International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 11 Issue: 08 | Aug 2024
p-ISSN: 2395-0072
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THE FUZZY ARITHMETIC OPERATIONS FOR REVERSE ORDER HEPTADECAGONAL FUZZY NUMBERS USING ALPHA CUTS TO HANDLING UNCERTAINTY FLEXIBLE STRATEGY G Mohana1, M Umamaheswari2 1 Research Scholar, Department of Mathematics, INFO Institute of Engineering Kovilpalayam, Coimbatore, Tamil
Nadu, India
2 Assistant Professor, Department of Mathematics, INFO Institute of Engineering Kovilpalayam, Coimbatore, Tamil
Nadu, India. --------------------------------------------------------------------------***----------------------------------------------------------------------Abstract In this paper introduces the new shape of fuzzy numbers is developed and named as Reverse order Heptadecagonal Fuzzy Numbers. This paper defines membership functions and Arithmetic Operations for Reverse order Heptadecagonal Fuzzy Numbers using an interval of Alpha cuts. Some prepositions for instance maximum and minimum Operations on Fuzzy equations; alpha cuts and Reverse order Fuzzy numbers have been introduced and proved. Numerical examples for this Arithmetic Operations are also given. Keywords: Fuzzy Number, Heptadecagonal Fuzzy Number, Reverse Order Heptadecagonal Fuzzy Number, Fuzzy Arithmetic Operations, Alpha –cut.
I.INTRODUCTION In modern world we may come across many uncertainty cases. The fuzzy set theory is to find out the best solution to the real-world problems where available data and information are not exact, in that situation fuzzy numbers can be applied in many fields such as control system, decision making and operation research etc This paper introduces Reverse order Heptadecagonal, RoHDFN with its membership functions. It has got several applications in real life. In case of Heptadecagonal fuzzy number one is the maximum characterizing supporting interval but in case of decagonal we have a flat segment of ά=1which is the characterizing supporting interval. The classification of fuzzy number and properties related to it, have paved the way for developing new notions. . Vipin Bala, Jitender Kumar* and M. S. Kadyan introduces Heptadecagonal Fuzzy Numbers. In the beginning, Zadeh (1965) studied the idea of fuzzy set theory. Ruth Naveena and Rajkumar (2019) discussed reverse order pent decagonal, nanogonal and decagonal fuzzy numbers with their arithmetic operations. The introduction section offers specification for the present work by addressing the limitations of traditional fuzzy number representations and the need for more nuanced and flexible approaches. It establishes the significance of introducing Reverse order Heptadecagonal Fuzzy Numbers and their utility in addressing complex and ambiguous uncertainty scenarios. This section also sets the stage for the innovative aspects of the research by highlighting the limitations of existing methods and the motivation for exploring new territory.
II. DEFINITIONS Definition 2.1 A fuzzy set is characterized by a membership function maps elements of a given universal set X to the real numbers in [0,1]. A fuzzy set Ñ in universal set Y is defined as Ñ = {(y, Ω Ñ(y))/y Y}. Ω Ñ: Y [0, 1]. Ω Ñ(y) is called the membership value y Y of in the fuzzy set Ñ.
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