Hexagon Hesitant Fuzzy Multi – Attribute Decision Making Based On TOPSIS

In this paper hexagon hesitant fuzzy set is used to solve the higher order uncertainties with TOPSIS method. Hexagon Hesitant Fuzzy Multi Attribute Decision Making problems faced by the farmer who plant monsoon crops in Villupuram District.


INTRODUCTION
Lotfi A. Zadeh introduce Fuzzy Set Theory in 1965 and further developed by Dubosis and Prade, R.Yager Mizomoto, J.Buckly and many others. The most useful representation in fuzzy is membership function. Conception of fuzzy number and fuzzy arithmetic is first developed by Zadeh [8] and Dubosis and Prade [2]. After the familiarization of fuzzy set Lotfi A.Zadeh bring in the concept of fuzzy number in 1975 [7]. It is special type of fuzzy set and mainly used to quantity qualitative and linguistic variable which are uncertain and vague in nature. Different type of fuzzy set [0,1] are explained to clear the vagueness. A fuzzy number is a number the estimation are not exactly correct in case of single valued function. Ranking Fuzzy Number revels leading part in decision making. The main problem in decision making is electing one among the collection. The decision maker should use fuzzy number in particular parameter to avoid non-reliable values when the parameter value is more than one. To make this happen Zadeh [1965] [4] introduced fuzzy set theory. The subject has become an interesting bough of Pure and Applied Science. Solving of Multi -Attribute Decision Making is the most practical application. Hesitant Fuzzy Set is initiated by Torra [6] this allows a factor be a set of different estimation between 0 and 1. Wang Et Al furnishes a prominent near by with HFSs to solve MCDM problems.In this paper, an addition has been made and developed near the proper the Hexagonal Hesitant Fuzzy Set (HHFS) come by means of decision making bundle TOPSIS. The difficult situation met by the cultivator in Villupuram District are scrutinized by means of our recently made Hexagonal Hesitant Fuzzy Multi -Attribute Decision Making (HHF -MADM) method.This topic has been proceeded in the given below patten. The theory of HFS, HHFSs and some of its is a set of certain values in [0,1], indicating the possible enrollment steps of the Element x ∈ to the set A.

Definition: Fuzzy number
To whole set of real numbers R is defined by a fuzzy set by the enrollment function ( ) satisfied normality convexity and piecewise continuity.

Definition: Hexagon Hesitant fuzzy Set
Let X be a firmed set, then a Hexagon Hesitant fuzzy Set (H h FS) D on X is explained as: ).

Definition: Hesitant Multiplicative Aggregation
To quantity the inborn stating granted by the decision maker, we employ Saaty's 1-9 scale with its relative meaning.

HEXAGON HESITANT FUZZY ALGORITHM BASED ON TOPSIS
Hwang and Yoon introduced the Multi Attributes Decision Making and its application from which a familiar execution for rank performance through resemblance to perfect clarification (TOPSIS) is applied in this paper. A basic precept is that to choose the possibility under hesitant fuzzy neighborhood. This approach implies following steps: Step 1: where W i ∈ [0,1] and ∑ = 1 For every assign according to their consequence over the problem, the hesitant value is given as Step 2: The degree can be calculated by the positive ideal and negative ideal, Step 4: The relative togetherness of different i A can be determined by the rule Step 5: Order the possibility agreeing to the cognate togetherness to the positive ideal and negative ideal clarification.

Hexagon Hesitant Fuzzy Function:
Johnson Savarimuthu .S and Kowsalya . S researched the dilemma faced the farmers who plant monsoon product in the Villupuram District. In this paper ,we broaden our research by investigation kharif crops farming in the same area. In Villupuram District, it has been noticed that the farmer reveal a much attention in vegetating kharif crops like Paddy ,Maize, Groundnut, Sugarcane, Turmeric ,Cotton, etc., kharif crops farming depends on natural source like rain and water reserves like river ,tanks and wells. Water sources of this district like Vidur , Sathanur and Komuki have rested serving water they perform only during rainy span. .

Figure3. Depth To Water Level
Water scarcity have become lot in this District due to collapse in the periodical rains. Scheduled to regular electricity failure tunnel hole cannot be operated. Because of this farmers has to buy diesel to operate diesel Engines.It is tough to buy loans from private bank and pay back their debts.

Alternatives
The major kharif crops cultivated in Villupuram District. We acquired these yield as our preferences. A 1

Attributes
We gathered some great problems faced by the through investigation and merged them into six major attributes and estimated into two forms, namely; (i) Profit Category (Distinguishing trait in universe) (ii) Expense Category (Distinguishing trait in universe) X 1 . Crop failure (Profit Category) -Crop failure results in drying of crop and uncapability to results the standing crops due to water shortage. X 2 . Crop debt (Expense Category) -Funds borrowing from personal money lenders, farming arrears to gather expenditure extends the payment.