• 제목/요약/키워드: Zadeh's extension principle

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A note on T-sum of bell-shaped fuzzy intervals

  • Hong, Dug-Hun
    • 한국지능시스템학회논문지
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    • 제17권6호
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    • pp.804-806
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    • 2007
  • 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.

퍼지 가중 평균을 이용한 다중 센서 데이타 융합 (Multisensor Data Combination Using Fuzzy Weighted Average)

  • 김완주;고중협;정명진
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 1993년도 하계학술대회 논문집 A
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    • pp.383-386
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    • 1993
  • In this paper, we propose a sensory data combination method by a fuzzy number approach for multisensor data fusion. Generally, the weighting of one sensory data with respect to another is derived from measures of the relative reliabilities of the two sensory modules. But the relative weight of two sensory data can be approximately determined through human experiences or insufficient experimental data without difficulty. We represent these relative weight using appropriate fuzzy numbers as well as sensory data itself. Using the relative weight, which is subjective valuation, and a fuzzy-numbered sensor data, the fuzzy weighted average method is used for a representative sensory data. The manipulation and calculation of fuzzy numbers can be carried out using the Zadeh's extension principle which can be approximately implemented by the $\alpha$-cut representation of fuzzy numbers and interval analysis.

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Cpk Index Estimation under Tw (the weakest t-norm)-based Fuzzy Arithmetic Operations

  • Hong, Dug-Hun
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제8권3호
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    • pp.170-174
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    • 2008
  • The measurement of performance of a process considering both the location and the dispersion of information about the process is referred to as the process capacity indices (PCIs) of interest, $C_{pk}$. This information is presented by the mean and standard deviation of the producing process. Linguistic variables are used to express the evaluation of the quality of a product. Consequently, $C_{pk}$ is defined with fuzzy numbers. Lee [Eur. J. Oper. Res. 129(2001) 683-688] constructed the definition of the $C_{pk}$ index estimation presented by fuzzy numbers and approximated its membership function using the "min" - norm based Zadeh's extension principle of fuzzy sets. However, Lee's result was shown to be invalid by Hong [Eur. J. Oper. Res. 158(2004) 529-532]. It is well known that $T_w$ (the weakest t-norm)-based addition and multiplication preserve the shape of L-R fuzzy numbers. In this paper, we allow that the fuzzy numbers are of L-R type. The object of the present study is to propose a new method to calculate the $C_{pk}$ index under $T_w-based$ fuzzy arithmetic operations.