Implementing Fuzzy TOPSIS in Cloud Type and Service Provider Selection

. Cloud computing can be considered as one of the leading-edge technologicaladvances in the currentIT industry. Cloud computing or simply cloud is attributed to the Service Oriented Architecture. Every organization is trying to utilize the benefit of cloud not only to reduce the cost overhead in infrastructure, network, hardware, software, etc., but also to provide seamless service to end users with the benefit of scalability. The concept of multitenancy assists cloud service providers to leverage the costs by providing services to multiple users/companies at the same time via shared resource.There are several cloud serviceproviders currentlyin the market and they are rapidly changing and reorienting themselves as per market demand. In order to gain market share, the cloud service providers are trying to provide the latest technology to end users/customers with the reduction of costs. In such scenario, it becomes extremely difficult for cloud customers to select the best service provider as per their requirement. It is also becoming difficult to decide upon the deployment model to choose among the existing ones. The deployment models are suitable for different companies. There exist divergent criteria for different deployment models which are not tailor made for an organization. As a cloud customer, it is difficult to decide on the model and determine the appropriate service provider. The multicriteria decision making method is applied to find out the best suitable service provider among the top existing four companies and choose the deployment model as per requirement.


Introduction
Cloud computing (CC) provides service to users adopting the distributed computing model.It provides computing resources and service to the users as per demand.Cloud computing enhances user's opportunity who can access infrastructure and software applications in a ubiquitous manner [1].Hardware and licensing costs can be leveraged by utilizing cloud computing and customers can be served in an efficient manner with the aid of scalability attribute.Service offerings in cloud are complex and are constantly evolving.On-demand resource provisioning, broad network access, resource pooling, rapid elasticity, and measured services are some of the key characteristics in cloud computing.Various organizations are trying to adopt cloud from their existing IT infrastructure.The scalability and potential cost effectiveness are attracting various organizations to shift to cloud environment.Recent surveys have revealed that various organizations are willing to transfer their applications to cloud to avail the diverse advantages it offers.The cloud computing market has been growing over the years and the service providers are trying to gain foot hold in the market with various offers in terms of services [2].There are several cloud service providers in current scenario who are providing services almost identical in nature but with variation in characteristics and offerings.The consumers often face difficulty in selecting the best cloud provider as per their requirement.Cloud providers including Amazon Web Services (AWS) and Microsoft give customers the choice to deploy their applications over a pool of virtual services with practically no upfront investment and with an operating cost proportional to their actual usage [3].The cloud service providers help the companies to concentrate on their core business areas, but there are certain factors and parameters which customers need to consider during choice of service [4].Cloud has different deployment models (Public, Private, 2 Advances in Fuzzy Systems and Hybrid) and different service models like SaaS, PaaS, and IaaS.Big IT organizations like Google, IBM, Microsoft, Amazon, etc., are offering various cloud services to users.It becomes an uphill task for a cloud customer or user to determine which company to choose [5,6].Also it becomes complex to decide on the deployment model.Customers are lacking relevant experience and information to assess the service providers capability in various occasions.
This paper analyzes the different criteria for choosing the suitable service provider along with the deployment model using the Multi Criteria Decision Making (MCDM concept).The evaluation will be done using the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method [7].MCDM method helps decision makers (DMs) in integrating objective measurements with value judgments that are based on collective group ideas instead of individual opinions.
The best alternative is deduced based on the shortest distance from the fuzzy positive ideal solution (FPIS) and farthest distance from the fuzzy negative ideal solution (FNIS).FPIS refers to maximization of benefit criteria while minimizing cost criteria whereas FNIS will maximize cost criteria and minimize benefit criteria.Utilizing the concept of Fuzzy TOPSIS, FPIS, and FNIS was defined and distance from each alternative from FPIS and FNIS was calculated.In final stage the closeness coefficient will help in determining the ranking order of the alternatives [6].
The current research work deals with the application of TOPSIS in the two most critical areas of concern, viz., selection of the suitable cloud service provider from the top 3 in current fiercely competitive cloud industry and most suitable cloud based on its type.Section 2 deals with related works.Section 3 describes the different cloud service providers and cloud types.Section 4 describes the MCDA techniques.Section 5 deals with fuzzy TOPSIS.Section 6 has two parts dealing with cloud service provider selection and cloud type selection using TOPSIS.Section 7 concludes the paper.
MCDA technique has found its application in several research areas to determine the best alternative among numerous alternatives with different set of criteria.In the current scenario there are multiple cloud service providers offering numerous attractive benefits to customers.Similarly, it is very difficult to determine the suitable cloud type for an organization.Fuzzy TOPSIS has been applied in this paper to determine the most suitable service provider and also the cloud type for an organization.

Related Work
In recent years there had been numerous studies on cloud service provider selection and cloud type selection.There are top cloud service providers offering plethora of services at different rate and multiple features.It becomes extremely difficult for a company to decide the best service provider and also the type of cloud to choose [8].Kumar and Rai (2016) have studied IaaS with 3 different sets of criteria and provided a framework on cloud simulation.Costa (2013) has worked on selection of cloud service providers using MACBETH

Cloud Computing and
Cloud Service Providers  We human beings face difficulty in finding the best alternative if there exists multiple criteria and in such situation MCDA can guide in proper decision making.As an example we may consider our current scenario where we have different cloud providers.All the cloud providers are competing against each other to gain the top position and have been trying to draw customers by providing different attractive and cost competitive features.There are distinctive features like control interface features, support services availability, and server OS types which are being offered by the cloud service providers.A customer needs to take decision on the distinctive features being offered by the cloud providers and select the one which is the best alternative among them.MCDA is developed based on the human thinking and their approach in decision making.There are several MCDA methods and techniques available, but the basic methodology is similar based on existing diverse set of criteria and decision making.MCDA consists of methodologies, application of theories, and techniques aiding and dealing with decision making problems.Decision making theory has been applied to solve various real-life problems where multiple conflicting criteria can exist.

MCDA Methods.
MCDA is part of operational research which aims to select the suitable or best alternative among several options with the aid of mathematical and computational tools.It consists of two main categories: Multiattribute Decision Making (MADM) and Multiobjective Decision Making (MODM).MCDA can also be categorized into 2 types, viz., (a) Multiattribute Utility Theory (MAUT) and (b) outranking methods.Using MAUT we try to find a function which determines the utility or usefulness of an alternative.Every action is linked with a marginal utility and a real number will represent the preference in the considered action.The resultant utility represents the addition of the marginal utilities.Outranking method helps in finding the alternative which is ranked higher when compared pairwise.Figure 2 shows the different branches of MCDA.

Analytic Hierarchical Process (AHP).
Analytic Hierarchical Process (AHP) was introduced by Thomas L Satty in 1980.This is a popular and widely used method for MCDA.Complex MCDM problems are divided into system of hierarchies.In final stage AHP deals with an M X N matrix where M refers to number of alternatives and N represents number of criteria.The matrix is formed considering the relative importance of alternatives against each criterion.Both qualitative and quantitative criteria are used in AHP to find the alternatives and attributes are not entirely independent of each other [12].Pair wise comparison is used in AHP and the attributes are structured into a hierarchical relationship.Hierarchy starts from top level and then proceeds towards the goal.Criteria, subcriteria, etc., represent the lower levels.The process execution in hierarchy tree initiates from the leaf nodes and it proceeds to the top level.Output level represents hierarchy related to the weight or the influence of different branches which originated at that level.In final stage the comparison is done and best alternative against each attribute is selected.

Analytic Network Process (ANP). Analytic Network Process (ANP) can be referred to as an extension or generalization of Analytic Hierarchy Process (AHP). ANP decision making technique is designed using unidirectional hierarchical relationships between different levels and taking upon the problem of dependence and feedback on different criteria. ANP considers interrelationships within decision levels and attributes using unidirectional hierarchical relationships. It models the decision problem by implementing ratio scale measurements based upon pair wise compare.
The interdependence between elements is effectively handled by ANP using composite weights and "super matrix".In many real world scenarios of decision making, ANP has been successfully applied.It has been observed that many decision making problems cannot be hierarchically structured as there is involvement of interaction and dependence between higher and lower level elements [13].Thus ANP is represented as a network instead of hierarchy.The feedback structure is devoid of the top-to-bottom form in hierarchy.It rather looks like a network with cycles connecting its component of elements which cannot be referred as levels and it loops to connect a component to itself.ANP has sources and sinks.Source node is the origin of paths of influence and is not the destination of paths.Sink node is a destination of paths of influence and is not an origin of paths.A full network may consist of source nodes, intermediate nodes which appear on the paths from source nodes and lie or fall on path to sink nodes and finally sink nodes.

Technique for Order of Preferences by Similarity to Ideal Solutions (TOPSIS).
In multicriteria decision making (MCDM) methods we know the ratings and weights of the criteria.TOPSIS was first developed by Hwang and Yoon for solving issues where multicriteria exist and decision making becomes a complex affair.In TOPSIS the performance ratings and weights of the criteria are provided with crisp values.C.T. Chen developed TOPSIS methodology further in solving multiperson and multicriteria decision issues in real world environment where fuzzy exists.Linguistic variables are used to determine weights of all existing criteria and ratings given on each alternative linked to each criterion as there exists fuzziness in decision data and group decision.
In Fuzzy TOPSIS we define the Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS).Then calculation is done on distance of each alternative from FPIS and FNIS.Finally ranking order of alternatives is determined using closeness coefficient.

Elimination and Choice Expressing Reality (ELECTRE).
Elimination and Choice Expressing Reality (ELECTRE) was introduced initially in 1966.This deals with "outranking relations" by performing pairwise comparison among alternatives under each criterion separately.Later several versions were developed like ELECTRE I, ELECTRE II, ELECTRE III, ELECTRE IV, and so on.ELECTRE belongs to the class of outranking methods and it involves up to 10 steps.Pairwise comparison is done between alternatives to find out the outranking relationships.The relationships in turn help in identifying and removing the alternatives which are dominated by others, resulting in a smaller set of alternatives.
ELECTRE method handles discrete criteria that are both qualitative and quantitative and provides ordering of alternatives.Ranking of alternatives is obtained by using graphs in an iterative procedure.This method starts comparing pair wise of alternatives under each criterion.The ELECTRE method finds a whole system of binary outranking relations among the alternatives.ELECTRE method at times is unable to identify the preferred alternative since the systems are not necessarily complete ones.It yields the core of leading alternatives.This method eliminates the less favorable ones thus giving a clear understanding of the alternatives.In cases where we need to deal with few criteria and large alternatives, this ELECTRE method will be useful.4.2.5.Fuzzy.Fuzzy set theory has been initially proposed by Zadeh in 1965 and is applied in areas of uncertain data or there is lack of precise information.Fuzzy can help in multicriteria decision making where there exist several uncertainties in available information.The decision pools help in finding selected alternative criteria using the fuzzy MCDA model.Weights are assigned to criteria which are evaluated in terms of linguistic values.Linguistic values are then assigned fuzzy numbers.Inside fuzzy set, fuzzy terms are described by linguistic variables which in turn are used to map the linguistic variables to numeric variables [14].
4.2.6.Goal Programming.Goal Programming is a MODM tool proposed by Charnes in 1955.In areas of multiple conflicting objects the Goal Programming is applied.This is an extension of Linear Programming.Multiple conflicting objective measures can be handled by the Goal Programming optimization procedure.Mathematical programming is combined with the logic of optimization in order to take decisions involving several objectives in different multicriteria decision making problems.

Motivations in Selecting TOPSIS
Method.TOPSIS is one of the most popular multicriteria decision making (MCDM) methods.It deals with the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution while determining the best alternative.TOPSIS is a well-known method due to the following reasons: (a) theoretical stringency, (b) effective usage of human thinking in selection process, (c) guides in decision making using rank alternatives in fuzzy environment, (d) proper implementation of subjective and objective criteria, (e) crisp values assigned to performance ratings and also to the weights of the criteria which helps in dealing with MCDM problems.

Brief Overview of TOPSIS Method
TOPSIS stands for Technique for Order Preference by Similarity to Ideal Solution.Here two artificial alternatives are hypothesized which are Ideal Alternative and Negative Ideal Alternative.Ideal Alternative is the one which has the best attribute values like maximum benefit attributes and minimum cost attributes.Similarly Negative Ideal Alternative includes the worst attribute values like minimum benefit attributes and maximum cost attributes.The TOPSIS method chooses the alternative which is nearest to the ideal solution and farthest from the negative ideal solution [15,16].The outline of the TOPSIS method is presented in the following.
Step 1. Evolution matrix is formed of m alternatives and n criteria, using the intersection of each alternative and criteria given as   , and then we have a matrix (  ) m x n Step 2. The matrix (  )  is then normalized to form the matrix.R = (  )    using the normalization method   =   /√∑ and the distance between the alternative i and the best condition where   and   are L2 -norm distances from the target alternative i to the worst and the best conditions, respectively.
Step 6. Calculate the similarity to the worst condition: = 1 if and only if the alternative solution has the best condition.  = 0 if and only if the alternative solution has the worst condition.
The three cloud companies are evaluated by three decision makers on a seven point linguistic scale comprising the values in Box 2.
The decision makers' opinion is considered for each criterion in Table 3.The fuzzy decision matrix of 3 cloud service providers is given by the following.
For cloud provider AWS, under the feature F 1 , the evaluation is The distance of the alternatives from B i from positive solution is calculated by This is done for all the 3 cloud platforms.
The separation measures from positive ideal solution and negative ideal solution are calculated [20].This is given in Table 7.
The closeness coefficient CC i is given by d i − / (d i + + d i − ) based on the separation measures obtained in Table 7.The separation measure in Table 7 is determined based upon the FPIS and FNIS.
The ranking order is determined from the closeness coefficient matrix and it was found Hybrid>Public>Private.The best alternative cloud type is Hybrid.

Conclusion
In today's smart era, competition is gradually increasing among the Cloud service providers in the market.It is getting steeper day by day as new entrants are joining in the service provider pool.Top cloud service providers are changing their strategies to retain their position in this volatile market.Hence they are very keen on selection of features which they are providing to the customers.So every provider offers a set of specific features which differ from those of the others.Now it is the client's responsibility to choose the appropriate vendor from the available ones based on their need.This vendor selection requires understanding and analyzing the features in deep, which is quite tedious if done manually.So there is a crying need of some technique which can perform this analysis automatically.This paper deals with TOPSIS methodology which helps us to select the most suitable service provider by analyzing its available offerings and features.It also studied in detail the different MCDA Advances in Fuzzy Systems methods available along with the TOPSIS methodology.The TOPSIS technique is applied in selecting the suitable cloud for an organization which is embracing cloud from on-premise architecture.However, the detailed study will help cloud consumers in selecting the best service provider and cloud service from a set of different offerings and cloud features.

Step 4 .
is the original weight given to the indicator V  , j = 1, 2 . . ...n Determine the worst alternative (  ) and the best alternative (  )  = {(max(  | i = 1, 2 . . .., m) | j ∈  − ), (min(  | i = 1, 2 . . ..m) j ∈  + )} ≡ {  | j = 1, 2 . . .n},   = {(min(  | i = 1, 2 . . .., m) | j ∈  − ), (max(  | i = 1, 2 . . ..m) j ∈  + )} ≡ {  | j = 1, 2 . . .n},where  + = {j = 1, 2, . . .., n | j associated with the criteria having a positive impact and  − = {j = 1, 2, . . .., n | j associated with the criteria having a negative impactStep 5. Calculate the L2 -distance between the target alternative i and the worst condition Cloud computing provides different benefits.Cloud services offer scalability.Dynamic allocation and deallocation of resources happen based on demand.Cost savings are another major advantage which happens due to cost reduction in capital infrastructure.Applications can be accessed across the globe and without the hardware configuration in the local machine also.Network is simplified, and client can access the application without buying license for individual machine.Storing data on cloud is more reliable as it is not lost easily.Private cloud as the name suggests refers to infrastructure which is linked to a concern either managed by an organization or third party.It may be present on premise or off site.In private cloud the service is offered to a specific organization and is not meant for public use.In terms of security private clouds are providing highest amount of security service.Private clouds can be built and managed by companies own infrastructure or by cloud service provider.
(V) Interfaces (APIs) (ii) PaaS.PaaS or Platform as a service delivers development or operating environments as a service.It is a combination of tools and services designed for coding and deploying the applications in an effective and efficient manner.The major difference with SaaS model is that PaaS is a platform for development/deployment of the software instead of readymade software delivered over the Internet.Few major examples include Salesforce.com'sForce.com,Azure from Microsoft, and Google App Engine.The major characteristics are the following: (a) A one stop solution for developing, testing, deploying, hosting, and maintaining applications (b) Web-based UI designing tools to create, modify, test, and deploy different UI scenarios (c) Multitenant architecture facilitating concurrent users (d) Load balancing, security, and failover capabilities for application to be deployed (e) OS and cloud programming APIs to create new apps for cloud or to cloudify the current apps (f) Tools to handle billing and subscription (iii) IaaS.The infrastructure cloud is responsible for storage and compute resources as a service which is basically used by various IT organizations for providing business solutions.Complete flexibility is provided in this approach to the user; users can choose among desktops, servers, and network resources.The entire infrastructure package can be customized by choosing anything from the list of CPU hours, storage space, bandwidth, etc.This cloud type has different categories like private, public, and hybrid.Public cloud consists of shared resources whereas private cloud is responsible for providing secure access to the resources and is managed by the organization it serves [9].This type of cloud is maintained by both internal and external providers.Some notable characteristics are the following: (a) Resources distributed as a service (b) Dynamic, on-demand scaling of resources (c) Utility based pricing model (d) Concurrent users on a single piece of hardware 3.3.Cloud Computing Benefits.3.4.Challenges behind Cloud Services.Cloud services cover various issues along with its advantages.Few such concerns are listed in the following: (a) Security and Privacy (b) Interoperability and Portability (c) Reliability and Availability (d) Performance and Bandwidth Cost 3.5.Cloud Service Providers.Cloud service providers refers to different organizations that offer infrastructure, network services, software, hardware components, etc. to different customers and business entities.Cisco, Citrix, IBM, Google, Microsoft, Rackspace, etc. are examples of cloud service providers.In the paper we have considered currently, the top cloud service providers in market are like Amazon Web Services, IBM Bluemix, and Google Cloud Compute.Evaluating the cloud service provider is not an easy activity, but it requires thorough analysis.This has been dealt with in this research article in detail.Cost cannot be the single criteria for selecting a service provider, but different offerings should also be considered in detail.The different fine prints in the agreement need to be analyzed by customers before selecting the provider.Google, Amazon, and Microsoft are notable examples of public cloud vendors.Some advantages of public cloud are (i) seamless data availability, Limitations of hybrid cloud are (i) higher cost, (ii) security aspects, (iii) compatibility issues.

4. Multicriteria Decision Analysis (MCDA) 4
[11]ackground of MCDA.Multicriteria Decision Analysis (MCDA) or Multi Criteria Decision Making is a subbranch of operational research which helps in decision making where several decision making criteria exist.Finding out the best option from the available alternatives is known as decision making.In real world scenario decision making is difficult where there are conflicting goals, different constraints, and unpredictable end results[11].Here the fuzzy set theory can be used where we are unable to conclude precisely.In 1951 the vector maximum problem was first introduced by Harold William Kuhn and Albert William Tucker.This can be considered as the basics of MCDA.Later in 1972 "Multiple Criteria Decision Making" conference was held in Columbia University.MCDA has been growing in rapid space in the following decades since then.The MCDA uses the mathematical and computational tools in selection of the best alternative among different choices which may have conflicting criteria.MCDA helps in finding the best alternative among different available choices with respect to specific criteria by decision maker.

Table 1 .
The three different decision makers are represented in Table1by D1, D2, and D3.

Table 1 :
Criteria assessed by decision makers.

Table 6 :
Assessment on different platforms by decision makers.