Fuzzy Sets

fuzzy learning algorithms require only a single pass through the training set. This produces a computationally efficient method of learning. The effectiveness of the fuzzy learning algorithms is compared with that of a feedforward neural network trained with back-propagation. P. Allen, "System engineering training at TRW's system development division," presented at 2nd Ann. Conf.

Fuzzy Logic has been proposed for information representation and manipulation in databases, being the current tendency to study mechanisms of flexible querying to traditional databases. SQLf has been one of the efforts in this tendency. On the other hand, there are many different dialects of SQL. There are two major standards: ANSI (American National Standards Institute) SQL and an updated

In this paper, we describe an intelligent signal analysis system employing the wavelet transformation towards solving vehicle engine diagnosis problems. Vehicle engine diagnosis often involves multiple signal analysis. The developed system first partitions a leading signal into small segments representing physical events or stateds based on wavelet mutli-resolution analysis. Second, by applying the segmentation result of the leading signal to the other signals, the detailed properties of each segment, including inter-signal relationships, are extracted to form a feature vector. Finally a fuzzy intelligent system is used to learn diagnostic features from a training set containing feature vectors extracted from signal segments at various vehicle states. The fuzzy system applies its diagnostic knowledge to classify signals as abnormal or normal. The implementation of the system is described and experiment results are presented.

""Origin–destination (O–D) matrix estimation methods based on traffic counts have been largely discussed and investigated. The most used methods are based on Generalised Least Square estimators (GLS) that use as input data a starting O–D matrix and a set of traffic counts. In addition to traffic counts, the analysts could know other general information about travel demand or link flows, based on their experience, or spot data, but few works deal with the matter of including effectively these sources of information.

This paper proposes a Fuzzy-GLS estimation method that allows to improve the estimation performances of classic GLS estimator by including, in addition to traffic counts, uncertain information about starting O–D demand (i.e. outdated estimates, spot data, expert knowledge, etc.). The methods explicitly take into account the relevant level of uncertainty by taking as much advantage as possible from the few vague available data. The method is developed using fuzzy sets theory and fuzzy programming that seems to be a convenient theoretical framework to represent uncertainty in the available data. A solution algorithm for the proposed problem is also presented. The method has been tested by numerical applications and then compared to the classical GLS method under different sets of constraints to the problem.""

Recommender Systems are a class of applications which are used to overcome the problem of information overload. They use the opinions of members of a community to help individuals in that community identify the information most likely to be interesting to them or relevant to their needs, by drawing on user preferences and filtering the set of possible options to a more manageable subset. The key element of such user-support systems is the user model. Traditional techniques used to create user models are usually too rigid to capture the inherent uncertainty of human behavior. Fuzzy sets can handle and process uncertainty in human decision-making and if used in user modeling can be of advantage as it will result in recommendations closely meeting user preferences. In this paper, a hybrid multi-agent recommender system is designed and developed where user's preferences; needs and satisfaction are modeled using interval type-2 (IT2) fuzzy sets. This results in improving the prediction accuracy of the system and hence better recommendations are generated. Experimental study was conducted on book recommender system and promising results were obtained.

 Abstract-Analytical Hierarchical Process (AHP) and Fuzzy Analytical Hierarchical Process (FAHP) are two methods both used for Multi Criteria Decision Making (MCDM). Consistency Ratio (CR) is checked for all data sets fed into both these methods and weight values are compared. As well as differences between weights determined by both methods and decision values have been compared and tried to understand the nature of both methods.

Risk is defined as the probability of a specific adverse event occurring within a specific period, while Quantitative risk assessment (QRA) is the development of a quantitative estimate of risk based on engineering evaluation and mathematical techniques by combining estimate of incident consequences and frequencies. In view of the increase in the use of railways as the mode of transportation for hazardous materials throughout the world, the associated risk analysis should be taken into concern. In this study, the failure frequency of the transportation of ammonia from the Petronas fertilizers Kedah (PFK) plant in Gurun (Northern part of Peninsular Malaysia), to the Chemical Company Malaysia (CCM) fertilizer's facilities in Port Klang (South-western part of Peninsular Malaysia) was evaluated by incorporating the human error assessment. The study highlighted the importance of human error contributions in the failure frequency analysis and its impact on the selected failure scenarios. Besides, it also shows that the application of the human error assessment and reduction technique (HEART), which is a useful human reliability analysis tool, should be used in parallel with the fuzzy arithmetic approach to reduce the uncertainties involved in the estimation of human error probabilities, and hence, to reduce the likelihood of incorrect risks estimates being assessed. The results suggested that the commonly applied approach in quantitative risk assessments, which only consider equipment failures in the failure frequency estimations, are clearly an underestimate of the potential causes of failures leading to hazardous material releases, and hence, the calculated risks based do not reflect the actual risks. © 2008 American Institute of Chemical Engineers Process Saf Prog, 2009

Career guidance for students, particularly in rural areas is a challenging issue in India. In the present era
of digitalization, there is a need of an automated system that can analyze a student for his/her capabilities,
suggest a career and provide related information. Keeping in mind the requirement, the present paper is an
effort in this direction. In this paper, a fuzzy based conceptual framework has been suggested. It has two
parts; in the first part a students will be analyzed for his/her capabilities and in the second part the
available courses, job aspects related to their capabilities will be suggested. To analyze a student, marks
in various subject in 10+2 standards and vocational interest in different fields have been considered and
fuzzy sets have been formed. On example basis, fuzzy inference rules have been framed for analyzing the
abilities in engineering, medical and hospitality fields only. In second part, concept of composition of
relations has been used to suggest the related courses and jobs.

Industrial control systems are nowadays exposed in environments with rapid and unstable parameter changes and uses measuring equipments with critical output sensitivity. In the case of thermal gas analyzer, measurement errors are contributed by temperature, gas flow, and pressure. Error compensation is a key problem for these control systems. In recent years, it has been proven in the literature that artificial neural network (ANN) is a reliable and low cost solution to manage errors. Among all the algorithms of ANN, the back propagation is commonly used because of its simplicity and learning methodology is easy to realize. However, it has two notable drawbacks: (a) it is likely to run into local minimum, and (b) convergence is slow. Thermal conductivity gas analyzer often works in adverse surroundings, which requires fast and accurate measurements. Therefore, a strong learning network is needed. This paper proposes a novel thermal gas analyzer using adaptive neuro-fuzzy inference system. The effectiveness and validity of the proposed method is verified by simulation studies using MATLAB. Fuzzy membership rules are created to allow regulation of learning parameters. Further, the fuzzy adaptive network model is constructed to train large data samples while the high precision compensation of sensor error is realized by the improved flow. Simulation results reveal that the convergence speed and output accuracy is improved and the learning parameters in thermal gas analyzer are automatically corrected by the proposed method in comparison with the back propagation algorithm of artificial neural network.

It is often remarked that politicians’ private lives are becoming feature of political communication in many advanced industrial democracies. However, there have so far been no genuinely comparative studies examining the personalised nature of political communication. Intimate Politics provides for the first time a systematic comparative analysis of such developments in Australia, France, Germany, Italy, Spain, the UK, and the US. Drawing on a wide range of primary and secondary sources it assesses the extent to which the private lives of politicians have become a feature of political communication in each democracy. The book provides a comprehensive account of the shifting boundaries between the public and private and whether any developments are universal or more advanced in some democracies than others, and seeks to explain why this might be. Intimate Politics will be of great value for students and scholars of communication and media studies and political science and is required reading for anyone who wants a fuller understanding of the transformation of mediated politics in advanced industrial democracies.

The evolutionary based computational approach has been matured into an extensive collection of concepts and techniques with the hype in the complexities of the problems which could not be easily dealt by the classical approach. The effectiveness and efficiency of these modern approaches are making them popular in the field of research and development. In this paper, we have focused on the involvement of a multi valued logical evolutionary based computational approach in the development of an effective system. This paper describes the area where fuzzy logic can be implemented effectively in system development life cycle. This paper explicitly mentions the application of Fuzzy Inference System (FIS) in one of the fact finding techniques of requirement analysis viz. rating scale question method to find the percentage level of the satisfaction of the user of an existing system or a new system.

Quantifying or, more generally, estimating the severity of the possible consequences of occupational accidents is a decisive step in any occupational risk assessment process. Because of the lack of historic information (accident data collection and recording are incipient and insufficient, particularly in construction) and the lack of practical tools in the construction industry, the estimation/quantification of occupational accident severity is a notably arbitrary process rather than a systematic and rigorous assessment.

Fuzzy models are regarded as linguistic modeling structures with well-defined functional blocks off inlput and output interfaces along with a processing module. The paper examines the functions of these modules and specifies the relevant optimization tasks emerging in fuzzy system identification. Considering several distinct levels of conceptual memorization realized within the fuzzy imodels ( subsequently resulting in establishing short-, medium-, and long-term memories), the corresponding learning policies are developed. The study includes also detailed simulation studies.

Prototype Theory offers one of the most accepted models for semantic memory organization. Lexical availability trials provide investigators with a faster and easier means of observing this cognitive organization, since lists of available lexicon are generated from associations relating some lexical elements with others. The experiments with lexical availability are able to activate one of the best-known lexical production mechanisms within experimental psychology: semantic category fluency. In this work we propose the appropriate means to reconstruct the community cognitive organization. This shared metastructure constitutes the concept of shared field of experience used as the base for availability trials. The key notion is the prototypicality of common vocabulary as the base for the construction of community models. To obtain a representation of these prototypes we use the mathematical framework of fuzzy sets.

The fundamental equations governing the operation of a dc motor are straightforward and are well presented in most undergraduate curricula, usually in a required energy-conversion or electrical-machinery class at the junior level. The physical implications of the equations regarding device behavior, and the need for speed control, are easily understood. Furthermore, students can readily develop a mental picture of the physical motor and its response.

We consider a finite, aperiodic, time homogenous, absorbing Markov chain on a fuzzy partition, for which each time an absorption occurs there is a resetting of the chain according to some initial (replacement) distribution. The resulting process is a Markov replacement chain on a fuzzy partition. We study certain aspects of the aggregated process emerging from the classical theory on hard partitions. The first aspect is lumpability, a technique for recovering from the large state space of a stochastic system. We provide necessary and sufficient conditions for strong lumpability on the transition probabilities of the original chains for the lumped processes to have the Markov property. The second aspect is the asymptotic characteristics of the lumped Markov chains. The results are compared with those existing in the classical theory of hard partitions. μ + = . Therefore

Bow-tie analysis is a fairly new concept in risk assessment that can describe the relationships among different risk control parameters, such as causes, hazards and consequences to mitigate the likelihood of occurrence of unwanted events in an industrial system. It also facilitates the performance of quantitative risk analysis for an unwanted event providing a detailed investigation starting from basic causes to final consequences. The credibility of quantitative evaluation of the bow-tie is still a major concern since uncertainty, due to limited or missing data, often restricts the performance of analysis. The utilization of expert knowledge often provides an alternative for such a situation. However, it comes at the cost of possible uncertainties related to incompleteness (partial ignorance), imprecision (subjectivity), and lack of consensus (if multiple expert judgments are used). Further, if the bow-tie analysis is not flexible enough to incorporate new knowledge or evidence, it may undermine the purpose of risk assessment.

The theory of dual numerical means of random and experienced variables is briefly described in the framework of the new theory of experience and the chance that arises as an axiomatic synthesis of two dual theories — the Kolmogorov theory of probability and the theory of believability. A new term is introduced for the numerical mean of the experienced variable — mathematical reflection, which is dual to the mathematical expectation of a random variable within the framework of the new theory. The basic properties and examples of dual numerical means are considered.

The difficulties associated with translating a set of scores into letter-grades are discussed. A novel method for automating this process, the Fuzzy Grading System, is developed and compared to traditional practices. Letter-grades are recognized to be f u u y descriptors of students' performance. Thus, operations aimed at defining letter-grade bouhdaries are naturally carried out in the context of fuzzy set theory and logic. The Fuzzy Grading System utilizes students' and instructor's performance measures in order to m d i y a set of collectively approved, a priori fuzzy grades, so as to produce a "fair" mark distribution. The validity of grades is increased by compensating for factors that are not directly accessible to simpler, traditional grading methods.

A restrained dominating set S ⊆ V (G) in a graph G is said to be restrained nonsplit-[1, 2] dominating set, if for every vertex v ∈ V − S, 1 ≤ |N (v) ∩ S| ≤ 2 and < V − S > is connected. The minimum cardinality of restrained nonsplit-[1, 2] dominating set (rns[1, 2]-set) is called restrained nonsplit-[1, 2] domination number and is denoted by γ rns[1,2] (G). In this article, we launch the new concept called restrained nonsplit-[1, 2] domination number of graphs.

Axiomatic design gives a design map to designers in order to establish a scientific basis, which improves design activities. In the classical axiomatic design (AD) approach, the relationships between functional requirements (FRs) and design parameters (DPs) are defined in crisp numbers notably ''0" or ''1". This definition restricts relevant designers due to the incomplete information or uncertainty in various circumstances. This study debates the adaptation of the current AD principles into fuzzy sets theory. Those transformations are expressed by the developed formulas to prove the independence degree of the design in quantitative manner. A numerical study illustrates the logic of the proposed ideas clearly. Consequently, the proposed methodology provides a genuine link to explain the correspondences among FRs and DPs in linguistic form.

Fuzzy logic is a form of many valued logic in which the truth values of variables may be any real number between 0 and 1. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. Fuzzy logic has been employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. The purpose of this review paper is to address the application of fuzzy logic to both address common challenges and incorporate human procedural knowledge into the vehicle control algorithms. Fuzzy logic is a powerful way to put engineering expertise into products in a short amount of time. It's highly beneficial in automotive engineering, where many system designs involve the experience of design engineers as well as test drivers. Classical logic only permits conclusions which are either true or false. However, there are also propositions with variable answers, such as one might find when asking a group of people to identify a color. In such instances, the truth appears as the result of reasoning from inexact or partial knowledge in which the sampled answers are mapped on a spectrum.

Two classes of metrics are introduced for spaces of fuzzy sets. Their equivalence is discussed and basic properties established. A characterisation of compact and locally compact subsets is given in terms of boundedness and p-mean equileft-continuity, and the spaces shown to be locally compact, complete and separable metric spaces.

This paper is based on the following assumption: that there exists a fuzzy tree structure and a distance between fuzzy trees which provides the basis for fuzzy decision-making. The paper provides the following: (1) a new definition of the fuzzy relational tree structure, (2) the development of a new comparative method for fuzzy trees and its experimental testing and evaluation, (3) a new descriptive method of military structures in a fuzzy tree format and the development of a fuzzy decision support system.

Material handling equipment selection problem (MHESP) is an important decision making area for the companies, since it has a direct effect on manufacturing and service productivity. In this study, an integrated fuzzy multi-criteria decision making methodology for MHESP is proposed. The proposed approach is utilized from fuzzy sets, Analytic Network Process (ANP) and Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE) approaches. Evaluation criteria for the MHESP is weighted by fuzzy-ANP (F-ANP) approach, then, alternative material handling equipments are evaluated by fuzzy-PROMETHEE (F-PROMETHEE) approach. The methodology is applied for a manufacturing company to prove its effectiveness. Finally, some sensitivity analyses are conducted to show the results’ sensitiveness to the changes of the weights of the evaluation criteria.

The aim of the work was to map and analyse benthic habitats in the Polish zone of the Baltic Sea using the Geographical Information Systems (GIS). The habitats definitions were analogous to those proposed in the HELCOM classification, which is based on two concepts—the euphotic zone has no clearly defined boundaries and the bottom sediments are defined on the basis of their fractions. The mapping was done using the theory of fuzzy sets.The fuzzy set map for each HELCOM category was created as a result of an intersection operation on two fuzzy set maps—the first showed bottom position relative to euphotic depth, and the second described the presence of a given sediment type on the bottom. The maps obtained were used to create a thematic map of habitats, which was generated at a pre-set significance level from the statistical analysis of a set of random realizations of habitat maps generated by stochastic simulation. The GIS-based analyses of the thematic map allowed a map of habitat groups to be developed and also allowed to find whether and to what extent the definitions proposed by HELCOM were applicable to the mapping of benthic habitats in the study area.

Recommender systems have grown to be a critical research subject after the emergence of the first paper on collaborative filtering in the Nineties. Despite the fact that educational studies on recommender systems, has extended extensively over the last 10 years, there are deficiencies in the complete literature evaluation and classification of that research. Because of this, we reviewed articles on recommender structures, and then classified those based on sentiment analysis. The articles are categorized into three techniques of recommender system, i.e.; collaborative filtering (CF), content based and context based. We have tried to find out the research papers related to sentimental analysis based recommender system. To classify research done by authors in this field, we have shown different approaches of recommender system based on sentimental analysis with the help of tables. Our studies give statistics, approximately trends in recommender structures research, and gives practitioners and researchers with perception and destiny route on the recommender system using sentimental analysis. We hope that this paper enables all and sundry who is interested in recommender systems research with insight for destiny.

The main strengths of collaborative filtering (CF), the most successful and widely used filtering technique for recommender systems, are its cross-genre or 'outside the box' recommendation ability and that it is completely independent of any machine-readable representation of the items being recommended. However, CF suffers from sparsity, scalability, and loss of neighbor transitivity. CF techniques are either memory-based or model-based. While the former is more accurate, its scalability compared to model-based is poor. An important contribution of this paper is a hybrid fuzzy-genetic approach to recommender systems that retains the accuracy of memory-based CF and the scalability of model-based CF. Using hybrid features, a novel user model is built that helped in achieving significant reduction in system complexity, sparsity, and made the neighbor transitivity relationship hold. The user model is employed to find a set of likeminded users within which a memory-based search is carried out. This set is much smaller than the entire set, thus improving system's scalability. Besides our proposed approaches are scalable and compact in size, computational results reveal that they outperform the classical approach.

Specific applications of fuzzy logic in project management are relatively few in comparison to other application areas. The criteria of project cost, project time, and project quality may be considered as project management internal measures of efficiency. The objective of this research is to present an approach that employs fuzzy decision making (FDM) to combine these three measures into one measure namely the project management internal efficiency (PMIE) which should represent an overall estimate of how well the project was managed and executed. The proposed approach for the evaluation of PMIE is illustrated on a case study. A fuzzy decision making system is designed and implemented using the MATLAB software for the evaluation of the PMIE. The methodology and procedure proposed in this research may be easily implemented by project management organizations. The evaluation of PMIE can serve for project managers and for project organizations as an indicator for the level of achievement of the project management internal objectives. PMIE may help in the evaluation of the performance of project teams.

This paper continues our research in fuzzy plane geometry. Previously, we studied fuzzy points and fuzzy lines. Now we investigate fuzzy circles and fuzzy polygons. We show that the fuzzy area of a fuzzy circle, or a fuzzy polygon, is a fuzzy number. We also argue that the fuzzy perimeter of a fuzzy circle, or a fuzzy polygon, is a fuzzy number. (~) 1997 Elsevier Science B.V.

Recommender Systems are a class of applications which are used to overcome the problem of information overload. They use the opinions of members of a community to help individuals in that community identify the information most likely to be interesting to them or relevant to their needs, by drawing on user preferences and filtering the set of possible options to a more manageable subset. The key element of such user-support systems is the user model. Traditional techniques used to create user models are usually too rigid to capture the inherent uncertainty of human behavior. Fuzzy sets can handle and process uncertainty in human decision-making and if used in user modeling can be of advantage as it will result in recommendations closely meeting user preferences. In this paper, a hybrid multi-agent recommender system is designed and developed where user's preferences; needs and satisfaction are modeled using interval type-2 (IT2) fuzzy sets. This results in improving the prediction accuracy of the system and hence better recommendations are generated. Experimental study was conducted on book recommender system and promising results were obtained.

Ոչ հստակ բազմությունները հանդիասնում են սովորական բազմությունների տեսության ընդլայնումը։ Եթե սովորական բազմությունների տեսության մեջ նշվում է հստակ կանոն,որով կարելի է պարզել՝ տվյալ տարրը պատկանում է այդ բազմությանը թե ոչ, ապա ոչ հստակ բազմությունների տեսությունը թույլ է տալիս տարրի՝ տվյալ բազմությանը պատկանելու չափ։ Այս տեսությունը, ինչպես կտեսնենք հետագա շարադրանքում, լայն հնարավորություններ է ընձեռում ոչ միայն մոդելավորման տեսանկյունից, այլև փորձագիտական գնահատականների վերլուծությունների տեսանկյունից։
Սույն աշխատանքում նկարագրված է տնեսագիտությունում ոչ հստակ բազմությունների կիրառության որոշ հնարավորություններ, մասնավորապես՝ դիտարկվել է ներդրումների անարդյունավետության ռիսկի գնահատման մոդելը, որոշումների կայացման մոդելը՝ ոչ հստակ նպատակների և սահմանափակումների համատեքստում, ինչպես նաև դիտարկվել է սպառողի վարքի I-M-T մոդելում ոչ հստակ բազմությունների կիրառության հնարավորությունը։ Աշխատանքում նաև անդրադարձ է կատարվել արհեստական բանականության մեջ կիրառվող փորձագիտական համակարգերի շրջանակում ուսումնասիրվող փորձագիտական գնահատականների ընդհանրացման ոչ հստակ բազմությունների մեթոդը, ինչպես նաև ոչ հստակ եզրակացության համակարգերը։
Ոչ հստակ բազմությունների տեսությունը բավականին արդյունավետ գործիք է հանդիսանում անորոշությունը և ոչ հստակ ձևակերպումները մոդելավորելու համար, ինչը ներկայումս բավականին պահանջված է ինչպես տնտեսագետների, այնպես էլ այլ գիտությունների ներկայացուցիչների կողմից։

For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I've finally done it in my co∼eventum mechanics! Now it remains for me to explain to everyone the co∼eventum mechanics in the most approachable way. This is what I'm trying to do in this work. The co∼eventum mechanics is another name for the co∼event theory, i.e., for the theory of experience and chance which I axiomatized in 2016 [1, 2]. In my opinion, this name best reflects the co∼event-based idea of the new dual theory of uncertainty, which combines the probability theory as a theory of chance, with its dual half, the believability theory as a theory of experience. In addition, I like this new name indicates a direct connection between the co∼event theory and quantum mechanics, which is intended for the physical explanation and description of the conict between quantum observers and quantum observations [4]. Since my theory of uncertainty satises the Kolmogorov axioms of probability theory, to explain this co∼eventum mechanics I will use a way analogous to the already tested one, which explains the theory of probability as a theory of chance describing the results of a random experiment. The simplest example of a random experiment in probability theory is the " tossing a coin ". Therefore, I decided to use this the simplest random experiment itself, as well as the two its analogies: the " "flipping a coin " and the " spinning a coin " to explain the co∼eventum mechanics, which describes the results of a combined experienced random experiment. I would like to resort to the usual for the probability theory " coin-based " analogy to explain (and first of all for myself) the logic of the co∼eventum mechanics as a logic of experience and chance. Of course, this analogy one may seem strange if not crazy. But I did not come up with a better way of tying the explanations of the logic of the co∼eventum mechanics to the coin-based explanations that are commonly used in probability theory to explain at least for myself the logic of the chance through a simple visual " coin-based " model that clarifies what occurs as a result of a combined experienced random experiment in which the experience of observer faces the chance of observation. I hope this analogy can be useful not only for me in understanding the co∼eventum mechanics.

The construction industry is plagued by occupational risky situations and poor working conditions. Occupational risk assessment (ORA) on workplace sites is the first and key step to achieve adequate safety levels, particularly to support decision-making in safety programs. Most construction safety efforts are applied informally under the premise that simply allocating more resources to safety management will improve safety on site. Moreover, there are many traditional methods to address ORA, but few have been adapted and validated for use in the construction industry, particularly in the design stage, for which traditional approaches do not give adequate answers. This paper presents a state-of-the-art on ORA traditional methods, for the construction industry, discussing their limitations and pointing advantages of using fuzzy sets approaches to deal with ill-defined situations.

We report on a fuzzy logic-based language understanding system applied to speech recognition. This system acquires conceptual knowledge from corpus data and organizes such knowledge into fuzzy logic inference rules. The system parses speech recognition results into conceptual structures in a robust manner, and thus is able to tolerate noise caused by speech recognition errors. We discuss the fuzzy inference rule learning method and explain its organization. Experimental results that demonstrate the ability of the system to deal with complex speech input instances are reported

Transformation in procurement technique aims to create a sustainability development and innovative outsourcing strategy. It can increase the probability of project success with quality and give an added value in money and contract times. Wide range of issues should be considered in producing a sincere and trusted decision within respective agencies. Our research proposed a procurement transformation model for selecting the optimal result of contractor selection under multi criteria environments. The corresponding data are centralizing, easy to manage and can be updated accordingly. Fuzzy comparing judgment is used as the method to overcome the ambiguity aspects in selecting significant preferences by decision maker regarding to the subjective opinion. Decision making process is represented by the integration of evaluation model to produce a final result. Finally, the model was tested in tender evaluation processes to determine the most beneficial contractor to perform the construction project.