A centroid ranking approach based **fuzzy** **MCDM** **method** is proposed to evaluate and select consulting firms, where criteria are classified to qualitative, benefit quantitative and cost quantitative ones. In the proposed model, ratings of alternatives versus qualitative criteria and the importance weights of all criteria are assessed in linguistic values represented by **fuzzy** numbers. Membership functions of the final evaluation values can be developed. The Euclidean distance based on centroid points is applied to defuzzify all the final **fuzzy** evaluation values to determine the ranking order of alternatives in order to complete the model. Formulas for the two centroid points on horizontal and vertical axes can be clearly developed. Finally, a numerical example has demonstrated the computational process of the suggested model.

Show more
In this study, it is divided into 4 (four) main phases, namely the identification phase, the data collection phase, the analysis phase and the conclusion drawing phase. In the first phase of identification, identification of problems and research objectives is carried out. In the second phase of data collection, the primary data were collected from interviews and questionnaires, secondary data were obtained from literature studies in the form of books and journals. In the third phase, namely analysis. The first analysis is to make a mind mapping that is writing everything that is in the mind in the form of problems, objectives, aspects, steps, and methods in research. The **method** used for this research is **Fuzzy** **MCDM** to get the alternative value offered. In the **Fuzzy** **MCDM** **method** to determine alternative values, previously it must go through stages beginning with determining the criteria and alternative research in Figure 3. Conceptual Framework of Hierarki structure **Fuzzy** **MCDM** Analysis.

Show more
The remainder of this paper is organized as follows. The **fuzzy** **MCDM** **method** used in proposed hybrid **method** is introduced and reviewed in section 1. In section 2, dynamic **fuzzy** hybrid **method** is proposed. Section 3 provides an empirical example for supplier selection, result analysis and discussion to illustrate the proposed **method**. Section 4 concludes the paper.

As concluded from this comparison, the priority rank of risk factors is same with proposed **fuzzy** **MCDM** **method** but the computations in utilized **fuzzy** AHP **method** is relatively high and limitation in applying other membership functions and **fuzzy** numbers rather than triangular **fuzzy** numbers, make it impractical in the field of construction risk assessment. Also there is no rational comparison between prioritized risk factors and as the result risk mitigation strategy cannot effectively be added to risk management process.

14 Read more

In this section, we briefly review the theory of **fuzzy** sets from [8-11]. In Fig.1, we see a graph of a crisp set and a **fuzzy** set. The **fuzzy** set A can look very different depending on the chosen membership function. Using this function, it is possible to assign a membership degree to each of the element in the universe of discourse X. Elements of the set could but are not required to be numbers as long as a degree of membership can be deduced from them. It is important to note the fact that membership grades are not probabilities. One important difference is that the summation of probabilities on a finite universal set must equal 1, while there is no such requirement for membership grades.

Show more
11 Read more

In this paper, a numerical **method** for solving '**fuzzy** dierential inclusions' is considered. The **fuzzy** reachable set can be approximated by the proposed **method** with complete error analysis which is discussed in detail. Moreover, the extrapolation **method** is employed for increasing the accuracy of the approximate solution. The **method** is illustrated by solving some linear and nonlinear **fuzzy** initial value problems.

13 Read more

---------------------------------------------------------------------------***--------------------------------------------------------------------------- ABSTRACT: - In this paper a numerical **method** for solving **fuzzy** transport equation is considered and also we use separable variable **method** to solve **fuzzy** transport equation. First described the preliminaries definitions, and then consider a finite difference scheme for the one dimensional transport equation, then described the **fuzzy** separation variable **method**. We use Matlab for numerical calculation. In this example, it obtains the Hausdorff distance between Finite different scheme solution and separable variable solution.

Show more
10 Read more

In this paper we analyzed and evaluated the reliability characteristic of the software product or project. Firstly we reviewed various pre defined models for the software quality and reliability in them as particular. It was diagnosed that although all the attributes relative to reliability are included in the ISO 25010 model other than scalability. Hence, we proposed a new model for software reliability with the availability, maturity, fault tolerance, recoverability along with scalability. Now, in order to check the consistency of the proposed model, we conducted the survey among the software industry people. 47 participants from various reputed software industry participated in the survey. We applied AHP **method** for insuring the consistency of the proposed reliability model. Results evaluated showed that the chosen sub characteristics for the software reliability are consistent. The relative ranking of the sub characteristics is scalability, maturity, fault tolerance, recoverability and then availability. This model can further be used for the evaluation of the overall quality of different software products or projects.

Show more
The purpose of this study was to prepare a cropland suitability map of Mon- golia based on comprehensive landscape principles, including topography, soil properties, vegetation, climate and socio-economic factors. The primary goal was to create a more accurate map to estimate vegetation criteria (above ground biomass AGB), soil organic matter, soil texture, and the hydrothermal coefficient using Landsat 8 satellite imagery. The analysis used Landsat 8 im- agery from the 2016 summer season with a resolution of 30 meters, time series MODIS vegetation products (MOD13, MOD15, MOD17) averaged over 16 days from June to August 2000-2016, an SRTM DEM with a resolution of 30 meters, and a field survey of measured biomass and soil data. In total, 6 main factors were classified and quality evaluation criteria were developed for 17 criteria, each with 5 levels. In this research the spatial **MCDM** (multi-criteria decision-making) **method** and AHP based GIS were applied. This was devel- oped for each criteria layer’s value by multiplying parameters for each factor obtained from the pair comparison matrix by the weight addition, and by the suitable evaluation of several criteria factors affecting cropland. General accu- racy was 88%, while PLS and RF regressions were 82.3% and 92.8%, respec- tively.

Show more
26 Read more

The paper adds to the entrepreneurial evaluation litera- ture in several ways. First, no prior study that we are aware of has examined critical factors of entrepreneurship as a driving force of entrepreneurial intensity. Second, few studies in the literature examine the performance of SMEs regarding this evaluation. The next contribution of this research is that there is no more study using **MCDM** in **fuzzy** environment to evaluate EI among the SMEs. This paper is intended to bridge these gaps. The remainder of the paper is as follows. In the next section, we review the existing literature. In Section 3, the methodologies such as FAHP, VIKOR, and TOPSIS are used to assess the criteria. Applications of the proposed methodologies in real-world situations and a comparison of the results are presented in Section 4. The results and discussion are discussed in Section 5. Finally, in Section 6, conclusion and future studies are given.

Show more
17 Read more

Many **MCDM** techniques are based on the additive concept along with the independence assumption, but each individual criterion is not always completely independent [8]. To solve the interactions among elements, the analytic network process (ANP) was proposed by Saaty. This technique is a mathematical theory that can solve all kinds of dependence systematically, but it doesn’t work completely or perfectly. This is because using the ANP to solve **MCDM** problems leads to different influence levels among the criteria based on the network relationship map (NRM). If we don't comprehend the causal relationship, and utilize the average **method** to calculate the final global priorities, the results of the assessed weights could be higher or lower than the real situation [9]. Consequently, the decision-making trial and evaluation laboratory (DEMATEL) was introduced. This is a powerful technique which can convert the relationship between cause and effect criteria into an intelligible structural model of the system, and propose the most important criteria which affect

Show more
13 Read more

Medical imaging has been an active area of research where abnormalities are detected non invasively. But dealing with medical images is a challenging task. Due to the complexity in the images, many of the structures are hardly visible; various soft computing techniques are applied by different researchers to process medical images. In order to carry out this task, intuitive ways have been found out to interpret and describe the inherent ambiguity and vagueness in the medical images in terms of intuitionistic **fuzzy** set theory. The efficiency of the use of IFS theory in medical image processing can be demonstrated in the context of contrast enhancement, segmentation where the performance is observed to be much better.

Show more
10 Read more

Step 3:- Pair-wise comparison of dimension The four dimensions data security DS, storage security SS, information security IS and access management AM and its pair-wise comparison matrix[r]

This paper presents a sequencing problem with the aid of triangular or trapezoidal **fuzzy** numbers. For finding the initial solution of this problem we have preferred the **fuzzy** quantifier and ranking **method**, also the optimal solution(order) by using the **method** of processing n jobs through two machines has been carried out. The solution procedure is illustrated with numerical example.

There are a lot of situations which differential in- clusion naturally occur, but this concepts do not extended to FIVP. A certain number of papers have been appeared where attempts have been made to investigate differential inclusions with uncertainty about some of their components de- scribed in terms of **fuzzy** sets. Most of authors continued the idea from Hallermeier, but it is a correction of FIVPs’ solving methods not really extension of crisp inclusion concepts. In other words if we consider real problem like oscillat- ing system with combined dry and viscous damp- ing, . . . in the case of **fuzzy** initial value, they can not be modeled by existence model of differential equations because their initial value vary along **fuzzy** interval and interval can ’t be determined exactly. As it is said, in the previous works au- thors used the concept of crisp inclusion to find- ing r − soultion of FIVP after discretizing it to m crisp differential equation. To overcome this dif- ficulty and generalizing the model to cover this kind of real problem, we suggest a new concept **Fuzzy** inclusions, which by it we mean that the problem that its initial value belongs to a **fuzzy** set. The origin of differential equations with a **fuzzy** right hand can be illustrated by the follow- ing example. Suppose, that there is a differential equation which models a real process:

Show more
13 Read more

In this paper, we have considered two person zero sum game with pay offs as triangular, trapezoidal and Octagonal **Fuzzy** Numbers. TOPSIS (Technique for order preference by similarity to ideal solution) procedure is proposed when the relative importance of strategies are not the same that is weights are assigned to the strategies.

Abstract. The problem of selecting the right stocks to invest in is of immense interest for investors on both emerging and developed capital markets. Moreover, an investor should take into account all available data regarding stocks on the particular market. This includes fundamental and stock market indicators. The decision making process includes several stocks to invest in and more than one criterion. Therefore, the task of selecting the stocks to invest in can be viewed as a multiple criteria decision making (**MCDM**) problem. Using several **MCDM** methods often leads to divergent rankings. The goal of this paper is to resolve these possible divergent results obtained from different **MCDM** methods using a hybrid **MCDM** approach based on Spearman’s rank correlation coefficient. Five **MCDM** methods are selected: COPRAS, linear assignment, PROMETHEE, SAW and TOPSIS. The weights for all criteria are obtained by using the AHP **method**. Data for this study includes information on stock returns and traded volumes from March 2012 to March 2014 for 19 stocks on the Croatian capital market. It also includes the most important fundamental and stock market indicators for selected stocks. Rankings using five selected **MCDM** methods in the stock selection problem yield divergent results. However, after applying the proposed approach the final hybrid rankings are obtained. The results show that the worse stocks to invest in happen to be the same when the industry is taken into consideration or when not. However, when the industry is taken into account, the best stocks to invest in are slightly different, because some industries are more profitable than the others.

Show more
18 Read more

Liou and Wang [16] presented ranking **fuzzy** numbers with integral value. Choobineh and Li [10] presented an index for ordering **fuzzy** numbers. Since then several methods have been proposed by various researchers which include distance **method** by Cheng [9]. Wang and Kerre [21,22] classified the existing ranking procedures into three classes. The first class consists of ranking procedures based on **fuzzy** mean and spread and second class consists ranking procedures based on **fuzzy** scoring whereas, the third class consists of methods based on preference relations and concluded that the ordering procedures associated with first class are relatively reasonable for the ordering of **fuzzy** numbers specially, the ranking procedure presented by Adamo [3] which satisfies all the reasonable properties for the ordering of **fuzzy** quantities. The methods presented in the second class are not doing well and the methods which belong to class three are reasonable. Stephen Dinagar and Kamalanathan [20] defined a distance based ranking procedure SD of PILOT to solve the maximize net present value.

Show more
11 Read more

This modelling is based on TSK **method** in which consequence part in the form of linear equation of the form: Y= mx+C. For modelling Adaptive Neuro-**Fuzzy** Inference System (ANFIS) tool from MATLAB is being used. The Neuro-adaptive learning **method** works similarly to that of neural networks. Neuro-adaptive learning techniques provide a **method** for the **fuzzy** modelling procedure to learn based on the information about a data set. **Fuzzy** Logic Toolbox software computes the membership function parameters that best allow the associated **fuzzy** inference system to track the given input/output data. The **Fuzzy** Logic Toolbox function that accomplishes this membership function parameter adjustment is called ANFIS. The ANFIS function can be accessed either from the command line or through the ANFIS Editor GUI as the functionality of the command line function ANFIS and the ANFIS Editor GUI is similar in nature. In this tool the decision making such as rule formulation, number of rule etc. is done automatically according to data provided in the form of .MAT format. Even though it can create output linear equation, but we can edit this equation according to need based tuning [8].

Show more