Keywords

1 Introduction

In modern industry manufacturing practices, it is a daily job to machine materials with mechanical properties like toughness, hardness and higher strength. In sectors like automobile, tool and die making utilizes materials such as ceramics, titanium, composites and refractory alloys, which are difficult for creating accurate and complicated shapes. Complex shapes machining on tougher materials cannot be done with conventional machining processes identified for material removal in the form of a chip. Due to such limitations of traditional machining processes, change in manufacturing has been taking place since 1940. New tools and new forms of energy were utilized in the latest manufacturing era to achieve more sophisticated designs on complex machine materials [13].

NTM Processes have vague data. Every NTM Process requires the specific value of parameters as an optimum value. Tables 1, 2 and 3 explain NTM process data cognitively. Data describes the extent of process operations compared to its maximum limits. In Table 1 [10], various shape applications of NTM Processes are explained in a cognitive way, where the scale of various operations performed by NTM processes are divided into “Good” and “Fair”, then with the eleven-point scale converted into quantitative values as per Table 5.

Table 1 Shape application of NTMPs [10] conversion based on eleven-point scale [12]
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Table 2 Material applications for metals and alloys [6] conversion based on eleven-point scale [12]
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Table 3 Economics of the various NTMPs [15] conversion based on eleven-point scale [12]
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In Table 2 material application for metals, alloys and non-metals explained with respect to various NTM processes is explained in quantitative form with the help of eleven-point scale.

In Table 3 economics of different NTM processes are explained considering various costs like capital cost, tooling cost, power consumption cost, material removal rate efficiency, and tool wear cost.

In Table 4 various methods used for NTM process selection are discussed with various aspects like flexibility, computational time, programming complexity, decision-makers involvement and type of data used for the analysis.

Table 4 Comparison of various methods for NTMPs Selections
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Material applications of metals and alloys are explained by [6], where he relates various NTM Processes applications with metals and non-metals. The scale used to describe the applications is “Poor”, “Fair” and “Good”. Economics of NTM Processes is the essential factor during selection for suitable application. Yurdakul and Cogun [15] divides economics of NTM processes in Power consumption cost, Material removal rate efficiency, Capital cost, Tool wear and Tooling cost with scale “Very low”, “low”, “Medium” and “High”. Table 5 shows eleven-point scale which can be used to convert linguistic variables into quantities.

Table 5 Measure of NTM process selection attribute [12]
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Various methods are utilized in NTM processes selection. These methods have different Operational approaches, different performances and different outputs. Table 4 explained by Boral S. Genetic algorithm is having medium flexibility with numerical work. On the other hand, an artificial Neural Network is highly flexible with Numerical data output with high computational time. Simulated annealing with medium flexibility and medium computational time with numerical results. The expert system method is widely used due to its operational approach with medium flexibility and medium computational time with numerical and textual outputs considered in NTM process selection. Further, the Case-Based Research (CBR) method depends on similarity and takes low computational time with numerical and textual outcomes considered practical by several researchers.

The selection of NTM processes is a multi-criteria decision-making problem. Researchers are finding hybrid methods to get the exact selection process. Table 6 shows that the Authors are working on getting results from various MCDM techniques. They are achieving it quite often while implementing NTM processes. It is observed that most of the methods are not considering the uncertainty involved in the problem. Also, it comes to notice that these methods are not user-friendly, and implementing them requires technical knowledge of NTMPs. Expert systems like AHP based expert system, QFD based expert system, Hybrid method combination of AHP and TOPSIS, Decision tree-based expert system, Diagraph-based expert system and online knowledge-based fuzzy expert system are discussed to verify the selection methods implemented and to observe the limitations in the processes.

Table 6 Existing non-traditional machining process selection systems with their limitations
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Chen [5] generalized the notion of bipolar fuzzy sets (FSs) to m-polar FSs. In a m-polar FS, the element’s membership value ranges over [0, 1]m interval, representing all the m features of the element (Akram [1]). These FSs are fit for numerous real-life problems wherein information arrives from n agents (n \(\ge\)2). The m-polar FSs have been largely used while modeling real-world problems which often involve multi-index, multi-object, multi-agent, multi-attribute, limits and/or uncertainty. These multipolar data further complicate the decision-making procedure in realistic scenarios thus initiating the multi-criteria decision-making (MCDM) problem. In resolving a MCDM task, the three preliminary steps to be followed include problem identification through determining the probable alternatives, assessment of alternatives depending on the condition provided by the decision-maker or decision-making experts and finally selection of the desired or best alternative. The m-polar FSs have been very effective tools in managing MCDM problems.

Research Gap

  • Available expert systems for selecting non-traditional machining do not consider subgroup of variables for selection of best NTM process; the m-polar fuzzy set algorithm considers multipolar information (variables with subgroups).

  • The m-polar fuzzy algorithm considers the percentage value of variables as input; it needs improved scaled information to the algorithm. Therefore, an eleven-point scale was used to present variables systematically.

  • The m-polar fuzzy set algorithm is used to solve various industry problems. However, it is not implemented for the selection of a non-traditional machining process.

2 Research Methodology

Research methodology followed to solve selection problem with the m-polar fuzzy set algorithm is explained below step by step.

Sr. No.

Steps to be followed [2]

1

Input A as Alternatives available

2

“P” as a input variable set

3

We are defining multipolar fuzzy soft relation R: A → P as per the alternatives and variables

4

The decision-maker requirement gives multipolar fuzzy subset Q over P, an optimal standard decision object

5

R(Q) and R(Q) calculate multipolar soft, rough approximation operators

6

Evaluate choice set C = R(Q) ⊕ R(Q)

7

Select the optimal decision Ok

2.1 Selection of a NTM Process for Non-metals to Obtain Through Cavities

The selection of the NTM process to obtain through cavities in non-metals with the optimum cost is a decision-making problem. Since every process has different properties, the material for the application is essential for the non-traditional machining process. The number of factors that can be considered for selecting the good NTM process, based on the decision-maker’s requirement such as good material, desirable through cavities and optimum cost. Suppose a person wants to select a non-traditional machining process for non-metals to achieve precision through cavities. There are four NTM alternatives available. The alternatives are a1 = USM, a2 = AJM, a3 = CHM, a4 = LBM. One can select the most suitable NTM process. The materials, through cavities and costs, are the variables for selecting a non-traditional machining process. In this case A = {a1, a2, a3, a4} is set of four nontraditional machining processes under consideration and let P = {p1, p2, p3} set of parameters related to the nontraditional machining process in A, where,

  • “p1” variable for the material,

  • “p2” variable for the through Cavities,

  • “p3” variable for the cost.

We present more features of these variables as follows:

  • The “Material” of the nontraditional machining process includes Ceramics, Plastics, Glass.

  • The “Through Cavities” of the Nontraditional machining process include Precision, Standard, rough.

  • The “Cost” of the Nontraditional machining includes Capital cost, Tooling Cost, and Power Consumption cost.

Features of these variables are the “Material” of the NTM process including ceramics, plastics and glass. The “Through Cavities” of the NTM process include Precision, Standard and rough. Finally, the “Cost” of the NTM includes Capital cost, Tooling Cost and Power Consumption cost.

Suppose that Person explains the “Effective selection of non-traditional machining process” with 3-polar fuzzy soft relation R: A → P, as given below, Table 7 shows linguistic decision matrix for alternatives and parameters.

Table 7 m-polar fuzzy linguistic decision matrix
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Table 8 gives eleven-point scale to convert linguistic variables into quantitative values, that can be used for writing decision matrix values in numbers.

Table 8 Quality scale for NTM process selection [12]
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Table 9 shows decision matrix for NTM process selection with numbers, combining Table 6 and Table 7.

Table 9 m-polar fuzzy decision matrix for NTM process selection
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Thus, R over A × P is 3-polar fuzzy soft relation, where material, through cavities and the cost of the operation are considered variables for the selection of NTM process. From the table, think “Material” of the non-traditional machining process ((a1, p1), 0.665, 0.5, 0.665) means that the non-traditional approach a1 is suitable to the ceramics, fair to the plastics and good to the glass. Let us assume that the expert suggested the most favorable standard decision object Q, which can be shown as 3-polar fuzzy subset of R as follows:

  • Q = (p1, 0.865, 0.745, 0.955), (p2, 0.955, 0.745, 0.335), (p3, 0.255, 0.335, 0.255).

From definition,

  • Qr (a1) = (0.665, 0.665, 0.665), Qr (a1) = (0.335, 0.5, 0.335),

  • Qr (a2) = (0.745, 0.665, 0.665), Qr (a2) = (0.665, 0.665, 0.335),

  • Qr (a3) = (0.5, 0.665, 0.335), Qr (a3) = (0.665, 0.665, 0.5),

  • Qr (a4) = (0.665, 0.665, 0.665), Qr (a4) = (0.665, 0.665, 0.745).

Now, 3-polar fuzzy soft rough approximation operators R(Q), R(Q), respectively, are given by.

  • R(Q) = (a1, 0.665, 0.665, 0.665),(a2, 0.665, 0.665, 0.665),(a3, 0.5, 0.665, 0.335),(a4, 0.665, 0.665, 0.665),

  • R(Q) = (a1, 0.335, 0.5, 0.335),(a2, 0.745, 0.665, 0.335),(a3, 0.665, 0.665, 0.5),(a4, 0.665, 0.665, 0.745).

These operators are very close to the decision alternatives yn, n = 1, 2, 3, 4.

  • R(Q) ⊕ R(Q) = (a1, 0.7773, 0.8325, 0.7773),(a2, 0.9146, 0.8878, 0.7773),(a3, 0.8325, 0.8878, 0.6675),(a4, 0.8878, 0.8878, 0.9146).

Thus, the Person will select the non-traditional process a1 (USM) to obtain through cavities in non-metals because the most favorable decision in the choice set R(Q) ⊕ R(Q) is a1.

2.2 Selection of a NTM Process for Metals to Obtain Through Cavities

The selection of the NTM process for through cavities in non-metals with the optimum cost is a decision-making problem. Since every process has different properties, the material for the application is essential for the NTM. There are many factors to consider when selecting the right NTM process, whether we are looking for good material, desirable through cavities and optimum cost. Suppose a person wants to select a NTM process for non-metals to achieve precision through cavities. There are four alternatives in his mind. There are four non-traditional machining alternatives available. The alternatives are a1 = USM, a2 = AJM, a3 = CHM, a4 = LBM. One can select the most suitable NTM process. The materials, through cavities and costs, are the variables for selecting a NTM process. In this case A = {a1, a2, a3, a4} is set of four nontraditional machining processes under consideration and let P = {p1, p2, p3} set of parameters related to the nontraditional machining process in A, where,

  • “p1” variable for the material,

  • “p2” variable for the through Cavities,

  • “p3” variable for the cost.

We present more features of these variables as follows:

  • The “Material” of the non-traditional machining process includes Aluminium, Steel, Titanium.

  • The “Through Cavities” of the Nontraditional machining process include Precision, Standard, rough.

  • The “Cost” of the Nontraditional machining includes Capital cost, Tooling Cost, and Power Consumption cost.

Suppose that Person explains the “Effective selection of nontraditional machining process” by forming a 3-polar fuzzy soft relation R: A → P, which is shown below,

Table 10 shows linguistic decision matrix for alternatives and parameters.

Table 10 Fuzzy Linguistic decision matrix
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Table 11 gives eleven-point scale to convert linguistic variables into quantitative values, that can be used for writing decision matrix values in numbers.

Table 11 Qualitative measure for NTM process selection [12]
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Table 12 shows decision matrix for NTM process selection with numbers, combining Tables 10 and 11.

Table 12 Decision matrix for NTM process selection
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Thus, R over A × P is 3-polar fuzzy soft relation in which materials, through cavities and cost of the operation, are considered variables for the non-traditional machining process. From the table, think “Material” of the non-traditional machining process ((a1, p1), 0.335, 0.50, 0.50) means that the non-traditional approach a1 is suitable to the ceramics, fair to the plastics and good to the glass. Let us assume that the expert suggested the most favorable standard decision object Q, which is a 3-polar fuzzy subset of R as follows:

  • Q = (p1, 0.865, 0.745, 0.955), (p2, 0.955, 0.745, 0.335), (p3, 0.255, 0.335, 0.255).

From definition,

  • Qr (a1) = (0.665, 0.665, 0.665), Qr (a1) = (0.665, 0.5, 0.5),

  • Qr (a2) = (0.665, 0.665, 0.665), Qr (a2) = (0.665, 0.665, 0.5),

  • Qr (a3) = (0.665, 0.665, 0.335), Qr (a3) = (0.665, 0.5, 0.5),

  • Qr (a4) = (0.665, 0.665, 0.665), Qr (a4) = (0.665, 0.665, 0.5),

Now, 3-polar fuzzy soft rough approximation operators R(Q), R(Q), respectively, are given by.

  • R(Q) = (a1, 0.665, 0.665, 0.665),(a2, 0.665, 0.665, 0.665),(a3, 0.665, 0.665, 0.335),(a4, 0.665, 0.665, 0.665),

  • R(Q) = (a1, 0.665, 0.5, 0.5),(a2, 0.665, 0.665, 0.5),(a3, 0.665, 0.5, 0.5),(a4, 0.665, 0.665, 0.5).

These operators are very close to the decision alternatives yn, n = 1, 2, 3, 4.

  • R(Q) ⊕ R(Q) = (a1, 0.8878, 0.8325, 0.8325),(a2, 0.8878, 0.8878, 0.8325),(a3, 0.8878, 0.8325, 0.8325),(a4, 0.8878, 0.8878, 0.8325).

Thus, the Person will select the non-traditional process a2 (AJM) to obtain through cavities in non-metals because the most favorable decision in the choice set R(Q) ⊕ R(Q) is a2.

3 Conclusion

A conceptual design of the multipolar fuzzy set is studied and implemented. Eleven-point scale is used to convert linguistic data of NTM processes compared to previous m-polar fuzzy set applications using data as a percentage of variables. Subgroups of variables are considered in the decision-making process. This approach helps solve the selection problem of the non-traditional machining process. Problem solved for non-metals resulted in the selection of USM as the best alternative. Problem solved for metals resulted in the selection of AJM as the best alternative. Previous work in this area shows the same results as obtained by the m-polar fuzzy set method. Further, this method is to be developed for exact uncertainty values in non-traditional machining processes.