A Deviation-Based Approach to Intuitionistic Fuzzy Multiple Attribute Group Decision Making

The aim of this article is to investigate the approach to multiple attribute group decision making (MAGDM) with intuitionistic fuzzy information. We first introduce a deviation measure between two intuitionistic fuzzy numbers, and then utilize the intuitionistic fuzzy hybrid aggregation operator to aggregate all individual intuitionistic fuzzy decision matrices into a collective intuitionistic fuzzy decision matrix. Based on the deviation measure, we develop an optimization model by which a straightforward formula for deriving attribute weights can be obtained. Furthermore, based on the intuitionistic fuzzy weighted averaging operator and information theory, we utilize the score function and accuracy function to give an approach to ranking the given alternatives and then selecting the most desirable one(s). In addition, we extend the above results to MAGDM with interval-valued intuitionistic fuzzy information.     

A Note on Linguistic Hybrid Arithmetic Averaging Operator in Multiple Attribute Group Decision Making with Linguistic Information

In this paper, we propose a linguistic hybrid arithmetic averaging (LHAA) operator, which is based on linguistic weighted arithmetic averaging (LWAA) operator and extended ordered weighted averaging (EOWA) operator, and study some desirable properties of the LHAA operator. The LHAA operator can not only reflect the importance degrees of both the given argument and its ordered position, but also relieve the influence of unfair arguments on the decision results by weighting these arguments with small values. Based on the LWAA and LHAA operators, we develop a practical approach to multiple attribute group decision making under linguistic environment. The approach first aggregates the individual linguistic preference values into a collective linguistic preference value for each alternative by using the LWAA and LHAA operators (it is worth pointing out that the aggregation process does not produce any loss of linguistic information), and then orders the collective linguistic preference values to obtain the best alternative(s). Finally, an illustrative example is also given to verify the approach and to demonstrate its feasibility and practicality.     

Minimizing Group Discordance Optimization Model for Deriving Expert Weights

This paper focuses on the problem of how to determine expert weights in multiple attribute group decision making. We first aggregate all the individual decision matrices into the collective decision matrix by means of the weighted arithmetic averaging operator, and then from the angle of minimizing group discordance, we establish a general nonlinear optimization model based on deviation function, and employ a genetic algorithm to solve our model so as to find the optimal expert weights. Moreover, we extend our model to uncertain multiple attribute group decision making, where the attribute values are interval numbers, and finally, apply our model to the plan evaluation of new model of cars of an investment company.     

Generalized Hybrid Aggregation Operators Based on the 2-Dimension Uncertain Linguistic Information for Multiple Attribute Group Decision Making

With respect to the multiple attribute decision making problems in which the attribute values take the form of the 2-dimension uncertain linguistic information, a new method based on the generalized hybrid operators is proposed. Firstly, the definition, properties, expectations and ranking method of 2-dimension uncertain linguistic information are introduced, and the operational laws the 2-dimension uncertain linguistic information are defined. Then some aggregation operators, including 2-dimension uncertain linguistic generalized weighted average operator, 2-dimension uncertain linguistic generalized ordered weighted average operator, and 2-dimension uncertain linguistic generalized hybrid weighted average operator, are developed, and some properties and special cases of them are also discussed. Finally, these operators are applied to multi-criteria decision making and an illustrative example is given to verify the developed approach and to demonstrate its effectiveness.     

Multiple Attribute Group Decision-Making Methods with Completely Unknown Weights in Intuitionistic Fuzzy Setting and Interval-Valued Intuitionistic Fuzzy Setting

The existing multiple attribute group decision-making approaches based on intuitionistic fuzzy sets (IFSs) or interval-valued intuitionistic fuzzy sets (IVIFSs) are considered as the situation that the weights of experts are given beforehand and the attribute weights are known or unknown. To better describe the uncertain decision environment and solve the corresponding decision problem, multiple attribute group decision-making methods with completely unknown weights of both experts and attributes are proposed in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting. Entropy weight models can be used to determine the weights of both experts and attributes from intuitionistic fuzzy decision matrices or interval-valued intuitionistic fuzzy decision matrices, and then the evaluation formulas of weighted correlation coefficients between alternatives and the ideal alternative are introduced in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting. The alternatives can be ranked and the most desirable one(s) can be selected according to the values of the weighted correlation coefficients for IFSs or IVIFSs. Finally, two numerical examples demonstrate the effectiveness of the proposed methods: they are capable for handling the multiple attribute group decision-making problems with completely unknown weights.     

Uncertain Power Average Operators for Aggregating Interval Fuzzy Preference Relations

In this paper, we investigate group decision making problems based on interval fuzzy preference relations. We define an uncertain power weighted average (UPWA) operator and an uncertain power ordered weighted average (UPOWA) operator, on the basis of the power average operator of Yager (IEEE Trans Syst Man Cybern A 31:724–731, 1988) and the uncertain geometric mean. In the situations where the weights of experts are known, we develop a method based on the UPWA operator for group decision making with interval fuzzy preference relations; and in the situations where the weights of experts are unknown, we develop a method based on the UPOWA operator for group decision making with interval fuzzy preference relations.     

Ease of reading of mandatory information on Canadian food product labels

Food product labels present individual product information, safety, nutrition, electronic inventory, container and environmental information, in various formats, languages and images. Some information is mandatory; much is promotional. The food label is an essential tool for regulators of safe food handling, nutrition policy and fair competition. Mandatory information on food labels in Canada is required to be presented in both English and French, readily discernable, prominently displayed and legible. This study examines the ease of finding and reading of mandatory label components on selected Canadian food products. A validated typographical scoring system assessed the lists of ingredients on a purposive sample of 100 food labels representing foods in all groups in Canada's Food Guide. Seven percent of the ingredient lists were easy to read; 26% were difficult to read and 67% were very difficult to read. Well‐educated resourceful readers in consumer focus groups examined food labels for key elements that influence ease of finding and reading information. Focus groups and typographical scoring identified: colour contrast, case, print style, print size, space between the lines, reverse print, organization, justification, type of surface, hyphenation and print reproduction as factors that affect ease of reading. Print that curves around a container, lack of paragraphing or point form organization make reading difficult; text blocks at right angles to each other make comparisons difficult; separation of the nutrition facts table from the list of ingredients makes decision making tedious. Inadequate spacing between lines of print creates problems for readers of English and exacerbates problems for readers of French. Words placed over illustrations, busy backgrounds or watermarks increase reading difficulty. Hazard statements, instructions and storage information imbedded in other information without added space or appropriate heading is difficult to find and read. Canadian consumers echo consumers in 28 European countries who find label information difficult to find and to read and want clear guidelines/regulations on the placement and the typography of mandatory food label components     

A Practical Procedure for Group Decision Making under Incomplete Multiplicative Linguistic Preference Relations

The aim of this paper is to investigate a group decision making problem with incomplete multiplicative linguistic preference relations. We first define the concept of an incomplete multiplicative linguistic preference relation, and then develop a simple algorithm to extend each incomplete multiplicative linguistic preference relation to a complete multiplicative linguistic preference relation. Finally, we develop a practical procedure for group decision making under incomplete multiplicative linguistic preference relations, and give a numerical example to illustrate the developed procedure.     

A Consensus Based Method for Multi-criteria Group Decision Making Under Uncertain Linguistic Setting

A two-stage (a consensus process and a selection process) approach is proposed to solve multi-criteria group decision making problems under an uncertain linguistic environment. Since achieving general consensus is a desirable goal in group decision making, the proposed method first develops a consensus reaching process in order to reach a satisfactory consensus. Based on the partial order of uncertain linguistic variables, the superiority index of one alternative over another for a given criterion and the overall superiority index of one alternative are defined. Then a procedure based on the superiority indices is described to select the best alternative(s). Given the decision makers’ desire for a consensus solution, a common framework based on the previous consensus model and the selection process is presented. Finally, a practical application is demonstrated to show the effectiveness of the proposed method.     

A Relative Entropy Approach to Group Decision Making with Interval Reciprocal Relations Based on COWA Operator

A new approach has been presented based on relative entropy to rank all the alternatives in the group decision making with interval reciprocal relations. First we introduced the continuous ordered weighted averaging operator and used it to aggregate all individual interval reciprocal relations to derive the priority vector. Then we define the consensus indicator of the interval reciprocal relations to determine the weights of experts in the group decision making. Based on the conception of relative entropy, we construct an optimization model to minimize the difference between the group priority vector and all individual priority vectors. We also give the solution to the optimal model, in which we obtain the formula to rank the given alternatives in the group decision making for the collective reciprocal relations and select the most desirable one. Finally, a numerical example shows that the developed approach is feasible and the result is credible.     

A linguistic decision process in group decision making

Assuming a set of linguistic preferences representing the preferences of the individuals, a linguistic choice process is presented. This is developed using the concept of fuzzy majority for deriving a collective linguistic preference, and the concept of nondominated alternatives for deriving the selected alternatives in the linguistic choice process. The fuzzy majorities are equated with fuzzy linguistic quantifiers. The collective linguistic preference is derived by means of a linguistic ordered weighted averaging operator whose weights are defined using a fuzzy linguistic quantifier. In order to obtain the nondominated alternatives, we present a novel reformulation of Orlovski's nondominance degree under linguistic information.     

A Decision Rule Aggregation Approach to Multiple Criteria-Multiple Participant Sorting

A system that aggregates case-based linguistic decision rules using a hybrid of the dominance-based rough set approach (DRSA) and the Dempster–Shafer (DS) theory of evidence is proposed for multiple criterion-multiple participant sorting. First, DRSA is employed to infer linguistic decision rules that estimate the preferences of a few participants by means of their evaluations of representative case sets. Next, DS theory is applied to aggregate the decision rules triggered by all participants’ evaluations of an alternative, thereby generating an overall decision recommendation for the alternative. The method is demonstrated on a numerical example.     

An exploration of the influence of food labels on South African consumers' purchasing behaviour

New labelling legislation in South Africa is expected to help consumers sustain a healthy lifestyle through the food choices they make. This study was undertaken to explore a sample of South African consumers' reasons for reading labels and the influence of food labels on their purchasing behaviour. The study was conducted using focus group discussions held with label reading consumers in Potchefstroom in the North West Province of South Africa. Findings suggested that these participants read food labels to assess the nutritional value, personal benefits, health attributes and product quality. Various purchasing influences were also identified, suggesting that consumers are in some cases motivated by food labels to purchase a product, or may be unresponsive to the label or indifferent by being aware of the information but not reluctant to buy a product that does not indicate essential information. Several indirect consideration factors such as situational factors (e.g. family), extrinsic (e.g. price) and intrinsic (e.g. taste) may contribute to the purchasing behaviour of some consumers. These findings are useful to propose a perceptual model of the way in which food labels influence purchasing behaviour of a sample of South African consumers and explain the role of food labels in the purchasing decision of label‐reading consumers. This information is especially significant for new packaging and labelling initiatives as it highlights the reasons why label‐reading South African consumers read label information.     

Interval-Valued Intuitionistic Fuzzy WASPAS Method: Application in Reservoir Flood Control Management Policy

Interval-valued intuitionistic fuzzy sets (IVIFSs) are very flexible tool to cope with the uncertainty arises in multi-criteria decision making (MCDM) problems. In recent times, MCDM problems with interval-valued intuitionistic fuzzy information have achieved more attention from researchers in different areas and consequently, several MCDM methods have been extended for IVIFSs. In this paper, a novel approach based on WASPAS method is developed under IVIFSs. The developed method is based on the operators of IVIFSs, some amendments in the classical WASPAS method and a new process for calculation of criteria and decision experts’ weights. In process for calculating weights, new procedures is propoesd to compute the decision experts’ weights and criteria weights based on interval-valued intuitionistic fuzzy information measures (entropy, divergence and similarity measures) to achieve more realistic weights. Innovative information measures are developed based on the exponential function for IVIFSs to determine the weights of the criteria and decision experts. Since the uncertainty is an unavoidable feature of MCDM problems, the developed method can be a constructive tool for decision-making in an uncertain environment. Further, an uncertain decision making problem of reservoir flood control management policy is implemented with interval-valued intuitionistic fuzzy information, which reveals the effectiveness and reliability of the proposed IVIF-WASPAS method. To validate the result, comparative analysis with existing methods and sensitivity analysis are presented under interval-valued intuitionistic fuzzy environment.     

Branding Decisions for Retailers’ Private Labels

Umbrella branding (UB) strategies for manufacturers’ products have received considerable attention in the literature. Not much is known about this strategy for private labels. Using a game-theoretic approach, we reassess the benefits of introducing a private label in a distinct category, and provide favorable conditions for the retailer to implement umbrella or individual branding for his private labels. We find that (1) UB leads to lower wholesale and retail prices for both national brands; (2) national brands’ manufacturers prefer individual branding over UB for private labels; and (3) the profitability of UB is not always guaranteed for the retailer.     

含有模糊权值的模糊质量综合评判

针对权值的不确定性,结合L-R模糊数的近似算法,用海明距离测度工具来度量不同评语集之间的差异,提出一种新的模糊质量评判方法,该方法能够更有效处理质量综合评判中的不确定性的非量化信息。用广义的归一化方法对模糊权值和模糊评判值归一化处理,使评判结果能够落在给定的区间内。此外,含有模糊权值的模糊质量综合评判方法,可以作为基本方法应用于质量工程的研究中。     

Are nutrition labels useful for the purchase of a familiar food? Evidence from Chinese consumers�� purchase of rice

Nutrition labeling has been accepted by Chinese consumers as an information source to learn about food quality and safety. This paper uses Chinese consumers’ rice purchase as an example to study how consumers use food nutrition labels to make purchase decision of a familiar food product. The goal is to understand how consumers seek information from the labels to make purchase when extensive experience with the food has been developed. Survey data from 400 random respondents in Beijing were analyzed using an empirical framework and a Mont Carlo integral econometrics model. We find that more than 50% of the consumers in Beijing have heard of food nutrition labels in general, 36.50% carefully use label information even if they are familiar with the food, and nearly 70% consider mandatory food nutrition labels as beneficial. Those who are more knowledgeable about rice nutrition labels are more likely to use the labels when purchasing rice, no matter how familiar they are with the product. Frequent users of nutrition labels are more likely to consider food mandatory nutrition labels as beneficial. This study suggests that consumers still use the label information to reassure the quality and safety of food despite a history of consumption.     

Revisions of labeling for personal watercraft: Part 1 – label development

This two-part paper presents a comprehensive case study related to the development and evaluation of warning labels. In particular, this two-part paper describes the development and evaluation of revised warning labels applicable to a class of products known as personal watercraft (PWCs), and serves as an example application of a general warnings design process described by Frantz et al. Part 1, presented in this paper, includes the process of project planning, identifying and analyzing hazards, and developing two preliminary warning labels to address PWC operational hazards. Included are discussions regarding the methods used to address problems frequently encountered in the development of warning labels. Topics of these discussions include the prioritization and selection of hazards to be addressed, message development strategies, avoiding information overload, and organizing the presentation of information using human factors models and concepts. The work conducted in Part 1 resulted in two preliminary labels: one label dealing with issues related to Collision Avoidance and a second label dealing with General Operational Hazards. Part 2, the companion article, describes the process of evaluating and revising the preliminary labeling to produce the final labels. Discussions regarding the methods used to address challenges related to the evaluation and revision of warning labels are provided. As a result of the entire process, revised labels for PWCs with increased uniformity will be used by PWC manufacturers, although flexibility for specific model features or future changes in design will be retained.     

Do private labels increase retailer bargaining power?

Like any new product, private label entry increases competition within a category leading to downward pressure on both wholesale and retail prices. But, given the higher margins for private labels and potential bargaining benefits for retailers, they have incentives to help private labels gain market share. The paper addresses two questions: First, do private labels enhance a retailer’s bargaining power with respect to manufacturers? Second, given the higher profitability and potential increase in bargaining power, does the retailer strategically set retail prices to favor and strengthen the private label? We find support for the “bargaining power” hypothesis, but qualified support for the “strategic retailer pricing” hypothesis. Retailers gain bargaining power through lower wholesale prices on imitated national brands. But the gain is greater in niche categories than in mass categories, suggesting that niche national brands with limited “pull” power lose greater bargaining power. In terms of strategic pricing, the retailer, on initially introducing the private label, strategically sets prices to help private labels gain market share in high volume mass market categories. But retail prices revert to the category profit maximizing price after a year when the private label gains a stable market share.