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http://dx.doi.org/10.5391/IJFIS.2008.8.3.170

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

Hong, Dug-Hun (Department of Mathematics, Myongji University)
Publication Information
International Journal of Fuzzy Logic and Intelligent Systems / v.8, no.3, 2008 , pp. 170-174 More about this Journal
Abstract
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.
Keywords
Fuzzy sets; Process; Capacity; Index; Fuzzy arithmetic operations;
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  • Reference
1 Dubois, H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, NewYork, 1980
2 Dubois, H. Prade, Addition of interactive fuzzy numbers, IEEE Transactions on Automatic Control 26 (1981)926-926   DOI
3 Hong, J.-K. Song and H. Y. Do, Fuzzy least-squares linear regression analysis using shape preserving operations, Information Sciences 138 (2001)185-193   DOI   ScienceOn
4 Kolearova, Additive preserving the linearity of fuzzy interval, Tetra Mountains Math. Publ. 6 (1994)75-81
5 H. Ling, Representation of associative functions, Publ. Math. Debrecen 12 (1965)189-212
6 J. Zimmermann, Fuzzy Sets Theory and ItsApplication, Kluwer Academic Publishers, Reading, 1991
7 H. Hong and H. Y. Do, Fuzzy system reliability analysis by the use of $T_w$(the weakest t-norm) on fuzzy number arithmetic operations, Fuzzy Sets and Systems 90 (1997)307-316   DOI   ScienceOn
8 H. Hong, Fuzzy measure for a correlation coefficient of fuzzy numbers under $T_w$(the weakest t-norm)-based fuzzy arithmetic operations, Information Sciences 176 (2006)150-160   DOI   ScienceOn
9 A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, parts 1 and 2, Information Science 8 (1975)199-249, 301-357
10 A. Zadeh, Fuzzy sets, Information and Control 8 (1965)338-353   DOI
11 H. Hong, On shape-preserving additions of fuzzy intervals, Jour. Math. Anal. Apple. 267 (2002)369-376   DOI   ScienceOn
12 E. McCoy, Using performance indexes to monitor production processes, in:Quality Progress, February 1991, pp. 49-55
13 A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, part3,Information Science 9 (1976)43-80
14 H. Hong, A note on $C _pk$ index estimation using fuzzy numbers, European J. Oper. Research 158 (2004)529-532   DOI   ScienceOn
15 H. Hong, Shapep reserving multiplications of fuzzy intervals, Fuzzy Sets and Systems 123 (2001)93-96   DOI   ScienceOn
16 T. Lee, $C _pk$ index estimation using fuzzy numbers, Euporian Journal of Operational Research 129 (2001)683-688   DOI   ScienceOn
17 Mesiar, Shape preserving additions of fuzzy interval, Fuzzy Sets and systems, 86 (1997)73-78   DOI   ScienceOn
18 Alsup, R. M. Watson, Practical statistical Process Control, Van Nostrand Reinhold, NewYork, 1993
19 Dubois, H. Prade, Operations on fuzzy numbers, International Journal of Systems Science 9 (1978)613-626   DOI