Yazılım seçiminde küresel bulanık topsıs yöntemi ile çok kriterli karar verme
Multi-criteria decision making of software packages using spherical fuzzy topsis
Yazar: MERVE CANPOLAT
Danışman: PROF. DR. CENGİZ KAHRAMAN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Endüstri Mühendisliği Ana Bilim Dalı / Endüstri Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2019
Konu: Endüstri ve Endüstri Mühendisliği = Industrial and Industrial Engineering
Dizin: Bulanık = Fuzzy

Özet:
Şirketler günümüz rekabet dünyasında yer edinebilmek için yeni yatırımlar yapmaktadır. Özellikle bu noktada dijitalleşme öne çıkmaktadır. Bu doğrultuda şirketlerin bilişim teknolojileri konusunda alacağı kararlar ve yapacağı yatırımlar kritik olmaktadır. Büyük ölçekli şirketlerde farklı amaçlara hizmet eden yazılımlar mevcuttur ve her geçen gün yenileri eklenmektedir. Bu yazılımların değerlendirilmesi ve seçimleri birden fazla kriteri gözeterek yapılmaktadır. Ayrıca tek bir karar verici olmadığı için görüşlerin karar vericilerin ağırlıkları orantısında birleştirilmesi önemlidir. 
Bu çalışmada yazılım seçim süreci bir Çok Kriterli Karar Verme problemi olarak ele alınmıştır. Bu sürecin içerisinde insan faktörü olduğu ve belirsizlik içerdiği için bulanık yöntemler daha uygun bulunmuştur. Yazılım seçiminde kullanılacak yöntem olarak küresel bulanık kümeleri temel alan TOPSIS yöntemi seçilmiştir. Küresel bulanık kümeler literatürde oldukça yeni yer alan bir yöntem olduğu için yazılım seçiminde bu yöntemi uygulamak açısından ilk olacaktır.  Bu doğrultuda önce bulanık mantık ve bulanık kümeler ile ilgili kavramlar daha sonra da uygulanacak olan yöntem açıklanmıştır. 
Çalışmanın devamında bir şirket uygulaması yer almaktadır. Büyük ölçekli bir firmanın bilişim teknoloji departmanında yapılan bu uygulamada dört alternatifi olan bir yazılım seçimi ve değerlendirilmesi yapılmıştır. Uygulamada ilk olarak, seçimi etkileyecek kriterler belirlenmiştir. Daha sonra belirlenen kriterler ve alternatifler doğrultusunda karar vericilerin görüşleri alınmıştır. Dilsel terimler temel alınarak alınan görüşler karar matrislerinin oluşturulmasında kullanmıştır. Oluşturulan karar matrislerine ilk olarak önerilen yöntem olan küresel bulanık TOPSIS yöntemi adımları uygulanmıştır. Karar vericilerden alınan kriterlerin önemi ve her alternatif için kriter değerlendirmesi birleştirilmiştir. Daha sonra ağırlıklı karar matrisleri oluşturulup skorları hesaplanmıştır. Ortaya çıkan skorlara göre ideal pozitif ve ideal negatif çözümler bulunmuş ve alternatifler sıralanmıştır.
Daha sonra elde edilen sonuçları küresel bulanık TOPSIS yöntemi ile karşılaştırmak adına sezgisel bulanık TOPSIS yöntemi aynı veri setine uygulanmıştır. Sezgisel bulanık TOPSIS yönteminde verilen hesaplamalar doğrultusunda ağırlıklı karar matrisleri oluşturulmuştur. Daha sonra ideal çözümlere olan uzaklıklarına göre sıralanmıştır. 
Çıkan sonuçlara göre iki yöntem de aynı alternatifi ilk sıraya koymuştur. Son sıradaki alternatifler de aynı çıkmıştır. Küresel bulanık TOPSIS uygulamasında SWAM operatörü ile olan uygulama ile SWGM operatörü ile yapılan uygulamada ikinci ve üçüncü sıradaki alternatiflerin sıralaması farklı çıkmıştır. İki birleştirme operatörünün dayandığı varsayımlar farklı olduğu için bu sonuç normal görülmektedir.

Abstract:
Companies are making investments in order to take a place in today's competitive market. With the development of technology, concept of digitalization is becoming increasingly important. As such, companies have to determine their strategies in this direction. New software for different business areas come into the market every day and companies have to select most suitable one from the alternatives. This selection are made with generally more than one people and considering more than one criteria. Because of these reasons, software selection problem was selected for subject of thesis. Generating a methodology that can be applicable in all software selection is one of the output of this study.
At the beginning of the study, literature review was done. Selection criteria and selection methods from literature were investigated. In most researches, the software is related to what area the criteria are also related to that area. Few studies determine selection criteria based on general perspective.  According to these studies, a set of criteria was created to be a guide for software evaluation. After criteria determination, approaches in studies are also evaluated. It was seen that there are different approaches to the problem in the literature. However, general opinion is one of Multi Criteria Decision Methods can be used for the software selection problem. Some of these studies used the fuzzy methods. It is thought that fuzzy methods can be more suitable because there is always an uncertainty and indecision in the processes that human beings are involved. For making decision in these processes are difficult and time consuming. Therefore, methods based on fuzzy logic can handle the uncertainty. 
Unlike the classical logic system, fuzzy logic is a system based on fuzzy sets that assigns membership degrees to the linguistic terms used in daily life.  In ordinary sets, an element is a member of a set or not. However, in fuzzy logic, there is membership degrees. In the fuzzy logic approach, an element belongs to the set or not as much as its membership degree. It have advantages in terms of using linguistic terms, being flexible and including uncertainty. In this study, fuzzy logic and fuzzy sets concept are explained in detail. A fuzzy system consists of input, fuzzier, rules, fuzzy engine, defuzzier and outputs. In this thesis, all these terms are explained. Fuzzy sets continue to evolve since the day it was defined. There are extensions to deal with problem of determining the membership degrees and expressing uncertainty in a better way.  The fuzzy extensions developed so far are as follows: Type-2 fuzzy sets, Interval-valued fuzzy sets, intuitionistic fuzzy sets, fuzzy multisets, nonstationary fuzzy sets and hesitant fuzzy sets. Finally, spherical fuzzy sets take part in literature as one of the extension of fuzzy set theory. Since it is quite new approach, using spherical fuzzy sets in software selection problem will be first. 
While number of fuzzy set extensions has increased, methods have also been developed that use these extensions in fuzzy multi-criteria decision making methods. Spherical Fuzzy TOPSIS method is one of these and it was selected as methodology. Spherical Fuzzy TOPSIS is based on spherical fuzzy distances. All operations and aggregation operations of method were given in the study. First step of Spherical Fuzzy TOPSIS is gathering opinions of decision makers and constructing decision matrices. For doing that, all opinions should be aggregated. In Spherical Fuzzy TOPSIS method, two aggregation method were proposed that are Spherical Weighted Arithmetic Mean (SWAM) and Spherical Weighted Geometric Mean (SWGM). Based on these two aggregation method, decision matrix should be created at first. After decision matrix, weighted decision matrix should be constructed. For evaluating fuzzy outputs, defuzzification are making with using score functions. Regarding score values, fuzzy positive ideal solution and fuzzy negative ideal solution are obtained. Then, distance of each alternative from the both positive and negative ideal solutions are calculated with based on Euclidean distance formula. Finally, closeness ratios are calculated and all alternatives are ranking in ascending order. Therefore, the alternative that have minimum closeness ratio is the best alternative. 
After the literature reviews and methodology explanations, one software selection problem was chosen from a big-size company. In this application, where in the Information Technologies department of the company, a software selection and evaluation process has been examined. In the selected problem, there are four alternative and three decision makers. Weights of each decision makers are different because of their management level and responsible functions. At the beginning, the criteria that will affect the selection was determined with decision makers. Not all criteria in the literature review were used, only criteria that is meaningful in the process of selected software and affect the selection. After that, opinions of decision makes based on linguistic terms are gathering. With using these linguistic terms, decision matrices were constructed. Both SWAM and SWGM aggregation methods were applied on data. Then weighted decision matrices were created. Then score values were calculated and ideal solutions were determined. At the end, alternatives were ranked based on closeness ratios. As a result, first alternative was found as best alternative in both aggregation way. 
For comparing the proposed methodology, Intuitionistic Fuzzy TOPSIS method were applied to the same data set. The same linguistic terms and criteria weights were used in this method to the comparison. In this method, IWFA operator is used for aggregation. First, decision matrix was construct based on IFWA operator that is an aggregation way. After that, weighted decision matrix was created. Based on weighted decision matrix, positive ideal and negative solutions are determined. Distances from positive and negative ideal solutions are also calculated with Euclidean distance formula. Lastly, closeness ratios are calculated and alternatives were ranked. 
According the results of both method, first alternative was in the first order. In terms of evaluating spherical fuzzy TOPSIS, last alternative is also same for both aggregation operator. The ranking of Spherical Fuzzy TOPSIS with SWAM and ranking with SWGM are different, the place of second and third alternative is in reverse. These results are normal because both aggregation method have use different assumption. On the other hand, although order of first alternative is same in intuitionistic fuzzy TOPSIS, order of other ones is different. It is thought that reason of it is way for determining the ideal solutions. In intuitionistic fuzzy TOPSIS method, positive and negative ideal solutions are determined based on membership degrees. However, in spherical fuzzy TOPSIS, it is done by score functions and score function considers all parameters. Therefore, non-membership degree and uncertainty degree can affect the result. Therefore, these results are suitable for the study. 
To sum up, a software selection problem was investigated in this study. Spherical fuzzy TOPSIS method was used in application. The first output of study is creating a generic criteria list to evaluate software. Then, a software selection problem was solved with spherical fuzzy TOPSIS. This study is important with regard to there is no other study that use this extension method. For further studies, a package program can be created for better and faster evaluation of software. In addition, new methods like spherical fuzzy VIKOR or spherical fuzzy ELECTRE can be developed and used for these problems.