CARRIER SELECTION WITH INTUITIVE FUZZY CLUSTERS IN DANGEROUS GOODS TRANSPORTATION

​ABSTRACT

The main purpose of this study was to explain the importance of Dangerous Goods Transportation and to determine the most appropriate method in choosing the carrier company. In the study, Fuzzy logic and its extensions, Multi-Criteria Decision Making and Fuzzy Multi-Criteria Decision Making methods are explained. Intuitive Fuzzy TOPSIS, one of the Fuzzy Multi-Criteria Decision Making methods, is explained on the application for the most appropriate supplier selection in Dangerous Goods Transportation. In addition, intuitive fuzzy sets from fuzzy set extensions and TOPSIS method, which is one of the fuzzy multi-criteria decision making methods, are examined in detail and the most appropriate company selection in dangerous goods transportation is explained on practice.

Keywords: Dangerous Goods transportation; ADR, Fuzzy Logic; FuzzyExtensions of Logic; Fuzzy Multi-Criteria Decision Making Methods; TOPSIS; Intuitive Fuzzy Sets.

1. INTRODUCTION

Hazardous substances are explosive, flammable, combustible and caustic substances in solid, liquid or gaseous state that harm human health, nature and goods in terms of their chemical, physical and structural properties and are stored and transported in special containers and conditions. Hazardous materials are products that can be used in all areas of the supply chain, difficult to store and transport, and risky. Studies to reduce the risk in its use and storage have been carried out by various institutions and organizations recently.

Due to the nature of dangerous goods, the qualifications and quantities of the company/carrier that will carry out this activity gain importance while being transported or transferred. Since the selection of such a company is peculiar, it is necessary to determine various criteria that will determine its selection. Especially recently, the increasing need for petroleum products; fuel, catalyst, etc. at every stage of production of such products. Due to the use of dangerous goods, developing science and technology and increasing needs, the need for the transportation of dangerous goods by various methods and the number of companies that will transport them have increased in parallel. This problem has been considered as a multi-criteria decision-making problem, since there are various candidate companies and criteria and decision makers.

2. LITERATURE SERVEY

Due to the increasing importance of dangerous goods transportation, studies in this field are increasing in the literature. Among the studies on supplier selection and dangerous goods transportation in the literature, there are mostly studies on Risk Management.

Looking at the All Incidents statistics from the US Department of Transportation Pipeline and Dangerous Goods Safety Administration Dangerous Goods Safety Agency portal, it is noteworthy that Highway dangerous goods transportation has the highest risk rate.

In the table and histograms below, Deaths, Injuries, Accidents and Property Damage Data occurred in the transportation of Dangerous Goods in the years 2011-2020 are given.

Table 1.

Table of accidents according to years and transportation types

Figure 2.1. Histogram of accidents by year and transport types

Adapted from the official website of the US Department of Transportation (https://www.transportation.gov.html, 2021)

3. CLASSİFİCATİON OF HAZARDOUS SUBSTANCES

The large number of dangerous goods requires a special approach for each of them. However, since it is very difficult for those who do this job to know the content and properties of each dangerous substance and to know the methods of taking the necessary precautions for each one in a timely manner, the classification of dangerous goods was needed.

Class numbers are due to a purely random order. Not ranked by degree of risk. The properties and display forms of dangerous goods for each class are as follows;

Class 1 – Explosives,

Class 2 – Gases,

Class 3 – Flammable Liquids,

Class 4 – Flammable Solids,

Class 5 – Oxidizing Agents,

Class 6 – Toxic and Infectious Substances,

Class 7 - Radioactive Substances,

Class 8 - Corrosive substances,

Class 9 – Substances and Articles with Different Hazards.

3.FUZZY LOGIC AND FUZZY SETS

3.1 Fuzzy Logic

Fuzzy logic theory was developed in 1965 by Dr. It was invented by Lütfi A. Zadeh. The basis of the theory is that the old Aristotelian logic does not give complete and precise results, instead, it is more clear solving the problems frequently encountered in daily life by using fuzzy sets and fuzzy numbers. There is uncertainty in many events that we encounter relatively in our daily lives. For example, when the word "cold" is said, it may be -50Cº for a person living in Alaska, and 10 Cº for a person living in Africa. The conversion of this uncertainty state to numerical values is expressed as fuzzy logic in the literature.

The concept of fuzzy logic, in its simplest form, seems to be a system that can be used in solving many problems, although the expressions "somewhat cold", "very weak", "very fast", "somewhat wrong" do not have a mathematical meaning.

3.2 Fuzzy Sets

In classical (traditional) set theory, an object is either a member of the set or it is not. On the other hand, fuzzy set is a subset of the set that takes infinite values, provided that the degrees of membership and non-membership are between 0 and 1.

The figures below show the normal and non-normal, monotonous and non-monotonic properties of membership functions.

Figure 3.1. (a). Normal fuzzy set.   Figure 3.2 (b). Non-normal fuzzy set

To be a normal fuzzy set, as shown in the figure, at least 1 membership degree must be equal to 1.

Figure 3.3. (a). Monotone fuzzy set.             Figure 3.4 (b). Non-monotonic fuzzy set

If the cluster is concave, it is Monotonous, and if it is convex, it is non-monotonic.

3.3 Fuzzy Numbers

In order for a number to be a fuzzy number, it must meet certain conditions.

1. x elements must be members of the special set of real numbers R

2. The α- cut is in the range [0,1] and Ãα = {x ∈ R: μà (x) ≥ α }

3. For the fuzzy number to be in the closed range, the set of the segment α must be closed. (Ã) = {x ∈ R: μà (x) > 0}

When all conditions are met, a convex set of fuzzy numbers with a continuous membership function is formed from the fuzzy set.

3.3.1 Triangular Fuzzy Numbers

The fuzzy number is shown as à = (    ) .

Figure 3.5. Triangular fuzzy number

3.4 Fuzzy Set Extensions

The introduction of fuzzy logic, which brought innovation to the whole world, by Lütfi A. Zadeh in 1965, led to an increase in studies in this field. As the studies increased, the deficiencies were discovered and criticized, and it brought a new dimension to the scientific world with the extensions of fuzzy logic by researchers in order to improve it. Firstly, second-order “Tp-2 fuzzy sets” were developed by Lütfi A. Zadeh as a result of changing the boundaries of membership functions with fuzzy numbers. Later, Atanasov introduced "intuitive 1" fuzzy sets in 1986 and " intuitive 2" fuzzy sets in 1989, as a result of adding the indecisiveness of decision makers. In 1999, "Neutrophic sets" were developed by Smarandache to solve problems with uncertain and inconsistent information. Garibaldi and Özen defended the idea that membership functions can change over time, and "Unsteady fuzzy sets" were discovered. With the addition of the hesitation factor, “Hesitant fuzzy sets” was first introduced to the literature by Tora in 2010. In 2013, Yager proposed a new concept called “Pythagorean fuzzy sets”, which is an extension of Intuitive fuzzy sets. “Spherical fuzzy sets” were developed by Kutlu Gündogdu and Kahraman to provide a wider set of solutions for decision makers. It was emphasized that the last developed fuzzy set was entered into the literature as a "Fermatean fuzzy set" by Senapati and Yager in 2019 and produced better solutions than all other sets.

4. MULTI-CRITERIA DECISION MAKING

As a concept, multi-criteria decision making (MCDM) is a classification, ranking and finally selection problem when the number of criteria and alternatives is large.

4.1 Multi-Criteria Decision Making Methods

4. 1.1 Analytical Hierarchy Process (AHP)

The analytical hierarchy process was introduced by Myers and Alpert in 1968 and started to be used by Thomas L. Saaty in the 1970s.

The solution steps of AHP are shown below:

1. Identifying the problem,

2. Determining the criteria and creating a hierarchical structure, provided that the purpose is the first,

3. Establishment of pairwise comparison matrices,

4. Calculating the weights of the criteria,

5. Calculating consistency ratios, continuing in case of consistency,

6. Reviewing decision makers when there is inconsistency, checking until consistency is achieved.

4. 1. 2 PROMETHEE Method

The PROMETHEE Method was first presented at a conference at Laval University in Canada in 1982. This method helps to solve problems through pairwise comparison of alternatives according to criteria. J.P. Various variations of the method have been proposed by Brans and B. Mareschal. PROMETHEE I- partial sorting, PROMETHEE II- complete sorting, PROMETHEE III- discrete sorting, PROMETHEE IV- continuous sorting.

This method has 7 stages and is shown below:

1. Evaluation of criteria and alternatives and determination of criteria weights,

2. Determining the functions that express the relationships between the criteria,

3. Pairwise comparison of alternatives for criteria according to preference functions,

4. Finding common preferences and comparing alternatives using them,

5. Calculation of positive and negative superiority values for alternatives,

6. Determination of partial rankings,

7. Determination of exact rankings.

4. 1. 3 ELECTRE method

The ELECTRE method was proposed by Bernard Roy in 1965 to solve multi-criteria problems by comparing alternatives. By weighting the criteria, they are summed and the most suitable alternative is selected.

The solution steps are shown below:

The decision matrix is created,

A weighted normalized decision matrix is created,

Determination of compatibility and incompatibility sets,

Creating Compatibility and Incompatibility Matrices,

Determination of Compatibility Superiority and Incompatibility Superiority Matrices,

Calculation of Superior and Inferior Network.

4. 1. 4 VIKOR method

The VIKOR method, which was developed for the decision makers to rank the alternatives and to select the best alternative, was proposed by Opricovic and Tzeng in 2004.

The steps of this method are shown below:

Creation of the decision matrix,

Calculation of the best () and worst () criteria values,

Generating the normalized decision matrix,

Weighting of the normalized decision matrix,

Calculation of  and  values,

Calculation of values,

Sorting alternatives and checking accuracy.

4. 1.5 TOPSIS method

The TOPSIS method was introduced in 1981 by Hwang and Yoon. It is known as an alternative to the ELECTRE method. The most distinctive feature of this method is to reach the ideal solution by finding the closest values to the best alternative and the farthest values to the worst alternative in line with the best and worst solutions.

The application steps of this method are shown below:

Creation of the decision matrix,

Generating the normalized decision matrix,

Generating a weighted normalized decision matrix,

Calculation of positive ideal solution and negative ideal solution ((),

Calculation of separation measures,

Calculation of the relative closeness to the positive ideal solution,

4.2 Intuitive Fuzzy TOPSIS

The difference of the heuristic fuzzy TOPSIS method from the standard TOPSIS method shown above is that the heuristic fuzzy numbers are used and the problem is solved by obtaining the heuristic fuzzy positive ideal solution and the heuristic fuzzy negative ideal solution as a result.

The set of alternatives is denoted by A= {, ,..., }, and the set of criteria C={, ,… ). Since the decision group is different and the decision maker is unique, they are ranked according to their importance, taking into account the knowledge and experience of the decision makers.

The weight vector of the decision maker is λ= {,;

,( k =1,2,…,l)  ve  =1 dir.

k. decision matrix of the decision maker  = ();

k. evaluated by the decision maker i. alternative j. the intuitive fuzzy value from the criterion is expressed by  = (,, ) 

Here ,  ve  and  k respectively. according to the evaluation of the decision maker i. alternative j. it indicates the degree of fulfillment, non-fulfillment and uncertainty (hesitancy) of the criterion.

The solution steps of the intuitive fuzzy TOPSIS method are shown below:

STEP 1: Determining the weights of decision makers

At this stage, linguistic expressions are transformed into heuristic fuzzy numbers to determine the weights of the decision makers.

k. Intuitive fuzzy number  = ( showing the importance of the decision maker; The weight values of the decision makers are calculated as shown below.

≥ 0, k = 1,2,3,…,l,

                                                                                (4.1)

STEP 2: Obtaining the unified decision matrix

After the decision makers have expressed their views on the alternatives, the unification process must be done to form the group decision. For this, a Unified decision matrix is created by using the IFWA (Intutionistic Fuzzy Weighed Averaging-Intuitive Fuzzy Weighted Average) method.

⊕ …      (4.2)

=⦋1-       (4.3)

(i=1,2,…,m; j=1,2,…,n) being the element of the combined decision matrix (R);

STEP 3: Determination of criterion weights

Since the weights of the criteria and the degree of importance for the decision makers are not the same in the problems considered, the heuristic fuzzy numbers given to the criteria are combined.

k. decision maker j. The evaluation for the criterion is expressed as  = (  fuzzy number and the weights of the criteria It is calculated by IFWA method as shown below;

The criterion weights are  W = ( ve  (j = 1,2,3…n) ;

=(,,…) =  ⊕ …    (4.4)

= ⦋1-  -        (4.5)

STEP 4: Generating a weighted aggregate decision matrix.

Using the values obtained in the second and third stages, a weighted combined decision matrix is created.

 = (,, ) ve (i=1,2,…,m; j= 1,2,…,n) 

The combined weighted decision matrix () is calculated as shown below;

 = R ⊗ W = (, ) = {(x.., .)│x∈ X}                                             (4.6)

 = 1- - - .+ .                                                                                (4.7)

STEP 5: Obtaining the positive and negative intuitive fuzzy ideal solution

The calculation of the positive and negative intuitive fuzzy ideal solution is shown below, with utility criteria set , cost criteria , positive intuitive fuzzy ideal solution, negative intuitive fuzzy ideal solution ;

 = (  ),= (,, ), j = 1,2,…,n                                         (4.8)

 = (  ),= (,, ), j = 1,2,…,n                                         (4.9)

= {( max i{}│j∈ ),( min i{}│j∈ }                                                (4.10)

= {( max i{}│j∈ ),( min i{}│j∈ }                                                 (4.11)

= (1- max i{- min i{}│j∈ ), (1- min i{- max i{}│j∈ )  (4.12)

= {( min i{}│j∈ ),( max i{}│j∈ }                                                 (4.13)

= {( min i{}│j∈ ),( max i{}│j∈ }                                                   (4.14)

STEP 6: Calculation of positive and negative discrimination measurements

Distance measurements such as Hamming and Euclidean distance measurements are used to calculate separation measures between alternatives, positive and negative heuristic fuzzy ideal solutions. The calculation of the distance with the Hamming and Euclidean methods is shown below:

a. Hamming distance method

 =          (4.15)

 =          (4.16)

b. Euclidean distance method

 =    (4.17)

=     (4.18)

= (1- min i{- max i{}│j∈ ), (1- max i{- min i{}│j∈ )       (4.20)

STEP 7: Calculating the closeness coefficient for each alternative

The calculation of the closeness coefficient for the positive and negative heuristic fuzzy ideal solutions is shown below;

=   , 0 ≤   ≤ 1 ,  i =1,2,…,m                                                                (4.21) 

STEP 8: Ranking of alternatives

In the seventh step, a ranking is made from the largest to the smallest in line with the calculated closeness coefficients. The alternative with the largest coefficient is selected as the best alternative.

5. EXAMPLE

In this study, eight criteria and three logistics companies were determined for the selection of carrier companies with intuitive fuzzy sets in dangerous goods transportation. Based on the evaluation of all three logistics companies according to the criteria by an expert group consisting of three people who do logistics work in different companies, the best carrier company in dangerous goods transportation was determined.

Figure 5.1. Hierarchical structure of criteria for carrier selection

STEP 1: Determining the weights of decision makers

Linguistic expressions were transformed into intuitive fuzzy numbers as shown in Table 5.2.

Table 5.2.

Scale of linguistic terms used to weight decision makers and criteria

Adapted from Biderci (2019)

Equation (4.1) was used to calculate the weights of the experts in the decision-making group and it is shown in Table 5.3.

Table 5.3.

Decision makers evaluation table

STEP 2: Obtaining the unified decision matrix

The evaluation of the alternatives by the three decision makers according to the criteria was made using the linguistic terms in Table 5.4 and shown in Table 5.5.

Table 5.4.

Scale of linguistic terms used to evaluate alternatives according to criteria

Table 5.5.

Table of evaluation of alternatives according to criteria by decision makers

The ideas of all three decision makers should be combined as group thought to form the unified decision matrix. In Equation (4.5), a combined decision matrix is created using the IFWA (Intutionistic Fuzzy Weighed Averaging) method.

Table 5.6.

Combined decision matrix

STEP 3: Determination of criterion weights

Since the weights and importance levels of the criteria are different for each decision maker, the intuitive fuzzy values given to the criteria should be combined. The evaluation of the criteria according to the decision makers is shown in Table 5.7.

Table 5.7.

Table of evaluation of criteria by decision makers

The weights of the criteria were calculated with the IFWA method shown in Equation (4.5) and the following values were found.

W= {(0,609; 0,337; 0.054), (0,743; 0,226; 0,031), (0,876; 0,118; 0,006), (0,680; 0,267; 0,053), (0,623; 0,324; 0,054), (0,876; 0,118; 0,006), (0,468; 0,482; 0,050); (0,750; 0,200; 0,050)}

STEP 4: Generating a weighted aggregate decision matrix.

The values of the combined decision matrix were multiplied by the weight vector and the values of the combined decision matrix were found as shown in Table 5.8.

Table 5.8.

Weighted aggregate decision matrix

STEP 5: Obtaining the positive and negative intuitive fuzzy ideal solution

Considering that the first one of the criteria discussed in the problem is cost and the others are benefit criteria, + is calculated by positive intuitive fuzzy ideal solutions,   is calculated by negative intuitive fuzzy ideal solutions Equations (4.8) and (4.9) and shown in Table 5.9

Table 5.9.

Positive and negative intuitive fuzzy ideal solutions

STEP 6: Calculation of positive and negative discrimination measurements

Normalized Euclidean distances were found using Equation (4.18) to calculate positive and negative discrimination measures and are shown in Table 5.10. Normalized Hamming distances were found using Equation (4.16) and are shown in Table 5.11.

STEP 7: Calculating the closeness coefficient for each alternative

Equation (4.21) was used to calculate the closeness coefficients of the alternatives using the Euclidean method and is shown in Table 5.10. For the Hamming method, it is shown in Table 5.11 using the same equation.

Table 5.10.

Positive and negative discrimination criteria and closeness coefficient table of alternatives (Euclidean distance method)

Table 5.11.

Positive and negative discrimination criteria and closeness coefficient table of alternatives (Hamming distance method)

STEP 8: Ranking of alternatives

The closeness coefficients of the alternatives shown in Tables 5.10 and 5.11 are ranked from largest to smallest, the alternative with the highest value is evaluated as the best, and the alternative with the smallest value is evaluated as the worst alternative. In this context, according to both Euclidean and Hamming methods, our alternatives are listed as A1> A3> A2 and the best company is selected as A1.

6. CONCLUSION

Almost all sectors of the industry depend on the use of fuel in some way. Timely and high-quality transportation of fuel is of great importance for the automotive and aviation industries, as well as for river and sea transportation. The main options for fuel transport are road (tanker), rail and less frequently sea and air transport. In most cases, carriers do it by road transport of fuel products. The main reason for this is that the delivery time is more comfortable and convenient. An extensive road network makes it possible to transport fuel both domestically and abroad. The important factor for fuel transportation is taking safety precautions and compliance with the standards regarding the transportation of dangerous goods. The transportation of fuel oil by road is a complex process, since these substances belong to the class of dangerous goods and pose a threat to both people and the environment. In this case, it is very important to choose the right vehicles, containers and tanks, to follow all the rules regarding loading, transport, unloading and storage, and also to prepare transport documents. To ensure safety, these substances are transported in special tanks that meet all fire safety requirements. In addition, changes in oxygen access and chemical and physical properties may occur during the transportation of fuels, which causes deterioration in the quality of the transported products. That is why such substances are transported in special containers protected from the air.

In this study, 3 companies that carry out the transportation of such materials were selected for the selection of carriers in fuel transportation. In order to choose the most suitable one among these companies, subjective evaluations were handled and linguistic expressions of the expert group that carried out the logistics business in 3 different companies were used. After the expert group evaluated each of the 3 companies according to 8 criteria, their linguistic expressions were converted to intuitive fuzzy numbers and the best carrier company was selected by using the Topsıs method, one of the multi-criteria decision making methods. In practice, both Euclidean and Hamming methods were used to calculate the positive and negative discrimination criteria and the closeness coefficients of the alternatives.

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