In this paper, we give a necessary and sufficient conditions for a continuous t−norm T that induces LR−shape preserving addition of LR−fuzzy intervals with unbounded support. Some of the results can be deduced from the results given in the paper of Mesiar in 1997. But, we give direct proofs of the results. Continuous t−norm based shape preserving additions of LR− fuzzy intervals with unbounded support is studied. The case for bounded support, which was a conjecture suggested by Mesiar in 1997, was proved by the author in 2002 and 2008. In this paper, we give a necessary and sufficient conditions for a continuous t−norm T that induces LR−shape preserving addition of LR−fuzzy intervals with unbounded support. Some of the results can be deduced from the results given in the paper of Mesiar in 1997. But, we give direct proofs of the results.
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A note on T-sum of bell-shaped fuzzy intervals
Dug Hun Hong 한국지능시스템학회 2007 한국지능시스템학회논문지 Vol.17 No.6
The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. Dombi and Gy?rbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. Recently, Hong [Fuzzy Sets and Systems 158(2007) 739-746] defined a broader class of bell-shaped fuzzy intervals. Then he study t-norms which are consistent with these particular types of fuzzy intervals as applications of a result proved by Mesiar on a strict t-norm based shape preserving additions of LR-fuzzy intervals with unbounded support. In this note, we give a direct proof of the main results of Hong.
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A note on T-sum of bell-shaped fuzzy intervals
Hong, Dug-Hun Korean Institute of Intelligent Systems 2007 한국지능시스템학회논문지 Vol.17 No.6
The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. Recently, Hong [Fuzzy Sets and Systems 158(2007) 739-746] defined a broader class of bell-shaped fuzzy intervals. Then he study t-norms which are consistent with these particular types of fuzzy intervals as applications of a result proved by Mesiar on a strict f-norm based shape preserving additions of LR-fuzzy intervals with unbounded support. In this note, we give a direct proof of the main results of Hong.
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Strong laws of large numbers for t-norm-based addition of fuzzy set-valued random variables
North-Holland ; Elsevier Science Ltd 2013 FUZZY SETS AND SYSTEMS Vol.223 No.-
This paper proposes a convergence theorem of fuzzy set-valued random variables under addition which is given by the general triangular normed extension principles. Applying the result with the known results of the various types for strong laws of large numbers of fuzzy set-valued random variables, we obtain a few interesting results of the strong laws of large numbers for triangular norm-based addition of fuzzy set-valued random variables. The finding of Teran [Strong law of large numbers for t-normed arithmetics, Fuzzy Sets and Systems 159 (2008) 343-360] is a special case of our results.
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SHAPE PRESERVING ADDITIONS OF LR-FUZZY INTERVALS WITH UNBOUNDED SUPPORT
Hong, Dug-Hun The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
Continuous t-norm based shape preserving additions of LR-fuzzy intervals with unbounded support is studied. The case for bounded support, which was a conjecture suggested by Mesiar in 1997, was proved by the author in 2002 and 2008. In this paper, we give a necessary and sufficient conditions for a continuous t-norm T that induces DR-shape preserving addition of LR-fuzzy intervals with unbounded support. Some of the results can be deduced from the results given in the paper of Mesiar in 1997. But, we give direct proofs of the results.
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