GFUZ : An interactive program for solving a multicriteria decision making problem

In this paper, an interactive approach for dealing with a linear programing model under multiple and conflicting objectives is presented. The technique used can be regarded as fuzzy mathematical programming. A compromise solution is determined by eliciting from a single decision maker, a curve of preference for given aspiration levels of the objectives involved. Software was developed for a personal computer and can be helpful in providing support to practitioners utilizing mathematical modelling to justify their decisions.     

knowCube: a visual and interactive support for multicriteria decision making

In this paper, we present a novel multicriteria decision support system (MCDSS), called knowCube, consisting of components for knowledge organization, generation, and navigation. Knowledge organization rests upon a database for managing qualitative and quantitative criteria, together with add-on information. Knowledge generation serves filling the database via, e.g. identification, optimization, classification or simulation. For “finding needles in haycocks”, the knowledge navigation component supports graphical database retrieval and interactive, goal-oriented problem solving. Navigation “helpers” are, for instance, cascading criteria aggregations, modifiable metrics, ergonomic interfaces, and customizable visualizations. Examples from real-life projects, e.g. in industrial engineering and in the life sciences, illustrate the application of our MCDSS.     

An interactive rectangle elimination method for biobjective decision making

This paper presents a new man-machine interactive method for biobjective decision making. It is specifically designed to cope with both the ill-defined nature of the decision problem and the high cost of computation points in the tradeoff (Pareto optimal) set. With this method, the decision maker may efficiently approximate the tradeoff set and/or estimate his preferred objective value. First, the notion of a rectangle representation of the tradeoff set by a set of points, called experiments, and a set of rectangles, defined by the experiments, is introduced. Next, a special class of decision makers is considered. For a decision maker in this special class, the rectangle representation of the tradeoff set defines a rectangle of uncertainty that contains the decision maker's preferred objective value. A measure of the worst ease uncertainity is formulated and minimized to yield an optimal strategy for interactively selecting experiments. Finally, this strategy is employed in a general interactive algorithm that works under minimal assumptions on the tradeoff set and on the decision maker.     

An interactive method for fuzzy multiple attribute group decision making

In this paper, we develop an interactive method for multiple attribute group decision making under fuzzy environment. The method can be used in situations where the information about attribute weights is partly known, the weights of decision makers are expressed in exact numerical values or triangular fuzzy numbers, and the attribute values are triangular fuzzy numbers. The method transforms fuzzy decision matrices into their expected decision matrices, constructs the corresponding normalized expected decision matrices by two simple formulas, and then aggregates these normalized expected decision matrices into a complex decision matrix. Moreover, the decision makers are asked to provide their preferences gradually in the course of interactions. By solving linear programming models, the method diminishes the given alternative set gradually, and finally finds the most preferred alternative. By using the method, the decision makers can provide and modify their preference information gradually in the process of decision making so as to make the decision result more reasonable. The method can not only reflect the importance of the given arguments and the ordered positions of the arguments, but also relieve the influence of unfair arguments on the decision result. Finally, a practical problem is used to illustrate the developed method.     

An interactive method for dynamic intuitionistic fuzzy multi-attribute group decision making

This paper investigates the dynamic intuitionistic fuzzy multi-attribute group decision making (DIF-MAGDM) problems, in which all the attribute values provided by multiple decision makers (DMs) at different periods take the form of intuitionistic fuzzy numbers (IFNs), and develops an interactive method to solve the DIF-MAGDM problems. The developed method first aggregates the individual intuitionistic fuzzy decision matrices at different periods into an individual collective intuitionistic fuzzy decision matrix for each decision maker by using the dynamic intuitionistic fuzzy weighted averaging (DIFWA) operator, and then employs intuitionistic fuzzy TOPSIS method to calculate the individual relative closeness coefficient of each alternative for each decision maker and obtain the individual ranking of alternatives. After doing so, the method utilizes the hybrid weighted averaging (HWA) operator to aggregate all the individual relative closeness coefficients into the collective relative closeness coefficient of each alternative and obtain the aggregate ranking of alternatives, by which the optimal alternative can be selected. In addition, the spearman correlation coefficient for both the aggregate ranking and individual ranking of alternatives is calculated to measure the consensus level of the group preferences. Finally, a numerical example is used to illustrate the developed method.     

An interactive computerized algorithm for multicriteria vehicle routing problems

The Multicriteria vehicle routing problem (VRP) is a VRP which allows several relevant objectives to be achieved. The use of an interactive computer program combined with a powerful vehicle routing algorithm can be a valuable tool in the hands of a scheduler who can apply his own skills and knowledge to full effect in conjunction with the speed and flexibility of the computer program.

An interactive computerized algorithm is developed that utilizes a heuristic algorithm to determine the most favorable vehicle routes for multicriteria VRPs. This algorithm takes into account that the problem being addressed may in fact be complicated by several conflicting objectives. Although many different objectives could be considered, the specific model presented here consists of the following three relevant objectives: minimization of the travel distance of vehicles, minimization of total deterioration of goods during transportation, and maximization of the total fulfillment of emergent services and conditional dependencies of stations.

The interactive algorithm successfully performs the trade-off between the achievement levels of the objectives through changes of the decision maker's goal priority structure, the target values of the objectives, and the subsets formation of stations.     

Consensus-based decision support for multicriteria group decision making

Consensus decision making is complex and challenging in multicriteria group decision making due to the involvement of several decision makers, the presence of multiple, and often conflicting criteria, and the existence of subjectiveness and imprecision in the decision making process. To ensure effective decisions being made, the interest of all the decision makers usually represented by the degree of consensus in the decision making process has to be adequately considered. This paper presents a consensus-based approach for effectively solving the multicriteria group decision making problem. The subjectiveness and imprecision of the decision making process is adequately handled by using intuitionistic fuzzy numbers. An interactive algorithm is developed for consensus building in the group decision making process. A decision support system framework is presented for improving the effectiveness of the consensus building process. An example is presented for demonstrating the applicability of the proposed approach for solving the multicriteria group decision making problem in real world situations.     

An interactive system for supporting multiobjective decision making

The purpose of this paper is to develop an interactive system for supporting the decision making process under multiple objectives and to empirically evaluate its performance. An interactive algorithm underlying the system is proposed with emphasis on the psychological aspects of the decision maker (DM). A choice process model is developed, based on pairwise comparison judgments of alternatives, because the judgments are basic and easy for a DM. A corresponding interactive algorithm is implemented and compared with other existing algorithms. Two kinds of comparative experiments, numerical and subject experiments, are conducted to verify the validity of the choice model as well as the practical effectiveness and the convergence of the algorithm.     

Modeling prioritized multicriteria decision making

We consider the problem of multicriteria decision making (MCDM) in the situation in which there exists a prioritization of criteria. A good example of prioritization among criteria occurs in the case of air travel, where concerns about passenger safety have a higher priority then economic concerns. Tradeoffs between saving on gasoline usage and jeopardizing passenger safety are unacceptable. We show how this prioritization of criteria can be modeled by using importance weights in which the weights associated with the lower priority criteria are related to the satisfaction of the higher priority criteria. We provide some models that allow for the formalization of these prioritized MCDM problems using both the Bellman-Zadeh paradigm for MCDM and the ordered weighted averaging (OWA) operator method.     

A new method selection approach for fuzzy group multicriteria decision making

Fuzzy multicriteria decision making (MCDM) has been widely used in ranking a finite number of decision alternatives characterized by fuzzy assessments with respect to multiple criteria. In group decision settings, different fuzzy group MCDM methods often produce inconsistent ranking outcomes for the same problem. To address the ranking inconsistency problem in fuzzy group MCDM, this paper develops a new method selection approach for selecting a fuzzy group MCDM method that produces the most preferred group ranking outcome for a given problem. Based on two group averaging methods, three aggregation procedures and three defuzzification methods, 18 fuzzy group MCDM methods are developed as an illustration to solve the general fuzzy MCDM problem that requires cardinal ranking of the decision alternatives. The approach selects the group ranking outcome of a fuzzy MCDM method which has the highest consistency degree with its corresponding ranking outcomes of individual decision makers. An empirical study on the green bus fuel technology selection problem is used to illustrate how the approach works. The approach is applicable to large-scale group multicriteria decision problems where inconsistent ranking outcomes often exist between different fuzzy MCDM methods.     

An interactive evolutionary multi-objective optimization and decision making procedure

With the advent of efficient techniques for multi-objective evolutionary optimization (EMO), real-world search and optimization problems are being increasingly solved for multiple conflicting objectives. During the past decade of research and application, most emphasis has been spent on finding the complete Pareto-optimal set, although EMO researchers were always aware of the importance of procedures which would help choose one particular solution from the Pareto-optimal set for implementation. This is also one of the main issues on which the classical and EMO philosophies are divided on. In this paper, we address this long-standing issue and suggest an interactive EMO procedure which will involve a decision-maker in the evolutionary optimization process and help choose a single solution at the end. This study uses many year’s of research on EMO and would hopefully encourage both practitioners and researchers to pay more attention in viewing the multi-objective optimization as a aggregate task of optimization and decision-making.     

An interactive computer system for multicriteria facility location

A computer system developed to assist a decision maker in finding his most preferred efficient solution to a multicriteria location model is described. The system requires interaction between the decision maker and optimization software to conduct a heuristic search of the set of efficient solutions to the location model. A command language developed to give the user control over the system and an optimization algorithm developed for finding efficient solutions are presented.     

A flexible consensus scheme for multicriteria group decision making under linguistic assessments

The present paper proposes a flexible consensus scheme for group decision making, which allows one to obtain a consistent collective opinion, from information provided by each expert in terms of multigranular fuzzy estimates. It is based on a linguistic hierarchical model with multigranular sets of linguistic terms, and the choice of the most suitable set is a prerogative of each expert. From the human viewpoint, using such model is advantageous, since it permits each expert to utilize linguistic terms that reflect more adequately the level of uncertainty intrinsic to his evaluation. From the operational viewpoint, the advantage of using such model lies in the fact that it allows one to express the linguistic information in a unique domain, without losses of information, during the discussion process.The proposed consensus scheme supposes that the moderator can interfere in the discussion process in different ways. The intervention can be a request to any expert to update his opinion or can be the adjustment of the weight of each expert’s opinion. An optimal adjustment can be achieved through the execution of an optimization procedure that searches for the weights that maximize a corresponding soft consensus index.In order to demonstrate the usefulness of the presented consensus scheme, a technique for multicriteria analysis, based on fuzzy preference relation modeling, is utilized for solving a hypothetical enterprise strategy planning problem, generated with the use of the Balanced Scorecard methodology.     

A fuzzy interactive decision making algorithm for bilevel multi-followers programming with partial shared variables among followers

This paper studies a class of bilevel multi-followers programming in which there are partial shared variables among followers. A fuzzy interactive decision making approach is proposed to derive a satisfactory solution for decision makers not only considering the dominated action of the leader but also treating the ratios of satisfaction between the leader and the followers. Finally, a numerical example is illustrated to demonstrate the feasibility of the proposed approach.     

A CHIM-based interactive Tchebycheff procedure for multiple objective decision making

This study presents a new solution procedure for multiple objective programming (MOP). It applies the concept of the normal boundary intersection (NBI) within the framework of the interactive weighted Tchebycheff procedure (IWTP). The proposed procedure is a collaborative approach to overcome the weak points inherent in both the NBI method and IWTP. In order to control the solution procedure of pinpointing a final solution properly, we parameterized the Pareto-frontier via a set of reference point vectors based on the convex hull of individual maxima (CHIM) instead of using the varying weights of each objective. Using well-distributed reference point vectors, we could identify well-distributed Pareto-optimal solutions, thereby eliminating the IWTP filtering stages and reducing the chance of missing the best compromise solution from the decision maker (DM)'s utility point of view. Moreover, by working with a sequence of progressively smaller subsets of reference point vectors, the DM can identify a final solution at earlier stages than with the IWTP.     

Impersonate human decision making process: an interactive context-aware recommender system

A considerable amount of information is quickly disseminated worldwide and users struggled to survive on such data tsunami. Context-recommender-aware systems (CAR) are then developed which enabling users to locate valuable and useful information from a large amount of disordered data. However, human decision-making contains multiple steps and a recursive loop, most users tend to adjust their decision many times instead of achieving the final decision-making immediately. Therefore, to replicate such a recursive process among multiple steps, the traditional CAR system should be altered as an interactive CAR (iCAR) system for improving the recommendation accuracy. In view of the deficiency in the present CAR, this study leads the concept of human-computer interaction in tradition CAR and establishes an interactive context-aware recommender System (iCAR). To validate the feasibility and applicability of the proposed iCAR system, a car rental website which is designed based on iCAR is shown as a demonstration. According to the car rental case shown, after couples of iterations, the decision criteria can be gradually clarified by the proposed algorithm of inferring engine. Also, iCAR can find users a car that most satisfies their requirements by using the contexts information. iCAR can improve the accuracy of traditional CAR system and provide user more precise recommendation results according to 3-dimensions information, including: user, item and context information. The iCAR system can be further expected to apply to various fields, such as online shopping or travel packages recommendations, to optimize recommendations results.     

Optimization and extensions of a fuzzy multicriteria decision making method and applications to selection of touristic destinations

The aim of the present paper is to optimize and extend the recent method in Chu and Lin (2009). We simplify the calculus taking into account the expected value of a fuzzy number can be expressed by using its α-cut sets. A collateral benefit is that the discussed method becomes applicable in any structure of data as triangular fuzzy numbers. Then, to cover a wider range of data - performances of alternatives versus criteria and importance weights of criteria - we extend the optimized method to trapezoidal fuzzy numbers and to the cases of importance weights of criteria/ratings of alternatives expressed by real numbers and ratings of alternatives/importance weights of criteria expressed by fuzzy numbers. Each theoretical development is illustrated by examples. The importance of the method to the selection of the best touristic destinations is discussed too.     

A novel soft rough set: Soft rough hemirings and corresponding multicriteria group decision making

In this paper, we investigate the relationships among rough sets, soft sets and hemirings. The concept of soft rough hemirings is introduced, which is an extended notion of a rough hemiring. It is pointed out that in this paper, we first apply soft rough sets to algebraic structure-hemirings. Further, we first put forward the concepts of C-soft sets and CC-soft sets, which provide a new research idea for soft rough algebraic research. Moreover, we study roughness in hemirings with respect to MSR-approximation spaces. Some new soft rough operations over hemirings are explored. In particular, lower and upper MSR-hemirings (k-ideal and h-ideal) are investigated. Finally, we put forth an approach for multicriteria group decision making problem based on modified soft rough sets and offer an actual example.     

An interactive case-based reasoning method considering proximity from the cut-off point

Case-based reasoning (CBR) models often solve problems by retrieving multiple previous cases and integrating those results. However, conventional CBR makes decisions by comparing the integrated result with the cut-off point irrespective of the degree of the adjacency between them. This can cause increasing misclassification error for the target cases adjacent to the cut-off point, since the results of previous cases used to produce those results are relatively inconsistent with each other. In this article, we suggest a new interactive CBR model called grey-zone case-based reasoning (GCBR) that makes decisions focusing additional attention on the cases near the cut-off point by interactive communication with users. GCBR classifies results automatically for the cases placed outside the cut-off point boundary area. On the other hand, it communicates with users to make decision for the cases placed inside the area by verifying characteristics of the dataset. We suggest the architecture of GCBR and implement its prototype.     

A parallel algorithm for real-time decision making: A rough set approach

We consider decision tables with the values of conditional attributes (conditions) measured by sensors. These sensors produce outputs after an unknown but finite number of time units. We construct an algorithm for computing a highly parallel program represented by a Petri net from a given decision table. The constructed net allows to identify objects in decision tables to an extent which makes appropriate decisions possible. The outputs from sensors are propagated through the net with maximal speed. This is done by an appropriate implementation of all rules true in a given decision table. Our approach is based on rough set theory (Pawlak, 1991). It also seems to have some significance for theoretical foundations of real-time systems.