Fuzzy Opinion Research Articles

Two new approaches for assessing the weights of fuzzy opinions in group decision analysis

The aggregation of fuzzy opinions is an important component of group decision analysis with fuzzy information. This paper proposes two new approaches for the assessment of the weights to be associated with fuzzy opinions. These approaches involve, respectively, the minimization of the sum of squared distances from one weighted fuzzy opinion to another, which is called the least squares distance method (LSDM), and the minimization of the sum of squared differences between the defuzzified values of any two weighted fuzzy opinions, which is called the defuzzification-based least squares method (DLSM). The two approaches are developed and numerical examples are presented to illustrate their simplicity and effectiveness in aggregating fuzzy opinions.

A new fuzzy multiple attributive group decision making methodology and its application to propulsion/manoeuvring system selection problem

In this paper, a new fuzzy multiple attribute decision-making (FMADM) method, which is suitable for multiple attributive group decision making (GDM) problems in fuzzy environment, is proposed to deal with the problem of ranking and selection of alternatives. Since the subjectivity, imprecision and vagueness in the estimates of a performance rating enter into multiple attribute decision-making (MADM) problems, fuzzy set theory provides a mathematical framework for modelling vagueness and imprecision. In the proposed approach, an attribute based aggregation technique for heterogeneous group of experts is employed and used for dealing with fuzzy opinion aggregation for the subjective attributes of the decision problem. The propulsion/manoeuvring system selection as a real case study is used to demonstrate the versatility and potential of the proposed method for solving fuzzy multiple attributive group decision-making problems. The proposed method is a generalised model, which can be applied to great variety of practical problems encountered in the naval architecture from propulsion/manoeuvring system selection to warship requirements definition.

An integrated multi-objective optimisation and fuzzy multi-attributive group decision-making technique for subdivision arrangement of Ro–Ro vessels

This paper focuses on developing a new multiple criteria decision-making (MCDM) methodology for subdivision arrangement of Ro–Ro vessels, which integrates the multi-objective optimisation with a fuzzy multi-attributive group decision-making (FMAGDM) technique. The study concentrates on the task of finding and then evaluating (or ranking) the finite number of pareto-optimal design alternatives (PODAs). A genetic algorithm based multi-objective optimisation technique, namely MOGA, is employed for optimisation purpose in terms of chosen design parameters such as damage stability, survivability, and cargo capacity. MOGA is the methodology where the solution space is searched for a set of PODAs, from which experts can express their opinions and choose the best PODA. The subjectiveness and imprecision of the ranking process is modelled as linear trapezoidal fuzzy numbers by means of linguistic terms. An attribute based aggregation technique for homogeneous and heterogeneous groups of experts is employed and used for dealing with the fuzzy opinion aggregation. Finally, a real case study on the subdivision arrangement of a Ro–Ro vessel is conducted to illustrate the effectiveness of the approach.

Integrated Multiple Attributive Decision Support System for Producibility Evaluation in Ship Design

Ship design today can be viewed as an ad hoc process. It must be considered in the context of integration with other design development activities, such as production, costing, quality control, and so forth. Otherwise, it is possible for the designer to design a ship that is difficult to produce, requires high material or labor cost, or contains some design flaws that the production engineers have to correct or send back for redesigning before production can be done. Any adjustment required after the design stage will result in a penalty of extra time or cost. Deficiencies in the design of a ship will influence the succeeding stages of production. In addition to designing a ship that fulfills producibility requirements, it is also desirable to design a ship that satisfies risk, performance, cost, and customer requirements criteria. More recently, environmental concerns, safety, passenger comfort, and life-cycle issues are becoming essential parts of the current shipbuilding industry. Therefore, "design for X paradigm" should also be considered during the ship design stages. An integrated multiple attributive decision support system for producibility evaluation in ship design (PRODEVIS) is developed to use by industry and researchers in evaluating the producibility of competing ship designs and design features during the early stages of ship design by taking into account cost, performance, risk, and "design for X paradigm" attributes. This developed approach is a fuzzy multiple attributive group decision-making methodology where feasible design alternatives are conducted by a ship production simulation technique. In this approach, an attribute-based aggregation technique for a heterogeneous group of experts is employed and used for dealing with fuzzy opinion aggregation for the subjective attributes of the ship design evaluation problem. The developed methodology is illustrated with a case study.

AGGREGATING FUZZY OPINIONS IN THE GROUP DECISION-MAKING ENVIRONMENT

This paper presents a new method for dealing with fuzzy opinion aggregation in group decision-making problems. The proposed method has the following advantages: 1 The experts' estimates do not necessarily have a common intersection at alpha -level cuts, where alpha 0,1 . 2 It can perform fuzzy opinion aggregation in a more efficient manner. 3 It does not need to use the Delphi method to adjust trapezoidal fuzzy numbers given by experts.

Arrow's theorem under fuzzy rationality

This paper deals with living systems at the individual and group levels. In particular, fuzzy set theory is applied to study Arrow's paradox in aggregation preference problems: such impossibility theorems are based on using the Aristotelian logic; thus Lukasievicz's censure to sciences founded on that logic is also fully applicable. In this paper we deal with “rationality” as a fuzzy property, by suggesting a definition of “fuzzy opinion” different from the classical fuzzy preference relation. Whenever this definition is applied, Arrow's theorems are deemed as results about the impossibility of complete rationality. Nevertheless, the possibility of proving the existence of rules with non-complete irrationality is revealed.