Algorithms for fuzzy multi expert multi criteria decision making (ME-MCDM)

Inherent complexity and uncertainty in a business environment necessitate the participation of many experts in multi criteria decision making. However, participation of many experts makes the conflict aggregation process difficult. To handle this difficulty, we propose two algorithms namely possibility measure and averaging conflict aggregation. In possibility measure, we integrate the possibility theory of fuzzy logic with a maximal containment method that is designed based on the decision problem. Possibility measure algorithm for ME-MCDM involves computationally expensive multiple information processing steps. Therefore to test and compare this algorithm, averaging conflict aggregation algorithm is proposed that requires fewer mathematical information processing steps. Based on the proposed algorithms, a decision support system (DSS) is developed. We present a case study of supplier evaluation to compare both of the proposed algorithms with the help of developed DSS.     

Multi‐criteria group decision‐making method based on TODIM with probabilistic interval‐valued hesitant fuzzy information

Probabilistic interval‐valued hesitant fuzzy sets (PIV‐HFSs) are suitable for aggregating information from different groups because the probabilistic information of all the groups can be included by using interval values. Moreover, decision makers (DMs) prefer to use interval values to provide evaluation information. Furthermore, the traditional multi‐criteria group decision‐making (MCGDM) approach has some limitations, such as obtaining the DMs' weights with inappropriate methods and neglecting the interactions amongst the criteria and the psychological characteristics of DMs. Motivated by these research background, the main contents of this study are as follows. First, PIV‐HFSs are proposed, and the convex combination operation is extended into PIV‐HFSs. Second, a hybrid MCGDM approach with PIV‐HFSs is suggested that is based on the maximizing deviation method, fuzzy analytic network process (FANP) and TODIM (an acronym in Portuguese for interactive and multi‐criteria decision‐making model). Third, an evaluation case of health management centres based on the service‐specific failure mode and effect analysis (FMEA) is considered. The results show that the most crucial secondary factor is frequency (0.35775) and that the most serious failure mode is the inaccurate check‐in. The results demonstrate that the proposed model can evaluate service quality effectively and that it performs better than other methods.     

Developing a group decision support system based on fuzzy information axiom

Information axiom, one of two axioms of axiomatic design methodology which is proposed to improve a design, is used to select the best design among proposed designs. In the literature, there are a lot of studies related to using of information axiom for the solution of decision making problems. Moreover, applications of information axiom have been increasing day by day. However, calculation procedure of information axiom is not only incommodious but also difficult for decision makers. In this paper, a decision support system (DSS) based on fuzzy information axiom (FIA) is developed in order to make this decision procedure easy. The developed system consists of a knowledge base module including facts and rules, inference engine module including FIA and aggregation method, and a user interface module including entrance windows. The main aim of this study is to present a DSS tool to help the decision makers to solve their decision problems by modifying data-base of the program. In this paper, an application procedure will be presented based on the optimal selection of location for emergency service to illustrate the implementation procedure of the proposed model.     

Developing and assessing an intelligent forex rolling forecasting and trading decision support system for online e‐service

An effective foreign exchange (forex) trading decision is usually dependent on effective forex forecasting. In this study, an intelligent system framework integrating forex forecasting and trading decision is first proposed. Based on this framework, an advanced intelligent decision support system (DSS) incorporating a back‐propagation neural network (BPNN)‐based forex forecasting subsystem and Web‐based forex trading decision support subsystem is developed, which has been used to predict the directional change of daily forex rates and provide intelligent online decision support for financial institutions and individual investors. This article describes the forex forecasting and trading decision method, the system architecture, main functions, and operation of the developed DSS system. A comparative study is conducted between our developed system and others commonly used in order to assess the overall performance of the developed system. The assessment results show that our developed DSS outperforms some commonly used forex forecasting and trading decision systems and can provide intelligent e‐service for forex traders to make useful trading decisions in the forex market. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 475–499, 2007.     

Hesitant Fuzzy Linguistic Maclaurin Symmetric Mean Operators and their Applications to Multi‐Criteria Decision‐Making Problem

Due to the limitation of knowledge and the vagueness of human being thinking, decision makers prefer to use hesitant fuzzy linguistic sets (HFLSs) to estimate alternatives. Some methods of HFLSs have been researched based on the more familiar means such as the arithmetic mean and the geometric mean; however, Maclaurin symmetric mean (MSM) that can be used to reflect the interrelationships among input arguments have not been applied to solve hesitant fuzzy linguistic multi‐criteria decision‐making problems. In this paper, two hesitant fuzzy linguistic harmonic averaging operators are proposed: the hesitant fuzzy linguistic MSM (HFLMSM) operator and the hesitant fuzzy linguistic weighted MSM (HFLWMSM) operator. Furthermore, an approach based on the HFLWMSM operator is proposed. Finally, to verify the validity and feasibility of the proposed approach, an illustrative example and corresponding comparison analysis are presented in the end.     

Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets

Decision making is one of the most complex administrative processes in management. In circumstances where the members of the decision making team are uncertain in determining and defining the decision making criteria, fuzzy theory provides a proper tool to encounter with such uncertainties. However, if decision makers cannot reach an agreement on the method of defining linguistic variables based on the fuzzy sets, the interval-valued fuzzy set theory can provide a more accurate modeling. In this paper the interval-valued fuzzy TOPSIS method is presented aiming at solving MCDM problems in which the weights of criteria are unequal, using interval-valued fuzzy sets concepts.     

面向产品协同设计的分布式决策支持系统研究

在传统决策支持系统基础之上,本文提出了面向协同设计的分布式决策支持系统的体系结构,分析了问题处理系统与分布式问题求解的过程,并讨论了分布式决策支持系统的、基于智能Agent集成控制的多库系统及其管理。     

Some Hesitant Fuzzy Information Aggregation Operators Based on Einstein Operational Laws

The performance and development review (PADR) evaluation in a company is a complex group decision‐making problem that is influenced by multiple and conflicting objectives. The complexity of the PADR evaluation problem is often due to the difficulties in determining the degrees of an alternative that satisfies the criteria. In this paper, we present a hesitant fuzzy multiple criteria group decision‐making methods for PADR evaluation. We first develop some operations based on Einstein operations. Then, we proposed some aggregation operators to aggregate hesitant fuzzy elements and the relationship between our proposed operators and the existing ones are discussed in detail. Furthermore, the procedure of multicriteria group decision making based on the proposed operators is given under hesitant fuzzy environment. Finally, a practical example about PADR evaluation in a company is provided to illustrate the developed method.     

Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making

For the real decision making problems, most criteria have inter-dependent or interactive characteristics so that it is not suitable for us to aggregate them by traditional aggregation operators based on additive measures. Thus, to approximate the human subjective decision making process, it would be more suitable to apply fuzzy measures, where it is not necessary to assume additivity and independence among decision making criteria. In this paper, an intuitionistic fuzzy Choquet integral is proposed for multiple criteria decision making, where interactions phenomena among the decision making criteria are considered. First, we introduced two operational laws on intuitionistic fuzzy values. Then, based on these operational laws, intuitionistic fuzzy Choquet integral operator is proposed. Moreover, some of its properties are investigated. It is shown that the intuitionistic fuzzy Choquet integral operator can be represented by some special t-norms and t-conorms, and it is also a generalization of the intuitionistic fuzzy OWA operator and intuitionistic fuzzy weighted averaging operator. Further, the procedure and algorithm of multi-criteria decision making based on intuitionistic fuzzy Choquet integral operator is given under uncertain environment. Finally, a practical example is provided to illustrate the developed approaches.     

Some new Pythagorean fuzzy Choquet–Frank aggregation operators for multi‐attribute decision making

Pythagorean fuzzy set (PFS) whose main feature is that the square sum of the membership degree and the non‐membership degree is equal to or less than one, is a powerful tool to express fuzziness and uncertainty. The aim of this paper is to investigate aggregation operators of Pythagorean fuzzy numbers (PFNs) based on Frank t‐conorm and t‐norm. We first extend the Frank t‐conorm and t‐norm to Pythagorean fuzzy environments and develop several new operational laws of PFNs, based on which we propose two new Pythagorean fuzzy aggregation operators, such as Pythagorean fuzzy Choquet–Frank averaging operator (PFCFA) and Pythagorean fuzzy Choquet–Frank geometric operator (PFCFG). Moreover, some desirable properties and special cases of the operators are also investigated and discussed. Then, a novel approach to multi‐attribute decision making (MADM) in Pythagorean fuzzy context is proposed based on these operators. Finally, a practical example is provided to illustrate the validity of the proposed method. The result shows effectiveness and flexible of the new method. A comparative analysis is also presented.     

软计算求解分布式多工厂多顾客的供应链准时化生产计划问题

描述了分布式多工厂、多顾客的供应链准时化生产计划问题,以实现最小化提前／拖期惩罚费用、生产成本、产品运输费用之和为目标建立了数学模型,将遗传算法与模糊逻辑相结合,设计了软计算方法求解模型,采用基于规则方法的模糊规则量化方法求解模糊决策,并将模糊决策嵌入遗传算法,使得算法具有比分枝定界法更快的寻优能力和更广的适应范围。实例计算结果表明了该模型和算法的有效性和应用潜力。     

A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making

As an extension of fuzzy set, a Pythagorean fuzzy set has recently been developed to model imprecise and ambiguous information in practical group decision‐making problems. The aim of this paper is to introduce a novel aggregation method for the Pythagorean fuzzy set and analyze possibilities for its application in solving multiple attribute decision‐making problems. More specifically, a new Pythagorean fuzzy aggregation operator called the Pythagorean fuzzy induced ordered weighted averaging‐weighted average (PFIOWAWA) operator is developed. This operator inherits main characteristics of both ordered weighted average operator and induced ordered weighted average to aggregate the Pythagorean fuzzy information. Some of main properties and particular cases of the PFIOWAWA operator are studied. A method based on the proposed operator for multiple attribute group decision making is developed. Finally, we present a numerical example of selection of research and development projects to illustrate applicability of the new approach in a multiple attribute group decision‐making problem.     

Development of a fuzzy decision support framework for complex multi‐attribute decision problems: A case study for the selection of skilful basketball players

The selection of skilful players is a complicated process due to the problem criteria consisting of both qualitative and quantitative attributes as well as vague linguistic terms. This study seeks to develop a decision support framework for the selection of candidates eligible to become basketball players through the use of a fuzzy multi‐attribute decision making (MADM) algorithm. The proposed model is based on fuzzy analytic hierarchy process (FAHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods. The model was employed in the Youth and Sports Center of Mugla, Turkey, with the participation of seven junior basketball players aged between 7 and 14. In the present study, physical fitness measurement values and observation values of technical skills were utilized. FAHP was used to determine the weights of the criteria and the observation values of technical skills by decision makers. Physical fitness measurement values were converted to fuzzy values by using a fuzzy set approach. Subsequently, the overall ranking of the candidate players was determined by the TOPSIS method. Results were compared with human experts’ opinions. It is observed that the developed model is more reliable to be used in decision making. The model architecture and experimental results along with illustrative examples are further demonstrated in the study.     

New doctors ranking system based on VIKOR method

Nowadays, we can use different websites that help us make decisions about various aspects of our lives. However, privacy protection prevents websites from providing personalised guidelines to users. We propose a novel doctor‐ranking system (DRS) based on multi‐criteria group decision‐making (MCGDM) method to address the problems of privacy protection. The following aspects differentiate our proposed DRS model from previous works: (a) textual information reviews are used to identify user preferences and complementary criteria, (b) criteria weights are determined by term frequency inverse document frequency (TF‐IDF) instead of Delphi method or expert opinion, (c) intuitionistic fuzzy sets (IFSs) are used to replace sentiment analysis to express subjective user criteria, and (d) VIsekriterijumsko KOmpromisno Rangiranjie (VIKOR) method for MCGDM with IFSs is used to solve the doctor‐ranking problem. We apply our proposed model to datasets from Haodf.com to compare the performance of our method with that of sentiment analysis and technique for order performance by similarity to ideal solution (TOPSIS) methods. The experimental results show that our method provides accurate ranking and increases the reliability of DRS.     

Extension of weighted aggregated sum product assessment with interval-valued intuitionistic fuzzy numbers (WASPAS-IVIF)

Different methods are proposed in the framework of multi attribute utility theory for multi criteria decision making. Among the proposed methods, weighted sum and weighted product models (WSM and WPM) are well known and widely accepted. To improve the accuracy of WSM and WPM, the weighted aggregated sum product assessment (WASPAS) method was proposed which used an aggregation operator on WSM and WPM. In this paper, an extended version of WASPAS method is proposed which can be applied in uncertain decision making environment. In the proposed WASPAS-IVIF method, the uncertainty of decision maker(s) in stating their judgments and evaluations regard to criteria importance and/or alternatives performance on criteria are expressed by interval valued intuitionistic fuzzy numbers. Two numerical examples of ranking derelict buildings’ redevelopment decisions and investment alternatives are presented. The results are then compared with the rankings provided by other methods such as TOPSIS-IVIF, COPRAS-IVIF and IFOWA. Combining the strengths of IVIFS in handling uncertainty with the enhanced accuracy of WASPAS makes the proposed method as a desirable method for multi criteria decision making in real world applications.     

Fuzzy quality function deployment: determining the distributions of effort dedicated to technical change

A model is presented that develops the Quality Function Deployment (QFD) House of Quality tool into a fuzzy‐set based multi‐criteria decision‐making process to determine the distributions of effort directed toward technical changes. When customers are polled for desired product‐specific attributes, the responses are typically defined by linguistic variables that represent a fuzzy set distribution. Fuzzy sets also define customer perceptions of the product attributes and technical expert opinions about product design criteria relative to marketplace competitors. Therefore, for each technical criterion, the following factors have an effect on the decision to implement change(s): (1) fuzzy sets providing evidence of customer need for attributes; (2) motivation to change to satisfy desired customer attributes; (3) motivation for technical criterion change; and (4) the strength of the relationships between the attributes and the technical criterion. Priority rankings are linked to the distributions of effort to apply in fulfilling continuous product improvement.     

Development of a decision support system for machining center selection

The machining centers are key resources for manufacturing companies in their dealing with their fierce competitive market environments. However, although selecting the most appropriate machining center is a very important decision for manufacturing companies, the availability of wide-range of types and models makes the selection process a complex and difficult task. In this study, a decision support system (DSS), namely MACSEL, is developed to help the decision makers in their machining center selection decisions. Several issues and applicability of the MACSEL is illustrated with case problems in the paper.Within the developed DSS, to select the feasible set of machining centers fifteen questions are placed in the elimination (pre-selection) module. The developed DSS uses fuzzy analytical hierarchy process (FAHP) or fuzzy technique for order preference by similarity to ideal solution (FTOPSIS), which are extended versions of multi-criteria decision making approaches, to rank the feasible machining centers. In the DSS, FAHP is used if a detailed pair-wise weighting of the hierarchically structured criteria is wanted. On the other hand, when a simpler separate weighting of each criterion is be considered as enough, FTOPSIS is used.     

Algorithms for complex interval‐valued q‐rung orthopair fuzzy sets in decision making based on aggregation operators,AHP, and TOPSIS

The interval‐valued q‐rung orthopair fuzzy set (IVq‐ROFS) and complex fuzzy set (CFS) are two generalizations of the fuzzy set (FS) to cope with uncertain information in real decision making problems. The aim of the present work is to develop the concept of complex interval‐valued q‐rung orthopair fuzzy set (CIVq‐ROFS) as a generalization of interval‐valued complex fuzzy set (IVCFS) and q‐rung orthopair fuzzy set (q‐ROFS), which can better express the time‐periodic problems and two‐dimensional information in a single set. In this article not only basic properties of CIVq‐ROFSs are discussed but also averaging aggregation operator (AAO) and geometric aggregation operator (GAO) with some desirable properties and operations on CIVq‐ROFSs are discussed. The proposed operations are the extension of the operations of IVq‐ROFS, q‐ROFS, interval‐valued Pythagorean fuzzy, Pythagorean fuzzy (PF), interval‐valued intuitionistic fuzzy, intuitionistic fuzzy, complex q‐ROFS, complex PF, and complex intuitionistic fuzzy theories. Further, the Analytic hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) method are also examine based on CIVq‐ROFS to explore the reliability and proficiency of the work. Moreover, we discussed the advantages of CIVq‐ROFS and showed that the concepts of IVCFS and q‐ROFS are the special cases of CIVq‐ROFS. Moreover, the flexibility of proposed averaging aggregation operator and geometric aggregation operator in a multi‐attribute decision making (MADM) problem are also discussed. Finally, a comparative study of CIVq‐ROFSs with pre‐existing work is discussed in detail.     

A Novel Approach for Linguistic Group Decision Making Based on Generalized Interval‐Valued Intuitionistic Fuzzy Linguistic Induced Hybrid Operator and TOPSIS

In the multiple attribute linguistic group decision making analysis with interval‐valued intuitionistic fuzzy linguistic information, seeking highly efficient aggregation method and order relation play a crucial role. In this paper, we redefine an interval‐valued intuitionistic fuzzy linguistic variable that considers principal component and propose generalized interval‐valued intuitionistic fuzzy linguistic induced hybrid aggregation (GIVIFLIHA) operator with entropic order‐inducing variable and interval‐valued intuitionistic fuzzy linguistic technique for order preference by similarity to an ideal solution (TOPSIS) order relation based on interval‐valued intuitionistic fuzzy linguistic distance measure. Then, some primary properties of the GIVIFLIHA operator are discussed, and a linguistic group decision‐making approach based on GIVIFLIHA operator and interval‐valued intuitionistic fuzzy linguistic TOPSIS order relation is proposed. Finally, a numerical example concerning the investment strategy is given to illustrate the validity and applicability of the proposed method, and then the method is compared with the existing method to further illustrate its flexibility.     

Induced intuitionistic fuzzy Choquet integral operator for multicriteria decision making

Yager (Fuzzy Sets, Syst 2003;137:59–69) extended the idea of order‐induced aggregation to the Choquet aggregation and defined induced Choquet ordered averaging operator. In this paper, an induced intuitionistic fuzzy Choquet (IFC) integral operator is proposed for the multiple criteria decision making. Some of its properties are investigated. Furthermore, an induced generalized IFC integral operator is introduced. It is worth mentioning that most of the existing intuitionistic fuzzy aggregation operators are special cases of this induced aggregation operator. A decision procedure based on the proposed induced aggregation operator is developed for solving the multicriteria decision‐making problem in which all the decision information is represented by intuitionistic fuzzy values. An illustrative example is given for demonstrating the applicability of the proposed decision procedure. © 2011 Wiley Periodicals, Inc.