Sains Malaysiana 40(6)(2011): 643–650

Incorporating Optimisation Technique into Zadeh’s Extension Principle for Computing Non-Monotone Functions with Fuzzy Variable

(Menggabungkan Teknik Pengoptimuman ke dalam Prinsip Perluasan Zadeh untuk Komputeran Fungsi-Fungsi Tak Bermonoton dengan Pembolehubah Kabur)

M. Z. Ahmad*

Institute for Engineering Mathematics, Universiti Malaysia Perlis, 02000 Kuala Perlis, Perlis, Malaysia

M. K. Hasan

School of Information Technology, Faculty of Technology and Information Science, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

Received: 23 February / Accepted: 1 June 2010

ABSTRACT

This paper proposes a new computational method for computing non-monotone functions that take a fuzzy interval as their arguments. The proposed method represents an implementation of optimisation technique into Zadeh’s extension principle. By taking into account the dependency problem that exists in fuzzy environment, the proposed method can avoid the effect of overestimation in computation. This problem usually arises when the same fuzzy interval is computed separately in fuzzy interval computation. The proposed method is simple to use and can be implemented in many practical applications. In order to show the capability of the proposed method, several non-monotone functions with trapezoidal fuzzy intervals are studied.

Keywords: Fuzzy set; optimisation; Zadeh’s extension principle

ABSTRAK

Makalah ini mencadangkan satu kaedah komputasi baru untuk komputeran fungsi-fungsi tak bermonoton yang mengambil selang kabur sebagai pembolehubahnya. Kaedah yang dicadangkan merupakan suatu perlaksanaan teknik pengoptimuman di dalam prinsip perluasan Zadeh. Dengan mengambilkira masalah kebergantungan yang wujud di dalam persekitaran kabur, kaedah yang dicadangkan ini dapat mengelakkan masalah terlebih anggaran dalam pengiraan. Masalah ini biasanya wujud apabila selang kabur yang sama dikira secara berasingan di dalam komputasi selang kabur. Kaedah ini mudah untuk dilaksanakan dan dapat diterapkan di dalam pelbagai penggunaan praktikal. Untuk menunjukkan kebolehan kaedah yang dicadangkan, beberapa fungsi tak bermonoton dengan selang kabur trapezoid dikaji.

Kata kunci: Pengoptimuman; prinsip perluasan Zadeh; set kabur

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*Corresponding author; email: mzaini@unimap.edu.my