Hierarchical semi-numeric method for pairwise fuzzy group decision making

Gradual improvements to a single-level semi-numeric method, i.e., linguistic labels preference representation by fuzzy sets computation for pairwise fuzzy group decision making are summarized. The method is extended to solve multiple criteria hierarchical structure pairwise fuzzy group decision-making problems. The problems are hierarchically structured into focus, criteria, and alternatives. Decision makers express their evaluations of criteria and alternatives based on each criterion by using linguistic labels. The labels are converted into and processed in triangular fuzzy numbers (TFNs). Evaluations of criteria yield relative criteria weights. Evaluations of the alternatives, based on each criterion, yield a degree of preference for each alternative or a degree of satisfaction for each preference value. By using a neat ordered weighted average (OWA) or a fuzzy weighted average operator, solutions obtained based on each criterion are aggregated into final solutions. The hierarchical semi-numeric method is suitable for solving a larger and more complex pairwise fuzzy group decision-making problem. The proposed method has been verified and applied to solve some real cases and is compared to Saaty's (1996) analytic hierarchy process (AHP) method.     

用区间直觉模糊集方法对属性权重未知的群求解其多属性决策

本文首先提出群区间直觉模糊有序加权几何(groupinterval-valuedintuitionistic fuzzy orderedweighted geometric,GIVIFOWG)算子和群区间直觉模糊有序加权平均(group interval-valued intuitionistic fuzzy ordered weighted averaging,GIVIFOWA)算子.利用GIVIFOWG算子或GIVIFOWA算子聚集群的决策矩阵以获得方案在属性上的综合区间直觉模糊决策矩阵(collectiveinterval-valuedintuitionistic fuzzy decision-matrix,CIVIFDM).然后定义了一个考虑犹豫度的区间直觉模糊熵(interval-valuedintuitionistic fuzzyentropy,IVIFE);通过熵衡量每个属性所含的信息来求解属性权重.最后,提出基于可能度的接近理想解的区间排序法(interval technique for order preference by similarity to an ideal solution,ITOPSIS)和区间得分函数法.在ITOPSIS法中,依据区间距离公式计算候选方案和理想方案的属性加权区间距离,进而采用ITOPSIS准则对各方案进行排序;在区间得分函数法中,算出CIVIFDM中各方案的得分值以及精确值,然后利用区间得分准则对各方案进行排序.实验结果验证了决策方法的有效性和可行性.     

A nonlinear-programming methodology for multi-attribute decision-making problem with interval-valued intuitionistic fuzzy soft sets information

Interval-valued intuitionistic fuzzy (IVIF) soft set is one of the useful extensions of the fuzzy soft set which efficiently deals with the uncertain data for the decision-making processes. In this paper, an attempt has been made to present a nonlinear-programming (NP) model based on the technique for order preference by similarity to ideal solution (TOPSIS), to solve multi-attribute decision-making problems. In this approach, both ratings of alternatives on attributes and weights of attributes are represented by IVIF sets. Based on the available information, NP models are constructed on the basis of the concepts of the relative-closeness coefficient and the weighted distance. Some NP models are further deduced to calculate relative-closeness of sets of alternatives which can be used to generate the ranking order of the alternatives. A real example is taken to demonstrate the applicability and validity of the proposed methodology.     

Fuzzy MCDM approach for selecting the best environment-watershed plan

In the real word, the decision-making problems are very vague and uncertain in a number of ways. Most of the criteria have interdependent and interactive features, so they cannot be evaluated by conventional measure method. Such as the feasibility, thus, to approximate the human subjective evaluation process, it would be more suitable to apply a fuzzy method in the environment-watershed plan topic. This paper describes the design of a fuzzy decision support system in multi-criteria analysis approach for selecting the best plan alternatives or strategies in environment watershed. The fuzzy analytic hierarchy process (FAHP) method is used to determine the preference weightings of criteria for decision makers by subjective perception (natural language). A questionnaire was used to find out from three related groups comprising 15 experts, including 5 from the university of expert scholars (include Water Resources Engineering and Conservation, Landscape and Recreation, Urban Planning, Environment Engineering, Architectural Engineering, etc.), 5 from the government departments, and 5 from industry. Subjectivity and vagueness analysis is dealt with the criteria and alternatives for selection process and simulation results by using fuzzy numbers with linguistic terms. It incorporated the decision-makers’ attitude towards the preference; overall performance value of each alternative can be obtained based on the concept of fuzzy multiple-criteria decision-making (FMCDM). This research also gives an example of evaluation consisting of five alternatives, solicited from an environment-watershed plan work in Taiwan, is illustrated to demonstrate the effectiveness and usefulness of the proposed approach. The result is useful for destination planning and the sustainability of watershed tourism resources as well.     

Multi-criteria decision-making using interval-valued hesitant fuzzy QUALIFLEX methods based on a likelihood-based comparison approach

QUALIFLEX is a very efficient outranking method to handle multi-criteria decision-making (MCDM) involving cardinal and ordinal preference information. Based on a likelihood-based comparison approach, this paper develops two interval-valued hesitant fuzzy QUALIFLEX outranking methods to handle MCDM problems within the interval-valued hesitant fuzzy context. First, we define the likelihoods of interval-valued hesitant fuzzy preference relations that compare two interval-valued hesitant fuzzy elements (IVHFEs). Then, we propose the concepts of the concordance/discordance index, the weighted concordance/discordance index and the comprehensive concordance/discordance index. Moreover, an interval-valued hesitant fuzzy QUALIFLEX model is developed to solve MCDM problems where the evaluative ratings of the alternatives and the weights of the criteria take the form of IVHFEs. Additionally, this paper propounds another likelihood-based interval-valued hesitant fuzzy QUALIFLEX method to accommodate the IVHFEs’ evaluative ratings of alternatives and non-fuzzy criterion weights with incomplete information. Finally, a numerical example concerning the selection of green suppliers is provided to demonstrate the practicability of the proposed methods, and a comparison analysis is given to illustrate the advantages of the proposed methods.

     

A new type-2 fuzzy set of linguistic variables for the fuzzy analytic hierarchy process

The fuzzy analytic hierarchy process (FAHP) has been used to solve various multi-criteria decision-making problems where trapezoidal type-1 fuzzy sets are utilized in defining decision-makers’ linguistic judgment. Previous theories have suggested that interval type-2 fuzzy sets (IT2 FS) can offer an alternative that can handle vagueness and uncertainty. This paper proposes a new FAHP characterized by IT2 FS for linguistic variables. Differently from the typical FAHP, which directly utilizes trapezoidal type-1 fuzzy numbers, this method introduces IT2 FS to enhance judgment in the fuzzy decision-making environment. This new model includes linguistic variables in IT2 FS and a rank value method for normalizing upper and lower memberships of IT2 FS. The proposed model is illustrated by a numerical example of work safety evaluation. Comparable results are also presented to check the feasibility of the proposed method. It is shown that the ranking order of the proposed method is consistent with the other two methods despite difference in weight priorities.     

A systematic approach for developing a new business model using morphological analysis and integrated fuzzy approach

Despite the growing importance of developing a novel business model, most previous studies on business model remain conceptual and theoretical. A paucity of empirical studies has hindered the use of the business model concept in practical purposes. Hence, this study proposes a systematic approach to new business model development (NBMD) that helps business practitioners to develop, evaluate and select the best business model to meet the business objectives. The proposed approach comprises two stages: identification of business model alternatives and business model evaluation and selection. During the first stage, a set of business model alternatives are derived by exploring all the possible combinations of a morphological matrix, and in the second stage, we conduct an evaluation and selection of a suitable business model. Morphological analysis (MA) has been employed for the derivation and aggregation of business model alternatives, and decision-making approach that integrates fuzzy extent analytic hierarchy process (FAHP) and fuzzy technique for order of preference by similarity to ideal solution (TOPSIS) methods is used as an evaluation and selection tool. Finally, to illustrate the applicability of proposed approach, a case study on the development of a business model for a Telco has been presented.     

Make-to-order or make-to-stock decision by a novel hybrid approach

This paper presents a strategic decision-making structure to determine whether a particular product should be produced under make-to-order (MTO) or make-to-stock (MTS) strategy. A novel hybrid methodology consisting of strengths, weaknesses, opportunities and threats (SWOT) analysis and analytic hierarchy process (AHP) is proposed. Utilizing AHP in SWOT analysis diminishes one of the main deficiencies of this strategic approach that is the restriction of employing quantitative calculation to evaluate the factors that affect the decision. AHP method improves the quantitative information basis of strategic decision-making processes. The traditional AHP requires exact judgments, but due to the complexity and uncertainty involved in real world decision problems, it is sometimes unrealistic or even impossible to require exact judgments. Consequently, a commonly used decision-making method, fuzzy analytic hierarchy process (FAHP) is suggested. FAHP’s connection to SWOT yields a novel hybrid method for partitioning of MTO/MTS products. At the end, the proposed fuzzy AHP-SWOT methodology is validated through a real case study.     

区间值模糊随机多准则决策方法

针对不完全信息的区间值模糊随机多准则决策问题,提出了两种求解方法。第一种方法利用离差最大化构建区间参数线性规划,通过区间数运算法则和定位规划求得最优准则权重向量、状态集结值区间决策矩阵与期望值区间决策矩阵,根据决策者风险偏好水平得到各方案的期望集结值从而确定排序。第二种方法将区间值模糊数决策矩阵转化为直觉模糊数决策矩阵,利用不完全的准则权重,通过规划模型求解,获取各方案在各自然状态下的加权记分函数值与加权精确函数值的区间,利用不完全的状态概率,得到各方案的记分函数期望值与精确函数期望值的区间,根据决策者风险偏好水平,求得各方案的记分函数与精确函数的期望集结值,进而确定方案的排序结果。算例分析验证了两种方法的有效性和可行性。     

Using the fuzzy analytic hierarchy process on optimum spatial allocation

This study uses the fuzzy analytic hierarchy process (FAHP) approach on a multiple criteria decision-making process made up of rational and emotional choices. The process involves setting evaluation criteria, constructing a fuzzy judgment matrix and weight vector, and then ranking the order of candidate alternatives by a fuzzy number in the fuzzy sequencing vector. This FAHP approach can provide hotel managers with a suitable way to determine the optimum spatial allocation. Also, creation of an artificial spatial allocation image by the image compositing technique allows hotel managers to see the future completed work before renovating, and the emotional judgment of the spatial image can take place immediately. Furthermore, the virtual image facilitates the reduction of communication time between hotel managers and designers and increases the level of satisfaction towards the final spatial allocation.

Relevance to industry

The FAHP approach addressed in this study can be applied to hotels, motels and related spaces where spatial allocation is needed and helps decision-makers or designers to choose the optimum alternative under the consideration of rational and emotional factors.     

A NEW METHOD FOR HANDLING MULTICRITERIA FUZZY DECISION-MAKING PROBLEMS

This paper presents a new method for handling multicriteria fuzzy decision-making problems, in which the characteristics of the alternatives are represented by interval-valued fuzzy sets, and some techniques are developed to calculate the degree of similarity between interval-valued fuzzy sets. The proposed method is more flexible than the one we presented earlier (Chen et al., 1989) because it allows the criteria values of the alternatives to be represented by real intervals rather than crisp real values between zero and one.     

A fuzzy AHP-DEA approach for multiple criteria ABC inventory classification

In order to efficiently control the inventory items and determine the suitable ordering policies for them, multi-criteria ABC inventory classification, which is one of the most common techniques of production and inventory control, is used. In this classification, other criteria in addition to annual dollar usage are taken into account and then the items are classified in three classes with different ordering policies, based on their priority. In this paper, we propose an integrated fuzzy analytic hierarchy process-data envelopment analysis (FAHP-DEA) for multiple criteria ABC inventory classification. The proposed FAHP–DEA methodology uses the FAHP to determine the weights of criteria, linguistic terms such as Very High, High, Medium, Low and Very Low to assess each item under each criterion, the data envelopment analysis (DEA) method to determine the values of the linguistic terms, and the simple additive weighting (SAW) method to aggregate item scores under different criteria into an overall score for each item. The integrated FAHP–DEA methodology is illustrated using a real case study.     

Prioritizing effective 7Ms to improve production systems performance using fuzzy AHP and fuzzy TOPSIS (case study)

This paper is aimed to present a fuzzy decision-making approach for prioritizing effective 7Ms to improve production systems performance. In this research systematic approach has been used for organization and production system inputs which named as 7Ms (Management, Manpower, Marketing, Method, Machine, Material, and Money). Linguistic values are used to assess the ratings and weights for 7Ms. These linguistic ratings can be expressed in trapezoidal or triangular fuzzy numbers. Then, a hierarchy multiple criteria decision-making (MCDM) model based on fuzzy-sets theory including FAHP and FTOPSIS are applied. The results obtained from AHP, FAHP; FTOPSIS were compared with each other. This research has been conducted on a manufacturing plant however the results can also be used for other types of organizations that are located in a competitive environment.     

Interval-valued intuitionistic fuzzy cosine similarity measures for multiple attribute decision-making

In this work, considering all information carried by the membership degrees, nonmembership degree, and hesitancy degree in interval-valued intuitionistic fuzzy sets (IVIFSs) as 3-D vector representations, we propose a cosine similarity measure and a weighted cosine similarity measure for IVIFSs based on the extension of the cosine similarity measure (angular coefficient) between intuitionistic fuzzy sets in 2-D vector space. Then, the weighted cosine similarity measure for IVIFSs is applied to multiple attribute decision-making problems under the interval-valued intuitionistic fuzzy environment. Through the similarity measure between the ideal alternative and each alternative, the ranking order of all alternatives can be determined and the best alternative can be easily identified as well. Finally, two illustrative examples are given to demonstrate the applications and efficiency of the proposed decision-making method.     

FALSCAL: A fuzzy multidimensional scaling algorithm

The conventionally adopted Alternating Least squares SCALing (ALSCAL) procedure of multidimensional scaling (MDS) is a valuable mathematical scheme for analyzing data in areas where organized concepts and underlying dimensions are inadequately defined or developed. Fuzzy set theory (FST) attempts to formulate human reasoning and perceptions, therefore targeting problems in areas where human factors significantly impact the result of decision-making. To our knowledge, the FST and ALSCAL approaches have not yet been integrated. This study integrates and modifies the FST and ALSCAL procedures. Fuzzy data collected from fuzzy questionnaires are adopted as the input of the MDS, ensuring that the uncertainty of input data can be incorporated into the analysis. The conventionally adopted ALSCAL procedure is then modified to cope with fuzzy input data by adopting the notion of fuzzy distances, fuzzy disparities and fuzzy ranking to represent the similarities between fuzzy data. Related approximation operations of the triangular fuzzy number are also introduced to facilitate computation in fuzzy ALSCAL.     

Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment

The paper presents the correlation and correlation coefficient of single-valued neutrosophic sets (SVNSs) based on the extension of the correlation of intuitionistic fuzzy sets and demonstrates that the cosine similarity measure is a special case of the correlation coefficient in SVNS. Then a decision-making method is proposed by the use of the weighted correlation coefficient or the weighted cosine similarity measure of SVNSs, in which the evaluation information for alternatives with respect to criteria is carried out by truth-membership degree, indeterminacy-membership degree, and falsity-membership degree under single-valued neutrosophic environment. We utilize the weighted correlation coefficient or the weighted cosine similarity measure between each alternative and the ideal alternative to rank the alternatives and to determine the best one(s). Finally, an illustrative example demonstrates the application of the proposed decision-making method.     

A ranking method for multiple attribute decision-making problems based on the possibility degrees of trapezoidal intuitionistic fuzzy numbers

To solve multiple attribute decision-making problems with attribute values or decision values characterized by trapezoidal intuitionistic fuzzy numbers (TIFNs), we define a trapezoidal intuitionistic fuzzy induced ordered weighted arithmetic averaging (TIFIOWA) operator, which is an extension of the induced ordered weighted arithmetic averaging operator. We derive and prove some related properties and conclusions of the TIFIOWA operator. To compare the TIFNs, we define possibility degrees of the TIFNs. Based on the possibility degrees of the TIFNs and the TIFIOWA operator, we construct a new method to determine the order of alternatives in multiple attribute decision making and to choose the best alternative. Finally, a numerical example shows that the developed method is feasible and effective.     

Multiattribute group decision-making based on Pythagorean fuzzy Einstein prioritized aggregation operators

Pythagorean fuzzy set (PFS) is a powerful tool to deal with the imprecision and vagueness. Many aggregation operators have been proposed by many researchers based on PFSs. But the existing methods are under the hypothesis that the decision-makers (DMs) and the attributes are at the same priority level. However, in real group decision-making problems, the attribute and DMs may have different priority level. Therefore, in this paper, we introduce multiattribute group decision-making (MAGDM) based on PFSs where there exists a prioritization relationship over the attributes and DMs. First we develop Pythagorean fuzzy Einstein prioritized weighted average operator and Pythagorean fuzzy Einstein prioritized weighted geometric operator. We study some of its desirable properties such as idempotency, boundary, and monotonicity in detail. Moreover we propose a MAGDM approach based on the developed operators under Pythagorean fuzzy environment. Finally, an illustrative example is provided to illustrate the practicality of the proposed approach.     

Soft computing based on new interval-valued fuzzy modified multi-criteria decision-making method

In this paper, a new interval-valued fuzzy modified TOPSIS (IVFM-TOPSIS) method is proposed that can reflect both subjective judgment and objective information in real life situations. This proposed method is based on concepts of the positive ideal and negative ideal solutions for solving multi-criteria decision-making (MCDM) problems in a fuzzy environment. The performance rating values and weights of criteria are linguistic variables expressed as triangular interval-valued fuzzy numbers. Furthermore, we appraise the performance of alternatives against both subjective and objective criteria with multi-judges for decision-making problems. Finally, for the purpose of proving the validity of the proposed method a numerical example is presented for a robot selection problem.