SELECTION OF AGRICULTURAL AIRCRAFT USING DODECAGONAL FUZZY RELATIONAL MAPPING(DgFRM)

Transcription

1 Volume 120 No , ISSN: (on-line version) url: SELECTION OF AGRICULTURAL AIRCRAFT USING DODECAGONAL FUZZY RELATIONAL MAPPING(DgFRM) A. Rajkumar 1, Vivek M 2, Aravinda Narayanan G 3 1 Assistant prof (S.G), 2,3 UG Student 1 Department of Mathematics, 2,3 Aeronautical, Hindustan Institute of Technology and Science, Chennai, India. June 25, 2018 Abstract The main purpose of agricultural aircraft is to spray pesticides and fertilizers in the farming area or lands. Agricultural aircraft are being used all over the world for farming. We are doing a study about the ranking of the best performance of agricultural aircraft by considering several parameters based upon linguistic principles of their qualities. UsingDodecagonal fuzzy numbers and by the help of Fuzzy RelationalMapping, the linguistic parameterization is made. The best performance of the agricultural aircraft can be attained by analyzing the result. Key Words: Agricultural aircraft, FRM, Dodecagonal Fuzzy Number, Ranking method, Best performance aircraft

2 1 INTRODUCTION An agricultural aircraft is built for the development of agriculture and it also reduces the work of the farmers. For hydro seeding, it is mostly and widely used. Crop duster or top duster is an aerial application of the agricultural aircraft. In an agricultural aircraft, mostly turboprop engines are used. In the United States and European countries, it was used widely. They used stereo typically small and simple aircraft for the agriculture purpose. The aircraft which were used by these countries will have spraying systems in the trailing edges and wind turbines usually drive pumps. Whereas in New Zealand and Australia they make use of high power and larger aircraft for the agriculture purpose because the farmlands in these countries are very big. The agricultural aircraft have been listed below from various manufacturers and designers. This list includes both active and retired aircraft. 1. Air Tractor AT 402B. 2. Fletcher FU Embraer EMB 202 Ipanema. 4. PZL M18 Dromader. 5. Antonov AN 2. This comparison would bring us the result in the ranking of best performance agricultural aircraft. 2 DEFINITIONS OF PARAMETERS: Definition 1: Hopper Capacity: Hoppers are made up of steels. It is a large pyramidal shape container which is used to carry the chemical products in the aircraft

3 Definition 2: Take-off Distance: For an agriculture aircraft, the take-off distance is very important performance. Here the runway length is minimal which is imperfect, instead of landing distance, it would decide to insert this parameter. Definition 3: Fuel Capacity: Fuel capacity is very important for an agriculture aircraft as it carries more load it consumes more amount of fuel. It is an amount of fuel in the aircraft fuel tank can carry. Definition 4: Thrust Produced: A thrust is also known as a force which moves the aircraft forward. To overcome the drag of an aircraft to the weight of a rocket, thrust is used. Thrust is generated by aircraft engines through some kind of propulsion. Definition 5: Aspect Ratio: It is the ratio between wing area and wing span.it also defined as the ratio of it sizes in different dimensions. Definition 6: A rate of Climb: It is the vertical speed of an aircraft. The rate of positive altitude changes with respect to distance and time. Definition 7: Range: It is the difference between small and large values. In an aircraft, the range is the maximum distance which can fly between take-off and landing by fuel capacity. Definition 8: Empty weight: The weight of the structure and other equipment are included

4 before adding of items for the operation. Definition 9: Maximum Speed: Maximumspeed is more than the cruise speed. The maximum potential of an aircraft is the maximum speed of an aircraft where all the forces acting on the aircraft will be equilibrium. 3 DODECAGONAL FUZZY RELATIONAL MAPPING(DgFRM) 1. A (DgFRM)signifies thecausal connection between spaces, domain space I and Range space T as nodes and causalities in the form of a certain graph from I to T called relations. 2. Let D g I 1... D g I n can be taken as the nodes of domain space I and D g T 1... D g T m be the nodes of the range space T. Let the matrix Q be dened as: Q = (q ij ) where q ij is the pronunciation of the certain edge I i T j (or I j T i ), Q is called the relational matrix of the DgFRMs. 3. Let A = (a 1...a n ), a i ɛ {0,1}. A is called the position vector of the domain space. Similarly let B = (b 1...b m ), b i ɛ{0, 1}. B is called the position vector of the range space When ai = 0or 1, if a i is OFF or ONindividually, for i = 1...n. Likewise b i = 0or1 if bi is OFF or ON individually, for i = 1...m. 4. Let Dg(M) be the adjacency matrix. The hidden pattern should be found out while D g I 1 is switched ON.The statics must pass through the relation matrix M, when input is tending as the vector A1 = (1,0,...,0) by multiplying A i by the dodecagonal matrix M. 5. If the constancy state of this dynamic system is an special state vector, then it is called a xed point. this active system is started by switching on D g I 1 and undertake that the DgFRMs completes down with T 1 and T m ON

5 Step 1: Let D g I 1...D g I n be the nodes of the domain space I of an DgFRM and D g T 1...D g T m be the nodes of the range space T of a DgFRM. Let D g (M) be the related adjacency matrix. Step 2: The hidden pattern should be found out while D g I 1 is switched ON.The statics must pass through the relation matrix M, when input is tending as the vector A1= (1, 0.0) by multiplying Ai by the dodecagonal matrix M. Step 3: The rst node is taken ON as A i = (1,0,...,0) gets a weight of attributes of Dodecagonal matrix which is signied as AiDg(M) weight. Step 4: The standard of pieces A i D g (M) average taken by adding the weight of characteristics. Step 5: The commen cement evolution activity is marked by( ) ie., A 1 D g (M) max weight that is re-create ai by 1 if a i is the maximal weight of the dodecagonal node (i.e.,a i = 1) on the other side a i by 0 (ie.,a i = 0) that is denoted by A2. Step 6: Thus the dynamical system ends with A 1 D g (M) max(weight) = A2HD(M)max(weight) says stability state of this active system is called the hidden pattern. Step 7: This is continued until we get the restriction cycle or a fixed point. TABLE I Linguistic Variables of Agricultural aircraft 4 LINGUISTIC VALUES OF DODECAGO- NAL FUZZY NUMBER Very Low development (0.2,0.4,0.6,0.8,1.0,1.2,1.4,1.6,1.8,2.0,2.2,2.4) Low development (1.4,1.6,1.8,2.0,2.2,2.4,2.6,2.8,3.0,3.2,3.4,3.6) Medium (2.6,2.8,3.0,3.2,3.4,3.6,3.8,4.0,4.2,4.4,4.6,4.8)

6 High development (3.8,4.0,4.2,4.4,4.6,4.8,5.0,5.2,5.4,5.6,5.8,6.0) Very High development (5.0,5.2,5.4,5.6,5.8,6.0,6.2,6.4,6.6,6.8,7.0,7.2) The Data given below is obtained from the Decision maker(experts) using the dodecagonal fuzzy number

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9 5 Calculation Ranking of the Aircraft s D g A 1, D g A 2, D g A 3, D g A 4, D g A 5 for the first conditions

10 Similarly, all the steps from P 2 to P9arrives and the average values are used in the following table. TABLE II The weight of the aircraft DDA 1, DDA 2, DDA 3, DDA 4, DDA 5 for the first criteria

11 Similarly, the weight aircraft DDA 1, DDA 2, DDA 3, DDA 4, DDA 5 for the secondninth criteria are found and tabulated in the final ranking table. To find the overall rank of the aircraft taken, we have to take the average of all the ranks of all the aircraft DDA 1, DDA 2, DDA 3, DDA 4, DDA 5 for all criteria. RANK 1:Antonov AN 2. RANK 2:Air Tractor AT 402B. RANK 2: Fletcher FU24. RANK 3:Embraer EMB 202 Ipanema. RANK 4: PZL M18 Dromader. The ranks are given by considering the average by ascending order. 6 CONCLUSION From the above result, wehereby submit that Antonov An2 is the best aircraft according to our thesis. Hence, we are proud to voice that the Antonov An2 aircraft has the best performance comparing to all other aircraft parameters mentioned above by using the Dodecagonal Fuzzy Relational Mapping(DgFRM). References [1] Gabriel Scherer Schwening, Alvaro Martins Abdalla. Selection of agricultural aircraft using AHP and TOPSIS methods in Fuzzy Environment. proceedings in 29th congress of the international council of the Aeronautical Sciences. [2] Dag deviren M, Yvuz S and Nevzat M. Weapon. selection using AHP and TOPSIS methods in Fuzzy Environment. Expert systems with applications,

12 [3] F.T. Jane. Jane s All World Aircarft, [4] P.Selvam, A. Rajkumar. Dodecagonal Fuzzy number (DDFN) IJCTA, [5] A.Victor Devadoss, N.Jose Parvin Praveena. A Study Of Decision Making Problems Using hexadecagonal FuzzyRelational Maps (HDFRMS).Inter national Journal of Pure and Applied Mathematics, [6] W B Vasantha Kandasamy, Florentin Smarandache. Fuzzy cognitive map and Neutroscophic cognitive map

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