A hybrid approach integrating Affinity Diagram, AHP and fuzzy TOPSIS for sustainable city logistics planning

City logistics initiatives are steps taken by municipal administrations to ameliorate the condition of goods transport in cities and reduce their negative impacts on city residents and their environment. Examples of city logistics initiatives are urban distribution centers, congestion pricing, delivery timing and access restrictions. In this paper, we present a hybrid approach based on Affinity Diagram, AHP and fuzzy TOPSIS for evaluating city logistics initiatives. Four initiatives namely vehicle sizing restrictions, congestion charging schemes, urban distribution center and access timing restrictions are considered.The proposed approach consists of four steps. The first step involves identification of criteria for assessing performance of city logistics initiatives using Affinity Diagram. The results are four categories of criteria namely technical, social, economical and environmental. In step 2, a decision making committee comprising of representatives of city logistics stakeholders is formed. These stakeholders are shippers, receivers, transport operators, end consumers and public administrators. The committee members weight the selected criteria using AHP. In step 3, the decision makers provide linguistic ratings to the alternatives (city logistics initiatives) to assess their performance against the selected criteria. These linguistic ratings are then aggregated using fuzzy TOPSIS to generate an overall performance score for each alternative. The alternative with the highest score is finally chosen as most suitable city logistics initiative for improving city sustainability. In the fourth step, we perform sensitivity analysis to evaluate the influence of criteria weights on the selection of the best alternative.The proposed approach is novel and can be practically applied for selecting sustainable city logistics initiatives for cities. Another advantage is its ability to generate solutions under limited quantitative information. An empirical application of the proposed approach is provided.     

Developments in fuzzy multicriteria analysis

Selecting or ranking available alternatives (observations/objects) with respect to multiple, often conflicting criteria in a fuzzy environment usually referred to as fuzzy multicriteria analysis is a problem of a major interest in information and engineering. Methodologies for addressing this problem have been developed from a variety of research disciplines, including statistics, econometrics, artificial intelligent, and operations research. This paper presents an overview of the developments in fuzzy multicriteria analysis. It discusses the complexity of fuzzy multicriteria analysis and analyses the existing approaches from four different perspectives for facilitating a better understanding of the recent development in this domain. Finally, the paper elaborates on the future research areas in fuzzy multicriteria analysis.     

Dealing with inconsistent judgments in multiple criteria sorting models

Sorting models consist in assigning alternatives evaluated on several criteria to ordered categories. To implement such models it is necessary to set the values of the preference parameters used in the model. Rather than fixing the values of these parameters directly, a usual approach is to infer these values from assignment examples provided by the decision maker (DM), i.e., alternatives for which (s)he specifies a required category. However, assignment examples provided by DMs can be inconsistent, i.e., may not match the sorting model. In such situations, it is necessary to support the DMs in the resolution of this inconsistency. In this paper, we extend algorithms from mous5ejor03 that calculate different ways to remove assignment examples so that the information can be represented in the sorting model. The extension concerns the possibility to relax (rather than to delete) assignment examples. These algorithms incorporate information about the confidence attached to each assignment example, hence providing inconsistency resolutions that the DMs are most likely to accept. Received: September 2004, Revised: June 2005 AMS classification: 90B50, 91B08, 90C05     

MCS—A new algorithm for multicriteria optimisation in constraint programming

In this paper we propose a new algorithm called MCS for the search for solutions to multicriteria combinatorial optimisation problems. To quickly produce a solution that offers a good trade-off between criteria, the MCS algorithm alternates several Branch & Bound searches following diversified search strategies. It is implemented in CP in a dedicated framework and can be specialised for either complete or partial search.     

A general model for voting systems with multiple alternatives

In this paper, the extension of simple games to the vector case is proposed. Games with multiple qualitative criteria and multi-criteria simple games are introduced as a natural tool for modelling voting systems and related social-choice situations. After formally defining these games, the special class of monotonic multi-criteria simple games is characterized. We show that these games enable the formulation and analysis of several collective decision models proposed in the literature. Furthermore, our model can be applied to group-decision problems which cannot be analyzed in the existing frameworks.     

A multiple criteria ranking method based on game cross-evaluation approach

The application of Data Envelopment Analysis (DEA) as an alternative multiple criteria decision making (MCDM) tool has been gaining more attentions in the literatures. Doyle (Organ. Behav. Hum. Decis. Process. 62(1):87?C100, 1995) presents a method of multi-attribute choice based on an application of DEA. In the first part of his method, the straightforward DEA is considered as an idealized process of self-evaluation in which each alternative weighs the attributes in order to maximize its own score (or desirability) relative to the other alternatives. Then, in the second step, each alternative applies its own DEA-derived best weights to each of the other alternatives (i.e., cross-evaluation), then the average of the cross-evaluations that get placed on an alternative is taken as an index of its overall score. In some cases of multiple criteria decision making, direct or indirect competitions exist among the alternatives, while the factor of competition is usually ignored in most of MCDM settings. This paper proposes an approach to evaluate and rank alternatives in MCDM via an extension of DEA method, namely DEA game cross-efficiency model in Liang, Wu, Cook and Zhu (Oper. Res. 56(5):1278?C1288, 2008b), in which each alternative is viewed as a player who seeks to maximize its own score (or desirability), under the condition that the cross-evaluation scores of each of other alternatives does not deteriorate. The game cross-evaluation score is obtained when the alternative??s own maximized scores are averaged. The obtained game cross-evaluation scores are unique and constitute a Nash equilibrium point. Therefore, the results and rankings based upon game cross-evaluation score analysis are more reliable and will benefit the decision makers.     

An intelligent-agent-based fuzzy group decision making model for financial multicriteria decision support: The case of credit scoring

Credit risk analysis is an active research area in financial risk management and credit scoring is one of the key analytical techniques in credit risk evaluation. In this study, a novel intelligent-agent-based fuzzy group decision making (GDM) model is proposed as an effective multicriteria decision analysis (MCDA) tool for credit risk evaluation. In this proposed model, some artificial intelligent techniques, which are used as intelligent agents, are first used to analyze and evaluate the risk levels of credit applicants over a set of pre-defined criteria. Then these evaluation results, generated by different intelligent agents, are fuzzified into some fuzzy opinions on credit risk level of applicants. Finally, these fuzzification opinions are aggregated into a group consensus and meantime the fuzzy aggregated consensus is defuzzified into a crisp aggregated value to support final decision for decision-makers of credit-granting institutions. For illustration and verification purposes, a simple numerical example and three real-world credit application approval datasets are presented.     

Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making

The purpose of this paper is to present a generalized hesitant fuzzy synergetic weighted distance (GHFSWD) measure, which is based on the generalized hesitant fuzzy weighted distance (GHFWD) measure and the generalized hesitant fuzzy ordered weighted distance (GHFOWD) measure proposed by Xu and Xia [Z. Xu, M. Xia, Distance and similarity measures for hesitant fuzzy sets, Inf. Sci. 181 (2011) 2128–2138.], and investigate its some desirable properties and special cases. The GHFSWD measure not only generalizes both the GHFWD and GHFOWD measures as well as the common hesitant fuzzy distance measures, but also reflects the importance degrees of both the given individual distances and their ordered positions. Then, based on the defined notions of positive ideal hesitant fuzzy set and negative ideal hesitant fuzzy set, we utilize the proposed GHFSWD measure to develop a method for multiple criteria decision making with hesitant fuzzy information. The method is flexible because it allows decision makers to provide preference with hesitancy and determine different decision results by choosing different decision strategies. Finally, a numerical example is provided to illustrate the feasibility and practicality of the proposed method.     

Extension of VIKOR method for decision making problem based on hesitant fuzzy set

The multiple criteria decision making (MCDM) methods VIKOR and TOPSIS are all based on an aggregating function representing “closeness to the ideal”, which originated in the compromise programming method. The VIKOR method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum of an “individual regret” for the “opponent”, which is an effective tool in multi-criteria decision making, particularly in a situation where the decision maker is not able, or does not know to express his/her preference at the beginning of system design. The TOPSIS method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative-ideal solution, but it does not consider the relative importance of these distances. And, the hesitant fuzzy set is a very useful tool to deal with uncertainty, which can be accurately and perfectly described in terms of the opinions of decision makers. In this paper, we develop the E-VIKOR method and TOPSIS method to solve the MCDM problems with hesitant fuzzy set information. Firstly, the hesitant fuzzy set information and corresponding concepts are described, and the basic essential of the VIKOR method is introduced. Then, the problem on multiple attribute decision marking is described, and the principles and steps of the proposed E-VIKOR method and TOPSIS method are presented. Finally, a numerical example illustrates an application of the E-VIKOR method, and the result by the TOPSIS method is compared.     

A multiple criteria decision making approach to manure management systems in the Netherlands

The intensification of livestock operations in the last few decades has resulted in an increased social concern over the environmental impacts of livestock operations and thus making appropriate manure management decisions increasingly important. A socially acceptable manure management system that simultaneously achieves the pressing environmental objectives while balancing the socio-economic welfare of farmers and society at large is needed. Manure management decisions involve a number of decision makers with different and conflicting views of what is acceptable in the context of sustainable development. This paper developed a decision-making tool based on a multiple criteria decision making (MCDM) approach to address the manure management problems in the Netherlands. This paper has demonstrated the application of compromise programming and goal programming to evaluate key trade-offs between socio-economic benefits and environmental sustainability of manure management systems while taking decision makers’ conflicting views of the different criteria into account. The proposed methodology is a useful tool in assisting decision makers and policy makers in designing policies that enhance the introduction of economically, socially and environmentally sustainable manure management systems.     

Concordant outranking with multiple criteria of ordinal significance

In this paper we address the problem of aggregating outranking statements from multiple preference criteria of ordinal significance. The concept of ordinal concordance of a global outranking situation is defined and an operational test for its presence is developed. Finally, we propose a new kind of robustness analysis for global outranking statements integrating classical dominance, ordinal and classical majority concordance in a same ordinal valued logical framework.Received: March 2004, Revised: October 2004, MSC classification: 90B50, 06A06, 03C80     

A new method for ranking fuzzy numbers and its application to group decision making

In this paper, a new method for comparing fuzzy numbers based on a fuzzy probabilistic preference relation is introduced. The ranking order of fuzzy numbers with the weighted confidence level is derived from the pairwise comparison matrix based on 0.5-transitivity of the fuzzy probabilistic preference relation. The main difference between the proposed method and existing ones is that the comparison result between two fuzzy numbers is expressed as a fuzzy set instead of a crisp one. As such, the ranking order of n fuzzy numbers provides more information on the uncertainty level of the comparison. Illustrated by comparative examples, the proposed method overcomes certain unreasonable (due to the violation of the inequality properties) and indiscriminative problems exhibited by some existing methods. More importantly, the proposed method is able to provide decision makers with the probability of making errors when a crisp ranking order is obtained. The proposed method is also able to provide a probability-based explanation for conflicts among the comparison results provided by some existing methods using a proper ranking order, which ensures that ties of alternatives can be broken.     

A fast method of ranking alternatives using fuzzy numbers

We show a very fast method of ranking alternatives using fuzzy numbers discussed in [1] and [2].     

An environmental input-output model with multiple criteria

It is often claimed that there is a trade-off between economic goals and the quality of the environment. For this reason, an environmental input-output optimization model with multiple objectives is formulated. The criteria are the minimization of factor costs to produce the Gross National Product and the minimization of net pollution for a given level of final demand. Using the LeChatelier-Samuelson principle, we analyze the changes in the production of the sectors and in the prices of the goods (described by the dual model) due to the change in the preferences of the decision makers. It can be shown that higher weights for the environmental objectives imply — in tendency —non-decreasing production of the sectors andnon-decreasing abatement activities. The changes of prices are ambiguous. The condition for increasing prices is given. To some degree, the opposite results can be achieved, if maximization of the value of final demand (or of private consumption) and minimization of net pollution under the constraints for primary input are taken as objective functions. In this case, increasing weights for environmental goals will leadin tendency tonon-increasing final demand and tonon-increasing net pollution. Under given conditions, higher environmental quality will be achieved bynon-increasing gross production and abatement activities.     

A fuzzy multiobjective programming algorithm in decision support systems

Multicriteria analysis is one of the analytical functions in the problem processing system of decision support systems (DSS). In this paper, an interactive and iterative fuzzy programming method for solving a quasi-optimization problem in complex decisions under constraints involving a multiple objective function is proposed. Comparing with an adapted gradient search method, a surrogate worth tradeoff method, and a Zionts—Wallenius method, an approximate preference structure is emphasized in the proposed method.     

Rough set approach to multiple criteria classification with imprecise evaluations and assignments

Dominance-based Rough Set Approach (DRSA) has been introduced to deal with multiple criteria classification (also called multiple criteria sorting, or ordinal classification with monotonicity constraints), where assignments of objects may be inconsistent with respect to dominance principle. In this paper, we consider an extension of DRSA to the context of imprecise evaluations of objects on condition criteria and imprecise assignments of objects to decision classes. The imprecisions are given in the form of intervals of possible values. In order to solve the problem, we reformulate the dominance principle and introduce second-order rough approximations. The presented methodology preserves well-known properties of rough approximations, such as rough inclusion, complementarity, identity of boundaries and precisiation. Moreover, the meaning of the precisiation property is extended to the considered case. The paper presents also a way to reduce decision tables and to induce decision rules from rough approximations.     

A ranking model in uncertain, imprecise and multi-experts contexts: The application of evidence theory

We consider ranking problems where the actions are evaluated on a set of ordinal criteria. The evaluation of each alternative with respect to each criterion may be imperfect and is provided by one or several experts. We model each imperfect evaluation as a basic belief assignment (BBA). In order to rank the BBAs characterizing the performances of the actions according to each criterion, a new concept called RBBD and based on the comparison of these BBAs to ideal or nadir BBAs is proposed. This is performed using belief distances that measure the dissimilarity of each BBA to the ideal or nadir BBAs. A model inspired by Xu et al.’s method is also proposed and illustrated by a pedagogical example.     

InterQuad: An interactive quad tree based procedure for solving the discrete alternative multiple criteria problem

In this paper an interactive procedure based upon a data structure called a quad tree is developed for solving the discrete alternative multiple criteria problem. Called InterQuad, the procedure has been designed with large discrete alternative problems in mind. InterQuad takes advantage of the ability of a quad tree to identify, store, and retrieve nondominated criterion vectors. Then, the user interacts with the nondominated criterion vectors stored in the quad tree in a fashion similar to that of the Combined Tchebycheff/Aspiration Criterion Vector Procedure of Steuer, Silverman and Whisman.     

Multicriteria decision-making method using the Dice similarity measure based on the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets

This paper proposes the concept of the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets (IVIFSs) with respect to adjustable weight vectors and the Dice similarity measure based on the reduct intuitionistic fuzzy sets to explore the effects of optimism, neutralism, and pessimism in decision making. Then a decision-making method with the pessimistic, optimistic, and neutral schemes desired by the decision maker is established by combining adjustable weight vectors and the Dice similarity measure for IVIFSs. The proposed decision-making method is more flexible and adjustable in practical problems and can determine the ranking order of alternatives and the optimal one(s), so that it can overcome the difficulty of the ranking order and decision making when there exist the same measure values of some alternatives in some cases. This adjustable feature can provide the decision maker with more selecting schemes and actionable results for the decision-making analysis. Finally, two illustrative examples are employed to show the feasibility of the proposed method in practical applications.     

Weight determination for consistently ranking alternatives in multiple criteria decision analysis

One of the most difficult tasks in multiple criteria decision analysis (MCDA) is determining the weights of individual criteria so that all alternatives can be compared based on the aggregate performance of all criteria. This problem can be transformed into the compromise programming of seeking alternatives with a shorter distance to the ideal or a longer distance to the anti-ideal despite the rankings based on the two distance measures possibly not being the same. In order to obtain consistent rankings, this paper proposes a measure of relative distance, which involves the calculation of the relative position of an alternative between the anti-ideal and the ideal for ranking. In this case, minimizing the distance to the ideal is equivalent to maximizing the distance to the anti-ideal, so the rankings obtained from the two criteria are the same. An example is used to discuss the advantages and disadvantages of the proposed method, and the results are compared with those obtained from the TOPSIS method.