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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.

      • 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>

      • KCI등재

        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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