Integrated Fuzzy Analysis and Group Decision Making Method for Collaborative Product Development

Group decision-making is one of the most important issues in product development. In order to tackle the vague and sometimes conflicting decision data, this paper presents a new approach based on fuzzy similarity and fuzzy compromise to deal with the fuzzy nature of group decisions. In the proposed method, a modified fuzzy Analytical Hierarchy Process method is used to get the criterion weights, a novel consensus aggregation algorithm is given to obtain the conflict-free results, and an improved compromise decision means is utilized to calculate the utilities of alternatives. Finally an integrated product development solution evaluation process is illustrated as a numerical example, and the corresponding software package is also developed. Introduction How to make the “best” decision when choosing from among a set of alternatives in a design process has been a common problem for research and application in product design. While there is not always sufficient information for design decisions, especially in the product planning and concept stages, the acquired information is often imprecise, incomplete and uncertain. In addition, the criteria for a decision are not always quantifiable or comparable, criteria may directly conflict or interact with one another, and multiple functional groups, each with different perspective and objectives, may all be involved in the design decision. So it is desirable to have an efficient approach capable of properly handling the multidimensional nature of the problem and adequately modeling the subjectiveness and imprecision of decision-making process. Many methods and tools have been used to aid decision-making in product development. But the traditional techniques [1][2] were likely to use quantitative methods, such as optimal techniques, mathematical programming and utility models etc, which neglect the human behavior and only can be applied to the case if the required data are sufficient. Some researches have been concerned with multi-attribute decision in design under uncertain conditions. Pugh's concept selection methods were extended with fuzzy set theory to measure the quality of a chosen concept[3]. Wang[4] used fuzzy distance measure method for ranking fuzzy number of design concept. Lin [5] applied linguistic approximation and fuzzy arithmetic operations to aid new product go/no-go decisions. A novel method of operating on fuzzy numbers to obtain a fuzzy-weighted average of desirability levels during design evaluation was proposed in [6]. These methods still can’t adequately tackle the uncertainty and vagueness of the proposed decision problem, especially from the view of group consensus. This paper presents a new approach based on fuzzy similarity and compromise decision to deal with the fuzzy nature of group decisions. The mathematical model and some preliminaries The design decision problem mentioned in this research can be modeled as a multi-person multi-criteria decision making (MCDM) problem. In traditional MCDM, performance rating and weights are measured in crisp numbers. The application of fuzzy set theory to MCDM provides an Advanced Materials Research Online: 2008-06-12 ISSN: 1662-8985, Vols. 44-46, pp 267-274 doi:10.4028/www.scientific.net/AMR.44-46.267 © 2008 Trans Tech Publications, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (#69819061, Pennsylvania State University, University Park, USA-18/09/16,21:15:23) effective means of formulating decision problems in the environment where the information available is subjective and imprecise. Various methods such as Fuzzy TOPSIS [9], Compromise programming [10], Fuzzy preference [11] were proposed. They can be classified into two categories of defuzzification and fuzzy preference relation. But most of the work hasn’t adequately considered the multi DM effects of this problem. Usually, the aggregation is calculated based on simple weighted average means that can’t represent the consensus of DMs well. While on the other hand, other researches tried to draw consensus from opinions of experts [12]. Hsu [13] proposed a method called similarity aggregation method (SAM) to aggregate individual opinions of experts based on measure near degree. Lee [14] presented a complex optimal aggregation method (OAM). Lo [15] proposed an Entropy method based on OAM. But they all have some limitations. In our view, transferring individual fuzzy opinions into a group consensus and aggregating weighted criterion fuzzy numbers are the two most important issues closely interrelated in group decision making, while most of the researches only consider one aspect of it. So we propose an integrated method for group decision support in product design environment. The general group decision making problem usually consists of a number of alternatives Ai(i = 1, 2, ..., n) to be evaluated against a set of criteria Cj (j = 1, 2, ... , m) by a group of DMs Dk (k=1,2, ..., s). Subjective assessments are often required for determining the performance of each alternative Ai (i = 1, 2, ..., n) with respect to each criterion Cj (j = 1, 2, ... , m), denoted as k ij A ~ , and the relative importance of each criterion, represented as wj, with respect to the overall objective of the problem. As a result, a decision matrix for the group decision-making problem can be obtained as: