Fuzzy number

About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.

Fuzzy Interpolation and Extrapolation: A Practical Approach

Abstract: Fuzzy interpolation does not only help to reduce the complexity of fuzzy models, but also makes inference in sparse rule-based systems possible. It has been successfully applied to systems control, but limited work exists for its applications to tasks like prediction and classification. Almost all fuzzy interpolation techniques in the literature make strong assumptions that there are two closest adjacent rules available to the observation, and that such rules must flank the observation for each attribute. Also, some interpolation approaches cannot handle fuzzy sets whose membership functions involve vertical slopes. To avoid such limitations and develop a more practical approach, this paper extends the work of Huang and Shen. The result enables both interpolation and extrapolation which involve multiple fuzzy rules, with each rule consisting of multiple antecedents. Two realistic applications, namely truck backer-upper control and computer activity prediction, are provided in this paper to demonstrate the utility of the extended approach. Experiment-based comparisons to the most commonly used Mamdani fuzzy reasoning mechanism, and to other existing fuzzy interpolation techniques are given to show the significance and potential of this research.

Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment

Abstract: As a generalized fuzzy number, the hesitant fuzzy element (HFE) has been receiving increased attention and has recently become a popular topic. However, we find that the occurring probabilities of the possible values in the HFE are equal, which is obviously impractical. Consequently, in this paper, we propose a hesitant fuzzy number with probabilities, called the hesitant probabilistic fuzzy number, and construct its score function, deviation function, comparison laws, and its basic operations. It is well known that in the context of a group of decision makers (DMs), one of the basic approaches to built consensus is to aggregate individual evaluations or individual priorities. Thus, to use the hesitant fuzzy numbers for consensus building with a group of DMs, we further propose a method called maximizing score deviation method to obtain the DMs’ weights under the HPFE environment, based on which two extended and four new ordered weighted operators are provided to fuse the HPFE information and build the consensus of the DMs. We also analyze the differences among these ordered weighted operators and provide their application scopes. Finally, a practical case is provided to demonstrate consensus building with a group of DMs under the HPFE environment using the proposed approaches.

Criticality Assessment Models for Failure Mode Effects and Criticality Analysis Using Fuzzy Logic

Abstract: Traditional Failure Mode and Effects Analysis (FMEA) has shown its effectiveness in defining, identifying, and eliminating known and/or potential failures or problems in products, process, designs, and services to help ensure the safety and reliability of systems applied in a wide range of industries. However, its approach to prioritize failure modes through a crisp risk priority number (RPN) has been highly controversial. This paper proposes two models for prioritizing failures modes, specifically intended to overcome such limitations of traditional FMEA. The first proposed model treats the three risk factors as fuzzy linguistic variables, and employs alpha level sets to provide a fuzzy RPN. The second model employs an approach based on the degree of match and fuzzy rule-base. This second model considers the diversity and uncertainty in the opinions of FMEA team members, and converts the assessed information into a convex normalized fuzzy number. The degree of match (DM) is used thereafter to estimate the matching between the assessed information and the fuzzy number characterizing the linguistic terms. The proposed models are suitably supplemented by illustrative examples.

Research on the multi-attribute decision-making under risk with interval probability based on prospect theory and the uncertain linguistic variables

Abstract: With respect to risk decision making problems with interval probability in which the attribute values take the form of the uncertain linguistic variables, a multi-attribute decision making method based on prospect theory is proposed To begin with, the uncertain linguistic variables can be transformed into the trapezoidal fuzzy number, and the prospect value function of the trapezoidal fuzzy number based on the decision-making reference point of each attribute and the weight function of interval probability can be constructed; then the prospect value of attribute for every alternative is calculated through prospect value function of the trapezoidal fuzzy number and the weight function of interval probability, and the weighted prospect value of alternative is acquired by using weighted average method according to attribute weights, and all the alternatives are sorted according to the expected values of the weighted prospect values; Finally, an illustrate example is given to show the decision-making steps, the influence on decision making for different parameters of value function and different decision-making reference point, and the feasibility of the method