On Generating t-Norms (t-Conorms) on Some Special Classes of Bounded Lattices

Emel A?ıcı 한국지능시스템학회 2022 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.22 No.1

In recent years, construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices have been studied extensively. This paper presents the continued study of the construction of t-norms and t-conorms on bounded lattices. We introduce new methods for constructing t-norms and t-conorms on an arbitrary bounded lattice. Furthermore, we provide illustrative examples for clarity. Subsequently, we demonstrate how our new construction methods differ from certain existing methods for the construction of t-norms and t-conorms on bounded lattices. Finally, we reveal that new construction methods can be generalized by induction to a modified ordinal sum for t-norms and t-conorms on an arbitrary bounded lattice.

ON A CLASS OF GENERALIZED TRIANGULAR NORMS

Jebril, Iqbal,Raissouli, Mustapha Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.2

Starting from a t-norm T, it is possible to construct a class of new t-norms, so-called T-generalized t-norm. The purpose of this paper is to describe some properties of this class of generalized t-norms. An algebraic structure as well as a binary relation among t-norms are also investigated. Some open problems are discussed as well.

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>

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.

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.

Applications of interval \textit{t}-norm fuzzy ideals of hemirings with interval valued characteristic function

Sanaa Anjum,Bilal Ahmad,Tasawar Abbas 원광대학교 기초자연과학연구소 2020 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.20 No.1

This communication reports the notions of interval t-norm fuzzy subhemirings, interval t-norm fuzzy ideals, quasi ideals, bi ideals, interior ideals and generalized bi ideals of hemirings with interval valued characteristic function. Some examples of such ideals are also discussed.

INTUITIONISTIC (T, S)-NORMED FUZZY SUBALGEBRAS OF BCK-ALGEBRAS

Kim, Kyung Ho 충청수학회 2007 충청수학회지 Vol.20 No.3

Using t-norm T and s-norm S, we introduce the notion of intuitionistic (T, S)-normed fuzzy subalgebra in BCK/BCI-algebra, and some related properties are investigated.

Yager의 t-norm을 이용한 적응 퍼지제어기

이평기,박상배 위덕대학교 부설 전자기술연구소 1998 전자기술연구소 논문집 : 위덕대 Vol.2 No.1

본 논문에서는 Yager의 t-norm을 이용하는 적응 퍼지제어기를 제안한다. 제안한 방법은 예측출력값을 구할 때 까지의 입출력 정보의 부재로 인한 나쁜 응답성능을 개선할 수 있다. 또한 이 방법은 Yager의 t-norm을 이용하므로써 추론시에 계산상의 복잡성을 피하고 규칙들의 가중치를 구하기 위해 필요한 D_(max) 선정의 어려움을 해결한다. In this paper, we propose a adaptive fuzzy logic controller using Yager's t-norm. The proposed method improves poor performance due to the lack of input and output data to calculate predictive output. Also the proposed method avoids the possible computational overload and alleviates the effort in searching D_(max) value by using Yager's t-norm in calculating weights of rules.

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.

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.