Mcdm WASPA in a Neutrosophic Environment Applied to Optimization of the Parameters for Minimization of Surface Roughness and Machining Deformation in Milling of Al Alloy Thin‑Walled Parts.

Hiovanis Castillo Pantoja ¹, Ángel Eugenio Infante Haynes ¹ .

¹  University of Holguin, Cuba, sotosilva74@gmail.com

¹  University of Holguin, Cuba, ehaynes@uho.edu.cu

 

 

*  Correspondence: sotosilva74@gmail.com

Abstract

The following research shows a methodology that combines the multicriteria method WASPAS and Neutrosophic, which seeks to improve decision making within the planning processes in machine shops. With WASPAS the best alternative is selected and Neutrosophic offers us the advantage of driving the concept of uncertainties and neutralities, and with it the values of the input variables for high speed machining to manufacture the rectangular piece of aluminum alloy 5083. With the evaluation of the criteria, when applying the method it is obtained as objective that the alternative ten is the best, therefore, when implementing the input parameters: S = 15000 rpm, doc= 0.10 mm, ts= 3.0 mm, F= 3600 m/min, the surface quality and low deformation of the part is guaranteed. It is concluded that the WASPAS multicriteria analysis method with neutrosophy is an excellent tool, with a low cost and good reliability, as a solution to be applied in machining shops to improve decision making in process planning processes from the optimal selection of machining parameters.

 

Keywords: Milling, Thin‑Walled, multi-criteria optimization, WASPAS, Neutrosophy, HSM.

 

1.Introduction

In today's organizations, prioritizing solutions to problems is a priority. One of the best and most widely used tools is the MCDM. This paper shows several authors who in one way or another have used the Weighted Aggregated Sum Product Assessment (WASPAS) method and its combinations to achieve this goal. [1] studies the combination of Although Failure Mode and Effect Analysis (FMEA) and WASPAS for the definition and assessment of risks related to systems, products and services. Hierarchies of possible corrective and preventive strategies are defined. [2, 3] incorporate the analysis of sustainability and how this is interrelated with economic processes, the first one; analyzes 41 indicators in 10 dimensions and subsequently manages to establish the order by countries with the best performance of the sustainability indicator, the result is established from the methods: WASPAS, MABAC, CODAS, and VIKOR, demonstrating its effectiveness. The second enriches his research by incorporating Fuzzy uncertainty analysis in manufacturing processes; in this case he uses WASPAS-SECA as a tool[4] to analyze the impact on the environment of the supply chain activity, identify the most important criteria and their weights, and establish the priorities of the different strategies, using a combination of entropy tools, Fuzzy and the MCDM method of WASPAS. Faced with the tasks of logistics resource planning, there are a group of barriers, government policies [5] in response to this problem, contributes as the objective of his research a framework with the use of Modified Step-Wise Weight Assessment Ratio Analysis (SWARA) and Weighted Aggregated Sum Product Assessment (WASPAS), finally its solution is effective, improving decision making and leads to improve the organizational activity of logistics. [6] approaches to answer the probelmatic of the manufacture of parts of complex structures in which the conventional machining is difficult to be accurate, its solution focuses on using the uncertainty analysis with the techniques and methods: Full Consistency Method (FUCOM), Similarity to Ideal Solution method fuzzy TOPSIS and fuzzy WASPAS. The planning of sustainable energy utilization is another area of study where MCDM has been used, [7] evaluates the impact of the utilization of energy generation technologies, for which it combines three techniques: Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), the Evaluation Based on Distance from Average Solution (EDAS) and the (WASPAS); with new principles related to the microgeneration stations with the energy technologies: solar thermal, solar panel, biomass boilers and micro wind. The research of [8] takes into consideration the importance of the use of renewable energy technologies, uses a MCDM methodology, where it identifies the risk criteria using Delphi method in a first stage, the framework in two following stages employs AHP and using Fuzzy Weighted Aggregated Sum Product Assessment (FWASPAS), as final result they obtain six strategies that define the best renewable energy technologies.[9] in the same way develops a program to establish the policies of how the society uses the energy, the multicriteria analysis model establishes: Level Based Weight Assessment (LBWA) with Weighted Aggregated Sum Product Assessment (WASPAS). Its study covers conventional and non-conventional forms, including biomass production, natural gas and diesel fuel. It integrates the Weighted Power Heronian (WPHA) and Weight Geometric Power Heronian (WGPHA) functions to the Waspas method. The development of production systems presents an opportunity to standardize tasks in order to obtain high productions, [10] establishes from the uncertainty in the qualitative evaluations of indicators that prevail in industrial processes, in the internet of things (IoT), robotics and automation; for this it is supported in the decision-making processes the spherical fuzzy sets (SFSs) are used for the applicability of the available data for the WASPAS method, and it is carried out to solve the contract processes that are carried out between companies.  

As can be seen, there are several ways in which the Weighted Aggregated Sum Product Assessment (WASPAS) multicriteria analysis method is used, however, its use does not appear through the neutrosophy, which constitutes a novelty applicable to the manufacturing process in thin pieces and in which the best quality is sought in the finishing of the pieces and without suffering deformation. 

2. Definition   

2.1 Sequential Interactive Model for Weighted Aggregated Sum Product Assessment (WASPAS)

The WASPAS method is a unique combination of two well-known MCDM approaches, i.e. weighted sum model (WSM) and weighted product model (WPM). Its application first requires development of a decision/evaluation matrix, X=[xij] m×n where xij is the performance of ith alternative with respect to jth criterion, m is the number of alternatives and n is the number of criteria.

2.2 Neutrosophic environment

Neutrosophy is a new branch of philosophy that studies the origin, nature and scope of neutralities created by Professor Florentin Smarandache. Its incorporation guarantees that the uncertainty of decision-making is taken into account [1-6]. The truth value in the neutrosophic set is as follow [7-11]:

Definition 1 [4, 12, 13]: Be  a universe of discourse, a Neutrosophic Set (NS) is characterized by three membership functions, , which satisfy the condition -0 ≤ ≤ ≤3 + x⸦X  and  denote the membership functions of true, indeterminate, and false of x in A, respectively, and their images are standard or non-standard subsets of . Let  be a neutrosophic evaluation of a mapping of a group of formulas propositional to , and for each sentence :

(1)

To facilitate the practical application in real-world problems [7], the use of Single-Value Neutrosophic Sets (SVNS) was proposed, through which it is likely to use linguistic terms to obtain greater interpretability of the results [8]. Let X be a universe of discourse, an SVNS A over X has the following form [9]:

(2)

Where

With

(3)

The intervals denote the memberships related to true, indeterminate and false from x in A, respectively [10]. For convenience reasons, a Single-Value Neutrosophic Number (SVNN) is expressed as A = (a, b, c), where a, b, c∈ [0.1] and 0 ≤ a + b + c ≤ 3.

Table 1: Linguistic terms used. Source: [14].

Let A = (a, b, c) be a single valued neutrosophic number, a score function S related to a single valued neutrosophic value, based on the truth-membership degree, indeterminacy-membership degree and falsehood membership degree is defined [15]:

(4)

2.3 Method development

Weighted Aggregated Sum Product Assessment (WASPAS), a method developed by Zavadskas (2012), groups two methods Weighted Sum Method (WSM) (MacCrimon, 1968) and Weighted Product Method (WPM), the procedures to perform the WASPA method are described below:To make the performance measures comparable and dimensionless, all the elements in the decision matrix are normalized using the following two equations:

Step 1. Initialize the matrix for solving the selection problem.

Step 2. Normalize the decision matrix.

 for beneficial criteria,        (1)

 for non-beneficial criteria,    (2)

Where xij is the normalized value of xij.

In WASPAS method, a joint criterion of optimality is sought based on two criteria of optimality. The first criterion of optimality, i.e. criterion of a mean weighted success is similar to WSM method. It is a popular and well accepted MCDM approach applied for evaluating a number of alternatives with respect to a set of decision criteria. Based on WSM method (MacCrimon, 1968; Triantaphyllou and Mann, 1989), the total relative importance of ith alternative is calculated as follows:

Step 3: Calculate the total relative importance based on the WSM method using equation

                                            (3)

where wj is weight (relative importance) of jth criterion. On the other hand, according to WPM method (Miller and Starr, 1969; Triantaphyllou and Mann, 1989), the total relative importance of ith alternative is evaluated using the following equation:

Step 4: Calculate the total relative importance based on WPM method using equation

                                            (4)

Step 5: A joint generalized weighted summative and multiplicative methods proposed by Zavadskas (2012) is shown in equation

A joint generalized criterion of weighted aggregation of additive and multiplicative methods is then proposed as follows (Saparauskas et al., 2011;):

+            (5)

 

In order to have increased ranking accuracy and effectiveness of the decisionmaking process, in WASPAS method, a more generalized equation for determining the total relative importance of ith alternative is developed (Zavadskas et al., 2012; Zavadskas et al., 2013a, b) as below:

+        (6)

The feasible alternatives are now ranked based on the Q values and the best alternative has the highest Q value. In Eq. (6), when the value of λ is 0, WASPAS method is transformed to WPM, and when λ is 1, it becomes WSM method. It has been applied for solving MCDM problems for increasing ranking accuracy and it
has the capability to reach the highest accuracy of estimation (Bagocius et al., 2013, 2014; Dejus and Antucheviciene, 2013; Hashemkhani Zolfani et al., 2013; Siozinyte and Antucheviciene, 2013; Staniunas et al., 2013; Chakraborty and Zavadskas, 2014). For a given decision-making problem, the optimal values of λ can be determined while searching the following extreme function (Zavadskas et al., 2012):

                                                                    (7)

The variances σ2(Qi(1)) and σ2(Qi(2)) can be computed applying the equations as given below:

                                          (8)

        (9)

The estimates of variances of the normalized initial criteria values are calculated as follows:

                (10)

Variances of estimates of alternatives in WASPAS method depend of the variances of WSM and WPM approaches as well as on the value of λ. It may be worthwhile to compute the optimal values of λ and assure the maximum accuracy of estimation. It may also be important to study the effects of optimal λ values on the final ranking of the alternatives.

3. Case study

High-speed milling operations were performed on Quick Machining Center Jet AV1612, equipped with HEI-CNC-System from DENHAIN for precise machining control with a maximum spindle speed of 20,000 rpm and feed speed of 25 m / min. The workpiece for the experiment was selected from Al 5083 alloy in rectangular shape with dimensions of 140 mm × 70 mm × 5 mm. The workpiece was mounted in a special fixture applying 6 bolts, additionally clamped on the bed of the machine tool. The chemical composition and physical properties of the workpiece material are given in Table 1 and 2 respectively.

Table 2.  Chemical Composition of the Aluminum Alloy 5083

 

 

 

Table 3. Physical Properties of 5083 Aluminum Alloy

 

Table 4. Mechanical Properties of Aluminum Alloy 5083

 

4. Application of the model                                                                                                                              

4.1 Determination of the weights of the criteria with neutrosophic numbers.

 

To run the model, by stating the established criteria and using the equations of the neutrosophic numbers, the weights of the criteria are evaluated and the dimensional deviation is taken into account. Table 5 shows the initial decision matrix, in which the criteria are evaluated, then the neutrosophic values of the criteria weights for the alternatives are represented in Table 6. Table 7 shows the results that showed lateral deviation as the criterion with the highest weight: W_Ra-Fd = 0.28808, W_Ra-Td = 0.35065 y W_TWD = 0.39021.

 

Table 5. Initial decision matrix

 

Table 6. Decision matrix of weights.

 

Table 7. Result of the hierarchy of weights.

5. WASPAS with a single value neutrosophic set (WASPAS-SVNS).

The solution of the WASPAS method begins with the normalization of the data in Table 8, taking the values of the results of the experimental work with the initial parameters, as shown in Table 9 and Table 9(Cont).

The results establish that the hierarchy for l=0.5, behave as follows: 10-1-20-24-15-14-13-18-18-19-21-4-2-17-5-11-7- 9-25-23-16-22-12-6-8-3, related in Table 10.

Table 8. Matrix of experimental data and results. Source:  [16]

 

Table 9. FMS normalized data of milling process parameters.

 

 

Table 9.(Cont.) FMS normalized data of milling process parameters..

 

Table 10. Optimum values per hierarchy for l=0.5.