The recent government tendering process being conducted in an electronic way is becoming an inevitable affair for numerous governmental agencies to further exploit the superiorities of conventional tendering. Thus, developing an effective webbased bid evaluation methodology so as to realize an efficient and effective government Etendering (GeT) system is imperative. This paper firstly investigates the potentiality of employing fuzzy analytic hierarchy process (AHP) along with fuzzy gray relational analysis (GRA) for optimal selection of candidate tenderers in GeT process with consideration of a hybrid fuzzy environment with incomplete weight information. We proposed a novel hybrid fuzzy AHPGRA (HFAHPGRA) method that combines an extended fuzzy AHP with a modified fuzzy GRA. The extended fuzzy AHP which combines typical AHP with interval AHP is proposed to obtain the exact weight information, and the modified fuzzy GRA is applied to aggregate different types of evaluation information so as to identify the optimal candidate tenderers. Finally, a prototype system is built and validated with an illustrative example for GeT to confirm the feasibility of our approach.
The basic principles of the tendering process have been applied to many business areas, such as purchasing goods, seeking service providers, business consulting, or the selection of main contractors for construction work [
Therefore, in order to solve the above problems, researchers have introduced the Etendering system [
Developing and promoting an efficient and effective government Etendering system so as to further optimize the conventional government tendering process is a complicated project that contains numerous subsystems. Webbased bid evaluation system is a crucial one of those subsystems, which aims at identifying the optimal tenderer with the given information of tenderers using efficient and effective methodologies or methods. In this paper, we will firstly investigate the potentiality of a combined methodology, which is a combination of extended fuzzy analytic hierarchy process (AHP) and modified fuzzy gray relational analysis (GRA), to meet the demands of government Etendering. The novel hybrid fuzzy AHPGRA (HFAHPGRA) methodology is proposed in a hybrid fuzzy environment, where the information of tenderers is expressed as four different types of numbers (real number, interval number, triangular number, and intuitionistic fuzzy number) with consideration of a reality that experts are most likely to express their evaluations on tenderers as different types of numbers. Compared with typical AHP and interval AHP, the extended fuzzy AHP can deal with interval preference matrices while typical AHP cannot. The extended fuzzy AHP can also obtain the exact weight information of alternatives while interval AHP cannot. The modified fuzzy GRA, rather than typical fuzzy GRA, can further aggregate four different types of evaluation information in one evaluation matrix.
The remainder of this paper is arranged as follows. Some related works are discussed in Section
The past decades have seen the rapid development of Internet technologies, communication technologies, computer technologies, certification technologies, and so forth. These technologies make it possible to realize the electronization and informatization of conventional tendering process. Both public and private sectors in various business categories agree that efficiencies can be made through the use of Eprocurement whilst maintaining quality and producing greater valueformoney [
However, the uptake of Etendering in numerous governmental agencies has been slower than expected despite the fact that Eprocurement systems have already been widely applied in many countries. The situation is that most systems are only used for providing procurement information, receiving bidding information and venders’ catalogs, and using purchase cards on procurement of small items [
Webbased bid evaluation system is a crucial part of the whole government Etendering system, which has been applied to identify the optimal tenderer given the information of different tenderers by means of Internet or artificial intelligence technologies. It aims at replacing traditional manual bid evaluation process so as to suppress bid collusion, develop efficiency, and save costs. Since traditional bid evaluation system can hardly satisfy modern bid evaluation because of the explosion of information and the uncertainty, vagueness, dynamicity, and complication of current bid evaluation environment, it is reasonable to develop an efficient and effective webbased bid evaluation system. Singh and Benyoucef [
However, restricted by their theoretical assumptions and mechanisms, the above systems are unable to adapt to a vague, uncertain, complicated, and dynamic tendering circumstance; that is, these systems are not suitable for government Etendering. In this paper, we will firstly apply the combination of extended fuzzy AHP and modified fuzzy GRA, namely, HFAHPGRA methodology, for government Etendering. The whole HFAHPGRA methodology is proposed in a hybrid fuzzy circumstance, where the evaluations of experts on tenderers’ attributes are expressed as different kinds of numbers, such as real number, triangular number, intuitionistic fuzzy number, and interval number. Additionally, we assume that both weight information of experts and attributes of tenderers are incompletely known. Thus, the evaluation environment can be described as accurately and objectively as possible during evaluation process.
There exist two kinds of concepts: clear concept and fuzzy concept. Clear concept refers to concepts that are certain, definite, and specific, such as “tree” and “flower.” On the contrary, fuzzy concept refers to those concepts that are uncertain, indefinite, and abstract, such as “good” and “beautiful.” In fact, fuzzy concepts are much more common. The common mathematical models are not able to deal with those fuzzy concepts because of their natures from birth.
Thus, exploring new mathematical theories to bridge the gap between mathematics and fuzzy concepts is imperative. Zadeh [
However, only using one of those different kinds of fuzzy numbers to describe evaluation information or attribute information is insufficient for government Etendering, because the webbased bid evaluation process involved is complicated and comprehensive. What is worse, the evaluation environment is uncertain, vague, and dynamic. Therefore, Xu [
Therefore, in this paper, we propose the extended fuzzy AHP to deal with the above problem. Additionally, we use four representation formats, including real number, interval number, triangular number (that are used to transform linguistic labels), and intuitionistic fuzzy number, to describe evaluation information and attribute information. This aims at expressing related bid evaluation information more objectively, authentically, and comprehensively.
Saaty [
The structure of typical AHP.
The basic idea of typical AHP is based on the pairwise comparison matrices. Each element of a matrix stands for the personal preference of decision maker on one alternative versus another one, which is usually expressed as linguistic terms. These linguistic terms can then be transformed into Likert numbers from one to nine or decimal numbers between 0 and 1. Consistence check of comparison matrix is realized by a consistency ratio
Though typical AHP is a convenient, flexible, and effective multicriteria decision making approach that combines qualitative analysis with quantitative analysis, it still has shortages in dealing with the transformation of qualitative information into quantitative information. Likert numbers are discrete and dispersive, while the preferences of decision maker are consecutive. Therefore, the theoretical assumption of the transformation of decision maker’s preferences into Likert numbers is defective. In order to alleviate such deficiency, we choose to translate preferences into interval Likert numbers so as to make the translation as reasonable as possible. After preferences are transformed into interval Likert number, singly typical AHP will be no longer available. Thus, we proposed an extended fuzzy AHP which combines typical AHP theory with interval AHP theory in this paper.
GRA method was originally proposed by Deng [
The basic process of GRA.
Generally, the elements of evaluation matrix of one GRA process are always expressed as values sharing the same date type. However, in this paper, the evaluation matrices consist of four different data types: real number, interval number, triangular number, and intuitionistic fuzzy number. Therefore, according to the different data types, we need to apply correspondingly different methods to realize the normalization and distance calculation during GRA process.
The integrated AHPGRA method has already been widely researched and applied to many areas [
This paper will firstly investigate the potentiality of a novel HFAHPGRA methodology. Four different types of fuzzy numbers (real number, triangular number, intuitionistic fuzzy number, and interval number) will be used to describe bid evaluation information so as to ensure the objectivity, authenticity, and comprehensiveness of the quantification process of bid evaluation information. The proposed novel HFAHPGRA methodology consists of two main stages: weight information obtaining and optimal tenderer identification.
Mostly, a decision maker cannot exactly express his/her personal preference on one alternative versus another one. In this paper, we assume a decision maker expresses his/her opinions by means of an interval multiplicative preference comparison matrix (IMPCM). Besides, different from the typical AHP, the extended fuzzy AHP in this paper has four levels including objective level, expert level, criteria level, and alternative level, shown in Figure
The structure of extended fuzzy AHP.
Let
The consistency and acceptable consistency of a realnumbered multiplicative preference comparison matrix (RMPCM) have been defined by Saaty [
The standard values of

1  2  3  4  5  6  7  8  9  10 



0  0  0.52  0.89  1.12  1.26  1.36  1.41  1.46  1.49 
However, the above definition is not applicable for IMPCM. Liu [
Then,
Therefore, by using expressions (
After checking the acceptable consistency of
According to the ranking principles of two interval weights (let
A twodimensional style of two interval weights.
Thus, the possibility degree matrices
(1) Transforming additive preference comparison matrix into multiplicative preference comparison matrix. Liu et al. [
(2) Since the consistency of
(3) Then, by normalizing the eigenvectors corresponding to the largest eigenvalues, the weight information of experts and evaluation criteria, which is presented as crisp values, can be obtained.
The attribute information generally consists of two types: real numbers and linguistic terms. For example, price is always represented in the format like real number or interval number, while most of the other attributes, such as feasibility, artistry, and functionality,, are shown as linguistic terms like “bad,” “medium,” “good,” and so forth. Therefore, quantifying these linguistic terms reasonably and effectively is a very important job. In this paper, we apply four representation formats, say, real number, interval number, triangular number, and intuitionistic fuzzy number, to enhance the reasonability and effectiveness of quantification process. Wei [
The relations between linguistic labels and triangular fuzzy number.
Linguistic labels  Triangular fuzzy number 

Very poor (VP)  (0.1, 0.2, 0.3) 
Poor (P)  (0.2, 0.3, 0.4) 
Slightly poor (SP)  (0.3, 0.4, 0.5) 
Fair (F)  (0.4, 0.5, 0.6) 
Slightly good (SG)  (0.5, 0.6, 0.7) 
Good (G)  (0.6, 0.7, 0.8) 
Very good (VG)  (0.7, 0.8, 0.9) 
The following steps display the process of using modified fuzzy GRA to identify the optimal tenderer.
For benefit attributes, consider
For cost attributes, consider
Liu [
In this section, we will illustrate an example for GeT system searching for the optimal tenderer so as to test the practicality and effectiveness of our proposed approach. The software prototype was developed in .net and ExtJS framework.
The illustrative example displays the identification of an optimal tenderer that has the biggest gray relational grade in a specified context. Figure
The operational procedure of identifying the optimal tenderer.
Figures
We assume that one governmental department wants to redecorate its whole office block, and the government tendering sector wants to get an appropriate decoration firm through open tendering online. First of all, the government tendering sector needs to set the evaluation criteria (Figure
After setting the right evaluation criteria, the preferences of government tendering sector on one expert versus the other should be inputted. The input information consists of expert ID and preference value, which is presented as interval value with Likert numbers as upper bound and lower bound. Then, click the corresponding “Add preference” button in Figure
Likewise, the preferences of each expert on one evaluation criterion versus the other should be inputted. The input information includes the expert ID, criterion ID, and preference value. Then, click the corresponding “Add preference” button in Figure
Figure
After inputting all the preference information and the rating information and clicking “Obtain weights” button in the top right corner of the window of Figure
Then, by clicking “Identify tenderers” button in the top right corner of the window of Figure
The graphical interface for setting evaluation criteria.
The graphical interface for inputting preferences of government sector and experts.
The graphical interface for inputting preferences of experts on criteria.
The graphical interface for inputting ratings of experts.
The graphical interface for obtaining weights of experts and evaluation criteria.
The graphical interface for identifying the optimal tenderers.
In this paper, we propose a hybridized methodology combining extended fuzzy AHP and modified fuzzy GRA together for government Etendering to identify the optimal tenderer efficiently and fairly under the circumstance where the ratings of attributes of tenderers are expressed as different kinds of fuzzy numbers and the weight information of experts and evaluation criteria is incompletely known. The main contributions of this paper can be summarized as follows.
Development of a methodology for webbased bid evaluation of government Etendering. The hybridized methodology combines fuzzy AHP and fuzzy GRA which are already widely applied in many other fields and confirmed to be effective, but such a combination has not been found in the area of government Etendering in the literatures.
Extension of fuzzy AHPGRA based methodology. We extend the fuzzy AHPGRA based methodology to hybrid fuzzy area so that different types of vague numbers can be calculated. This extension effectively solves a problem that experts are most likely to express their evaluations on tenderers as numerous kinds of fuzzy numbers. What is more, we assume that the weight information of experts and evaluation criteria is incompletely known. This assumption just suits the reality.
Development of a prototype system for government Etendering, which enables better transparency and less costs so as to exploit the superiorities of tendering to the full.
However, our current approach still has limitations. Although there already exist many upperlevel ontologies and domainspecific ontologies, few ontologies express the attributes of tenderers as numerous types of fuzzy numbers. Thus, it is urgent to overcome this limitation in our future works so as to reduce the difficulties of putting our proposed approach into practice.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The work has been supported by China National Natural Science Foundation (no. 51375429 and no. 71301142), Zhejiang Natural Science Foundation of China (no. LY13E050010 and no. LQ13G010004), and Zhejiang Science and Technology Plan of China (no. 2014C33084).