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Fuzzy number
About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.
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TL;DR: This paper proposes dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy Sets, hesitant fuzzy set, and fuzzy multisets as special cases, and investigates the basic operations and properties of DHFSs.
Abstract: In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type 𝑛 fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Then we investigate the basic operations and properties of DHFSs. We also discuss the relationships among the sets mentioned above, use a notion of nested interval to reflect their common ground, then propose an extension principle of DHFSs. Additionally, we give an example to illustrate the application of DHFSs in group forecasting.
540 citations
04 May 1998
TL;DR: A robust fuzzy logic system is introduced, one that can handle rule uncertainties and make use of type-2 fuzzy sets for this purpose, and a new operation that is called type-reduction is introduced.
Abstract: This paper introduces a robust fuzzy logic system, one that can handle rule uncertainties. We make use of type-2 fuzzy sets for this purpose. The development of a type-2 fuzzy logic system has led to a new operation that we call type-reduction. In the course of this development, we also study set operations on type-2 sets, properties of membership grades of type-2 sets, type-2 relations and their compositions, and defuzzification.
540 citations
TL;DR: F fuzzy risk priority numbers (FRPNs) are proposed for prioritization of failure modes, defined as fuzzy weighted geometric means of the fuzzy ratings for O, S and D, and can be computed using alpha-level sets and linear programming models.
Abstract: Failure mode and effects analysis (FMEA) has been extensively used for examining potential failures in products, processes, designs and services. An important issue of FMEA is the determination of risk priorities of the failure modes that have been identified. The traditional FMEA determines the risk priorities of failure modes using the so-called risk priority numbers (RPNs), which require the risk factors like the occurrence (O), severity (S) and detection (D) of each failure mode to be precisely evaluated. This may not be realistic in real applications. In this paper we treat the risk factors O, S and D as fuzzy variables and evaluate them using fuzzy linguistic terms and fuzzy ratings. As a result, fuzzy risk priority numbers (FRPNs) are proposed for prioritization of failure modes. The FRPNs are defined as fuzzy weighted geometric means of the fuzzy ratings for O, S and D, and can be computed using alpha-level sets and linear programming models. For ranking purpose, the FRPNs are defuzzified using centroid defuzzification method, in which a new centroid defuzzification formula based on alpha-level sets is derived. A numerical example is provided to illustrate the potential applications of the proposed fuzzy FMEA and the detailed computational process of the FRPNs.
539 citations
TL;DR: A fuzzy Petri net model (FPN) is presented to represent the fuzzy production rule of a rule-based system in which a fuzzy productionrule describes the fuzzy relation between two propositions and an efficient algorithm is proposed to perform fuzzy reasoning automatically.
Abstract: A fuzzy Petri net model (FPN) is presented to represent the fuzzy production rule of a rule-based system in which a fuzzy production rule describes the fuzzy relation between two propositions. Based on the fuzzy Petri net model, an efficient algorithm is proposed to perform fuzzy reasoning automatically. It can determine whether an antecedent-consequence relationship exists from proposition d/sub s/ to proposition d/sub j/, where d/sub s/ not=d/sub j/. If the degree of truth of proposition d/sub s/ is given, then the degrees of truth of proposition d/sub j/ can be evaluated. The formal description of the model and the fuzzy reasoning algorithm are shown in detail. The upper bound of the time complexity of the fuzzy reasoning algorithm is O(nm), where n is the number of places and m is the number of transitions. Its execution time is proportional to the number of nodes in a sprouting tree generated by the algorithm only generates necessary reasoning paths from a starting place to a goal place, it can be executed very efficiently. >
534 citations
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03 Dec 2007TL;DR: The new concepts were introduced by Mendel and Liang allowing the characterization of a type-2 fuzzy set with a superior membership function and an inferior membership function; these two functions can be represented each one by atype-1 fuzzy set membership function.
Abstract: Type-2 fuzzy sets are used for modeling uncertainty and imprecision in a better way. These type-2 fuzzy sets were originally presented by Zadeh in 1975 and are essentially "fuzzy fuzzy" sets where the fuzzy degree of membership is a type-1 fuzzy set. The new concepts were introduced by Mendel and Liang allowing the characterization of a type-2 fuzzy set with a superior membership function and an inferior membership function; these two functions can be represented each one by a type-1 fuzzy set membership function. The interval between these two functions represents the footprint of uncertainty (FOU), which is used to characterize a type-2 fuzzy set.
534 citations