Membership function

About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.

PANFIS: A Novel Incremental Learning Machine

Abstract: Most of the dynamics in real-world systems are compiled by shifts and drifts, which are uneasy to be overcome by omnipresent neuro-fuzzy systems. Nonetheless, learning in nonstationary environment entails a system owning high degree of flexibility capable of assembling its rule base autonomously according to the degree of nonlinearity contained in the system. In practice, the rule growing and pruning are carried out merely benefiting from a small snapshot of the complete training data to truncate the computational load and memory demand to the low level. An exposure of a novel algorithm, namely parsimonious network based on fuzzy inference system (PANFIS), is to this end presented herein. PANFIS can commence its learning process from scratch with an empty rule base. The fuzzy rules can be stitched up and expelled by virtue of statistical contributions of the fuzzy rules and injected datum afterward. Identical fuzzy sets may be alluded and blended to be one fuzzy set as a pursuit of a transparent rule base escalating human's interpretability. The learning and modeling performances of the proposed PANFIS are numerically validated using several benchmark problems from real-world or synthetic datasets. The validation includes comparisons with state-of-the-art evolving neuro-fuzzy methods and showcases that our new method can compete and in some cases even outperform these approaches in terms of predictive fidelity and model complexity.

Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm

Abstract: Archimedean t-conorm and t-norm are generalizations of a lot of other t-conorms and t-norms, such as Algebraic, Einstein, Hamacher and Frank t-conorms and t-norms or others, and some of them have been applied to intuitionistic fuzzy set, which contains three functions: the membership function, the non-membership function and the hesitancy function describing uncertainty and fuzziness more objectively. Recently, Beliakov et al. [3] constructed some operations about intuitionistic fuzzy sets based on Archimedean t-conorm and t-norm, from which an aggregation principle is proposed for intuitionistic fuzzy information. In this paper, we propose some other operations on intuitionistic fuzzy sets, study their properties and relationships, and based on which, we study the properties of the aggregation principle proposed by Beliakov et al. [3], and give some specific intuitionistic fuzzy aggregation operators, which can be considered as the extensions of the known ones. In the end, we develop an approach for multi-criteria decision making under intuitionistic fuzzy environment, and illustrate an example to show the behavior of the proposed operators.

Fuzzy sets and probability: misunderstandings, bridges and gaps

Abstract: One of the most controversial issues in uncertainty modeling and information sciences is the relationship between probability theory and fuzzy sets The literature pertaining to this debate is surveyed The authors address some classical misunderstandings between fuzzy sets and probabilities They consider probabilistic interpretations of membership functions that may help in membership function assessment Nonprobabilistic interpretations of fuzzy sets are identified The literature on possibility-probability transformations is examined, and some lurking controversies on that topic are clarified Several subfields of fuzzy set research where fuzzy sets and probability are conjointly used are discussed >

A Linguistic Approach to Decisionmaking with Fuzzy Sets

Abstract: A technique for making linguistic decsions is presented. Fuzzy sets are assued to be an appropriate way of dealng with uncertainty, and it b therefore cncluded that decisions taken on the basis of such infomation must themselves be fuzzy. It b inappriate then to present the decision in numencal form; a statement in natural angug is much better. For brevity only a single-stage multlabute decsion problem is considered. Solutions to such problems are shown using ideas in linguisc approximation and truth qualiction. An extensive example illuminates the basic ideas and techniques.

Generalized hesitant fuzzy sets and their application in decision support system

Abstract: Hesitant fuzzy sets are very useful to deal with group decision making problems when experts have a hesitation among several possible memberships for an element to a set. During the evaluating process in practice, however, these possible memberships may be not only crisp values in [0,1], but also interval values. In this study, we extend hesitant fuzzy sets by intuitionistic fuzzy sets and refer to them as generalized hesitant fuzzy sets. Zadeh's fuzzy sets, intuitionistic fuzzy sets and hesitant fuzzy sets are special cases of the new fuzzy sets. We redefine some basic operations of generalized hesitant fuzzy sets, which are consistent with those of hesitant fuzzy sets. Some arithmetic operations and relationships among them are discussed as well. We further introduce the comparison law to distinguish two generalized hesitant fuzzy sets according to score function and consistency function. Besides, the proposed extension principle enables decision makers to employ aggregation operators of intuitionistic fuzzy sets to aggregate a set of generalized hesitant fuzzy sets for decision making. The rationality of applying the proposed techniques is clarified by a practical example. At last, the proposed techniques are devoted to a decision support system.