In this paper we propose a new induced ordered weighted averaging (IOWA) operator for expert opinions aggregation, namely, the average-induced OWA (AIOWA) operator. The AIOWA operator defines the order-induced variable as the similarity of each individual expert's opinion with respect to the average opinion of the group, as the average opinion is notably an important piece of information of the group opinion and often used as an approximate estimate of the group opinion with equal weights. The new operator facilitates to capture the distribution characteristics of the opinion data with respect to the consensus and constructs a nonlinear aggregation of individual opinions. Further, we extend the new operator to the situation where the experts' opinions are represented by probability density functions (PDFs). Last, we incorporate the entropy-orness optimization model into the proposed aggregation operator. The new operator makes the aggregation process more flexible in terms of application problems. Two case studies are conducted to show the effectiveness of the proposed operators. The result is promising.

In decision making, a group of experts give opinion on an event say X. There is a need to get a group consensus on X. It is usually not possible to have all experts with the same opinion. Therefore, one needs to fuse different opinions into one opinion (i.e., group opinion). The challenge for this task is the situation that the number of experts is too small, as this situation does not justify the use of the average statistics to come up with a group opinion. This paper addresses this challenge. The main idea of the approach to solve this group decision problem is to consider that the group consensus or opinion is a non-linear function of individual opinions and the non-linear function is further represented by a series of iterations to update the weights in a linear function (i.e., the weighted average of individual opinions). An example is given to illustrate the effectiveness of the approach.

The Likert scale is often used in subjective knowledge management (e.g., assessment and decision making) in enterprise systems. The scales typically have 5, 7, or 9 number of rating bars. A controversial issue is: what would be an optimal number of rating bars (5, 7, or 9) for a particular application problem or for all problems? The study reported in this paper addressed this issue. The study particularly restricted to the number of rating bars being 5, 7, and 9 (denoted as S5, S7, S9), as they are commonly used in practice. A cell phone interface design was taken as a test-bed, and twenty participants were involved in the experiment. A new criterion to evaluate a subjective rating scale was developed first and then the experiment was carried out. The study concluded that S7 is the best among the three scales. The contribution of this paper includes: (1) confirming that different numbers of rating bars in a subjective rating scale can have significant effects on the subjective measurement or assessment and (2) providing a new criterion to evaluate a subjective rating scale.

In this article, we focus on the issues of fuzzy data dependencies. After introducing the notion of semantic equivalence degree, fuzzy functional and multivalued dependencies are defined. A set of sound and complete inference rules, similar to Armstrong's axioms for classic cases, for fuzzy functional dependencies (FFDs) and fuzzy multivalued dependencies (FMVDs) are proposed. The strategies and approaches for compressing fuzzy values by FFDs and FMVDs are investigated. By such processing, the unnecessary elements are eliminated from a fuzzy value and its range is compressed. © 2002 Wiley Periodicals, Inc.

Based on the semantic equivalence degree the formal definitions of fuzzy functional dependencies (FFDs) and fuzzy multivalued dependencies (FMVDs) are first introduced to the fuzzy relational databases, where fuzziness of data appears in attribute values in the form of possibility attributions, as well as resemblance relations in attribute domain elements, called extended possibility-based fuzzy relational databases. A set of inference rules for FFDs and FMVDs is then proposed. It is shown that FFDs and FMVDs are consistent and the inference rules are sound and complete, just as Armstrong's axioms for classic cases. © 2002 Wiley Periodicals, Inc.

Entity-relationship–extended entity-relationship models play a crucial role in the conceptual design of relational databases as well as object-oriented databases. Recently, several approaches have been proposed to enhance object-oriented databases (OODBs) using fuzzy set theory. In this paper, we introduce a fuzzy extended entity-relationship model to cope with imperfect as well as complex objects in the real world at a conceptual level. In particular, we provide the formal approach to mapping a fuzzy extended entity-relationship model to a fuzzy object-oriented database schema. © 2001 John Wiley & Sons, Inc.

Fuzzy conceptual data modeling is concentrated on in this paper. Based on possibility theory, A conceptual data model IFO is extended. Different levels of fuzziness are introduced and the corresponding graphical representations are given. IFO data model is this extended to fuzzy IFO data model, denoted IF/sub 2/O in the paper. Attention is paid to the fuzzification of objects and relationships, specially on that of ISA relationships.

In this paper, we propose notions of equivalence and inclusion of fuzzy data in relational databases for measuring their semantic relationship. The fuzziness of data appears in attribute values in forms of possibility distribution as well as resemblance relations in attribute domain elements. An approach for evaluating semantic measures is presented. With the proposal, one can remove fuzzy data redundancy and define fuzzy functional dependency. © 2000 John Wiley & Sons, Inc.