Triangular Fuzzy Numbers Multiplication: QKB method
Publish place: Fuzzy Optimization and Modeling Journal، Vol: 3، Issue: 2
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_FOMJ-3-2_004
تاریخ نمایه سازی: 20 مرداد 1400
Abstract:
Triangular Fuzzy numbers (TFNs) are vast and common representation of fuzzy data in applied sciences. Multiplication is a very indispensable operation for fuzzy numbers. It is necessary to decompose fuzzy systems such as fully triangular fuzzy regression models where the unknown and unrestricted triangular fuzzy coefficients multiplied by known TFNs as data input. Tens of research works and application of triangular fuzzy regression have dealt with degenerated existing multiplication expressions. This paper highlighted the drawbacks of such expressions and propounded a simple method (named as QKB method). The method is a straightforward method where there is no exaggeration for multiplying two or more TFNs. It respects the trinity-order condition of a TFN where the number without it cannot be considered as a TFN. Besides, it is suitable for known and unknown multiplied TFNs with conserving homogeneity principle such that the resultant of two symmetric TFNs has to be symmetric either, to prove that a proposed new membership function for a TFN (named quantified membership function) has been used. Illustrative examples have shown the soundness of the proposed method and the drawbacks of existing expressions. Furthermore, its expression of multiplication is more efficient than other expression on the needs of computation.
Keywords:
Triangular fuzzy numbers (TFNs) , Trinity order condition , homogeneity principle , quantified membership function
Authors
Abdullah Al-Qudaimi
Hodeidah University
Kuljeet Kaur
École de Technologie Supérieure (Université du Québec), Montréal, Canada
Shahid Bhat
Thapar Institute of Engineering and Technology, Patiala, India