Application Of Fuzzy Set Theory Research Articles

Complex Equipment FMECA Method and Application Based on the Product Family

The Failure Mode, Effects and Criticality Analysis of the complicated equipment is difficult to implement. Therefore, this paper puts forward a product family FMECA method based on the analysis process and analysis. At the same time, the application of the fuzzy set and evidence theory are applied in the product family partition algorithm, which considering the complex equipment development early RMS attribute value fuzzy, uncertainty and the non-quantitative and other characters. Besides the method of effective application support complicated equipment based on the product platform of fault information database building methods is given in this paper.

A fuzzy inference and categorization approach for supplier selection using compensatory and non-compensatory decision rules

Fuzzy set theory has been used as an approach to deal with uncertainty in the supplier selection decision process. However, most studies limit applications of fuzzy set theory to outranking potential suppliers, not including a qualification stage in the decision process, in which non-compensatory types of decision rules can be used to reduce the set of potential suppliers. This paper presents a supplier selection decision method based on fuzzy inference that integrates both types of approaches: a non-compensatory rule for sorting in qualification stages and a compensatory rule for ranking in the final selection. Fuzzy inference rules model human reasoning and are embedded in the system, which is an advantage when compared to approaches that combine fuzzy set theory with multicriteria decision making methods. Fuzzy inference combined with a fuzzy rule-based classification method is used to categorize suppliers in qualification stages. Classes of supplier performance can be represented by linguistic terms, which allow decision makers to deal with subjectivity and to express qualification requirements in linguistic formats. Implementation of the proposed method and techniques were analyzed and discussed using an illustrative case. Three defuzzification operators were used in the final selection, yielding the same ranking. Factorial design was applied to test consistency and sensitivity of the inference rules. The findings reinforce the argument that including stages of qualification based on fuzzy inference and categorization makes this method especially useful for selecting from a large set of potential suppliers and also for first time purchase.

Application of Fuzzy Set Theory and SPOT Satellite Images in Site Selection of Public Libraries (Case Study: Saqqez City, Iran)

Easy availability to public libraries is one of the main keys in successful presentation of public library services with high quality will be valueless for those have not access to them. Availability to services should be configured in such a way that maximizes easiness and facility for potential and de facto users. In present research the required number of public libraries and establishment situation of public libraries in Saqqez city in Kurdistan province in North West of Iran were investigated and evaluated by using fuzzy set theory and SPOT 5 satellite images in 2009. In addition, optimum regions for generation of new public libraries were distinguished in city area in form of recommended map. Results showed that weighting variables classes were determined between 0-1 (profusion proportion). Fuzzification each one of effective factors using IDRISI software terminated and after was assigned type and shape membership function. Final map of suitable regions for construction of new public libraries in saqqez city area indicates that none of the libraries were situated in suitable regions.

FAHP 기법에 의한 농업용저수지의 추가저수량 확보사업 우선순위 결정

본 논문은 퍼지집합이론을 이용한 다기준 의사결정(MCDM) 과정에 관한 연구이며, 농업용 저수지의 수자원계획 평가에 관한 가장 합리적이고 효율적인 방법을 찾기 위해 FAHP를 이용하여 각각의 대안들에 대한 우선순위를 정하였다. 농업용 저수지의 추가저수량 확보를 위해 의사결정자 및 수혜자가 동시에 만족하는 조건을 조사하여 6개의 주 기준을 설정하고 이에 따른 10개의 대안을 설정하여 우선순위를 결정하고자 하였으며, 우선순위를 결정에서의 불확실성과 모호성을 규명하기 위해 퍼지수와 언어변수를 정의하였다. 또한 적절한 의사결정모형의 제시를 위해 의사결정 방법에 따른 분석결과를 비교 검토하였으며 FAHP 기법 적용의 타당성을 논의하였다. This paper presents the application of fuzzy set theory in multi criteria decision making (MCDM). FAHP (Fuzzy Analytic Hierarchy Process) method was used to rank alternatives to find the most reasonable and efficient way of agricultural reservoir water resources assessment. 6 criteria and 10 subcriteria had been identified and compared to secure agricultural water resources. Fuzzy numbers and linguistic variables were presented to address inherently uncertain or imprecise data. Comparison analysis of decision making method was also carried out to find a way of suitable decision making and validity of FAHP was discussed.

A novel application of intuitionistic fuzzy sets theory in medical science: Bacillus colonies recognition

This paper addresses four new distance measures as tools in pattern recognition for intuitionistic fuzzy sets (IFSs). Following the discussion on literature of distance measures, proposed measurement scales and the proof of their properties would be presented. In order to show the reliability of addressed formulations, this paper employs them in a part of medical diagnosis progress in bacillus colonies identification. The performed experiments test validity and reliability of the proposed models by running pattern recognition process on sixty cases of four different bacilli. Resulted outcomes by IFSs approach are compared with similar measures in regular fuzzy. Numerical comparisons reveal effectiveness of the proposed distance measurement scales and related pattern recognition progress.

Application of fuzzy membership matrix in medical diagnosis and decision making

The eld of medicine and decision making are the most fruitful and interesting area of applications of fuzzy set theory. In real life situations, the imprecise nature of medical documentation and uncertain information gathered for decision making requires the use of \fuzzy. In this paper, procedures are presented for medical diagnosis and for fuzzy decision model. Examples are illustrated to verify the proposed approach.

Fuzzy Set Theory and Concepts: A Proposal for Concept Formation and Operationalization

AbstractThe quantity-quality debate in social sciences also concerns concept formation and operationalization. The first approach has strong naturalist assumptions, while the second one focuses on the historical specificity of concepts. The solution to overcome this divide would be finding a path which balances the two perspectives. In this article we argue that fuzzy set theory can be a helpful tool for concept formation and operationalization. The application of fuzzy set theory to concept formation and operationalization provides, first, the opportunity of looking at concepts as complex constructs made up of attributes logically interconnected one with the other and, second, of measuring them accordingly. Thus, after presenting our general argument, we show a theoretical and an empirical application of how to use fuzzy sets in concept formation and operationalization.

Application of fuzzy sets theory in an EOQ model for items with imperfect quality and shortage backordering

This article investigates an inventory model for items received with imperfect quality and shortage backordering in the fuzzy sense, where, upon the arrival of order lot, 100% screening process is performed and the items of imperfect quality are sold as a single batch at a discounted price, prior to receiving the next shipment. The objective here is to determine the optimal order lot size and the optimal backordering quantity to maximise the annual total profit. Two fuzzy models have been proposed. We first propose a model with fuzzy defective rate. Then, the model with fuzzy defective rate and fuzzy annual demand is presented. For each case, we employ the signed distance, a ranking method for fuzzy numbers, to find the estimate of the total profit per unit time in the fuzzy sense, and then derive the corresponding optimal lot size and optimal backordering quantity. Numerical examples are provided to illustrate the results of proposed models.

Cluster Detection Analysis Using Fuzzy RelationalDatabase

In order to handle imprecise and ambiguous information, the application of fuzzy set theory for the design of database, information storage and retrieval systems has been gaining popularity recently. This paper gives emphasis on the basic characteristics of fuzzy relational databases, their properties, along with the data clustering in database systems. Indian premier league dataset has been considered for the detection of clusters. Several clustering parameters like centroid, radius and Manhattan distance measure have been applied. The definition of clusters as well as the membership function has been implemented using PL/SQL. The results obtained from Indian premier league batting statistics dataset detect two clusters, namely Cluster 1 and Cluster 2. Finally, this article proposed a fuzzy database organization and clustering of records which provides efficient and accurate fuzzy retrieval.

Application of Fuzzy Set Theory to Quantitative Analysis of Correctness of the Mathematical Model Based on the ADI Method during Solidification

The explicit finite difference (EFD) method is used to calculate the casting temperature field during the solidification process. Because of its limited time step, the computational efficiency of the EFD method is lower than that of the alternating direction implicit (ADI) method. A model based on the equivalent specific heat method and the ADI method that improves computational efficiency is established. The error of temperature field simulation comes from model simplification, the acceptable hypotheses and calculation errors caused by different time steps, and the different mesh numbers that are involved in the process of numerical simulation. This paper quantitatively analyzes the degree of similarity between simulated and experimental results by the hamming distance (HD). For a thick-walled position, the time step influences the simulation results of the temperature field and the number of casting meshes has little influence on the simulation results of temperature field. For a thin-walled position, the time step has minimal influence on the simulation results of the temperature field and the number of casting meshes has a larger influence on the simulation results of temperature field.

Application of a fuzzy set theory for supplier’s selection

The paper gives information on methods of supplier’s selection assessment based on the fuzzy set theory. The decision-making algorithm is presented. The concrete example is cited concerning cement supplier’s selection for one of the construction enterprises in Penza when producing reinforced concrete. The supplier’s criteria were price, quality of supplied raw materials, available free space for power increase and reliability. For estimating the weight coefficient values, matrix of pairwise criteria comparisons was formulated. Matrix of multiplicative quantitative assessments was made. A set of optimal alternatives taking into account the weight of various quality criteria was determined using the weighted intersection of fuzzy sets. The weight coefficients of criteria were determined based on calculated values of the right eigenvector matrix of pairwise comparisons with further multiplying by the number of criteria. The calculation results of the weight coefficients of supplier’s criteria are presented.

English

  The selection of the appropriate combination of materials for a manufacturing company is one of the important points to achieving high competitiveness in the market. Besides, an appropriate choice of materials is very important as it helps to reach optimum production rate and efficiency. Today’s market offers many more choices for materials alternatives. There are also many factors one should consider as part of the appropriate combination of materials selection process, including productivity, wastage, cost, style, etc., consequently, evaluation procedures involve several objectives and it is often necessary to compromise among possibly conflicting tangible and intangible factors. For dealing with these problems, multiple criteria decision making (MCDM) has been found to be a useful approach to solve this kind of problem. Most of the MCDM models are basically mathematical and disregard qualitative and subjective considerations. The application of fuzzy set theory allows incorporating the vague and imprecise linguistic terms and qualitative information into the decision process. This paper devises a fuzzy hybrid analytical hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) approach to the problem of thesis subject selection. Fuzzy AHP is used to formulate and calculate the weight of each criterion, and fuzzy TOPSIS is proposed to prioritize combination material alternatives from the best to the worst ones. A case study on Kaach Company was put forward to illustrate the performance of the proposed methodology.   Key words: Combination of material, material selection, fuzzy analytical hierarchy process (AHP), fuzzy technique for order preference by similarity to ideal solution (TOPSIS).

Fuzzy variable linear programming with fuzzy technical coefficients

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming (LP) with fuzzy variables. In this paper, an approximate but convenient method for solving these problems with fuzzy non-negative technical coefficient and without using the ranking functions, is proposed. With the help of numerical examples, the method is illustrated.

MARKET SEGMENT EVALUATION AND SELECTION BASED ON APPLICATION OF FUZZY AHP AND COPRAS-G METHODS

Market segment evaluation and selection is one of the critical marketing problems of all companies. This paper presents a novel approach which integrates fuzzy analytic hierarchy process (FAHP) and COPRAS-G method for market segment evaluation and selection. Fuzzy AHP is used to calculate the weight of each criterion, and COPRAS-G method is proposed to prioritize market segments from the best to the worst ones. The application of fuzzy set theory allows incorporating the vague and imprecise linguistic terms into the decision process. This study can be used as a pattern for market segment selection and future researches. A case study on a chair manufacturing company is put forward to illustrate the performance of the proposed methodology.

An evaluation of project completion with application of fuzzy set theory

The project management contains such elements as management of time, cost, communications, procurement, quality, risk or scope of project. Each of these fields can be considered as a set of constraints, and then there is a possibility to verify their fulfillment in sense of an enterprise's constraints and its environment. These constraints determine a completion of project activities and its success or failure, finally. The paper aims to present a problem of project management in terms of fuzzy constraints satisfaction problem, and then the using of constraint programming techniques to the evaluation of project completion. A fuzzy constraints satisfaction problem enables a description of data in distinct, as well as imprecise form, in a unified framework. It seems especially important in case of unique activities of project, when their estimation is based on linguistic information from experts.

A study of the relationship between customer relationship management contents and benefits in hospitals: An application of fuzzy set theory

Previous studies on customer relationship management (CRM) focused mainly on exploring how CRM techniques can improve organizational benefits, what key success factors and influential elements can adapt to CRM, etc. However, the integration of CRM contents into organizational activities to achieve CRM benefits requires further investigation. This study evaluated the interrelationships between CRM contents and CRM benefits using fuzzy set theory; and also provides suggestions on how to introduce CRM contents to CRM benefits in actual hospital settings. Analytical results based on a series of expert interviews indicated that CRM contents could impact the promotion of CRM benefits, especially focus on the category of data collection, the key item including data collection of optimum practices, internal processes, patients’ basic information, healthcare marketplace, etc. Decision makers could prioritize CRM contents and decide the implement schedule of CRM contents. Additionally, through evaluation of CRM contents, the decision makers can assess the importance of different categories of CRM contents and determine the priority for investing in CRM activities by ranking these categories. Key words: Customer relationship management (CRM), fuzzy set theory, analytic hierarchy process (AHP), CRM content, CRM benefit.

Characterizations of fuzzy intra-regular Abel-Grassmann's groupoids

Mostly, models of real life problems are consist of uncertainties. Fuzzy set theory is one of the tool for handling such uncertainties and for applications of fuzzy set theory we have used non-associative algebraic structure namely AG-groupoids. Specifically, we have discussed the -fuzzy left ideals,-fuzzy ideals, -fuzzy semiprime ideals and -fuzzy bi-ideals in an AG-groupoid. We have characterized intra-regular AG-groupoids by the properties of their ideals and -fuzzy ideals. Key words: AG-groupoid, left invertive law, medial law, paramedial law, -fuzzy ideals and -fuzzy bi-ideals.

Assessing the groundwater quality by applying fuzzy logic in GIS environment– A case study in Southwest Iran

Water quality is a key environmental issue concerning the agricultural sector. Here, the application of fuzzy set theory for decision-making in the assessment of groundwater quality for agricultural purposes is being discussed. The experiments conducted in this study area located, Shahrekord plain that, lies in the Chaharmahal and Bakhtiari province, in the southwest Iran. Four groundwater parameters (EC, Mg, Na and Ca) are selected for water quality analysis and thematic maps are drawn for each of the parameters with the Kriging model. Different Fuzzy membership functions obtained from the related literature were employed and the weights for each parameter were calculated according to Analytic Hierarchy Process (AHP) that relies on pair wise comparisons. The Fuzzy theory showed 14.22% of the study area as having high groundwater quality, 19.86% as having moderate quality, 48.90% as having margin quality and 16.99% as having poor quality. In order to evaluate the accuracy of this method, eight different points were randomly selected. It is concluded that the Fuzzy method allows for obtaining results that correspond to the current conditions in the study area.

Multicriteria Decision Support System for Regionalization of Integrated Water Resources Management

Successful implementation of integrated water resources planning and management (IWRM) requires delineation of regions that are relatively homogeneous with respect to multiple criteria, including hydrographic, physical-environmental, socioeconomic, and political-administrative aspects. The water resources planning and management (WARPLAM) DSS is presented as tool for regionalization in support of IWRM through: (1) GIS processing of spatial data related to multiple criteria for defining the homogeneity of clustered base units (e.g., catchments) with respect to multiple criteria; (2) application of fuzzy set theory to development of composite measures of homogeneity over all criteria for alternative clustering of adjacent base units; and (3) development of a modified dynamic programming clustering algorithm that guarantees consistent optimal solutions based on user preferences on the relative importance of the suite of criteria considered for regionalization. The viability of WARPLAM DSS as a tool for regional delineation in support of IWRM is demonstrated through a case study application to the Tocantins-Araguaia River Basin, the second largest in Brazil.

Optimization of the Fuzzy Investment Portfolio under Conditions of Uncertainty

The problem of portfolio optimization under uncertainty is considered. For its solution the application of fuzzy sets theory is suggested. Fuzzy portfolio optimization problem is stated; its model is provided and investigated, as well as the algorithm of its solution is presented in the article. The problem of multicriteria fuzzy portfolio optimization is also considered and investigated. This problem includes two main criteria – portfolio profitability and risk. A mathematical model of this problem is constructed, explored and the sufficient conditions for its convexity are obtained. For better estimation of stock profitability, Fuzzy Group Method of Data Handling (FGMDH) for stock price forecasting is suggested. The experimental investigations of the suggested approach are carried out and their results – optimal portfolios based on the projected stock prices are presented, and its efficiency is evaluated.