Theory of fuzzy integrals and its applications

Real and Complex Analysis

The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

The necessity of dealing with uncertainty in real world problems has been a long-term research challenge that has originated different methodologies and theories. Fuzzy sets along with their extensions, such as type-2 fuzzy sets, interval-valued fuzzy sets, and Atanassov's intuitionistic fuzzy sets, have provided a wide range of tools that are able to deal with uncertainty in different types of problems. Recently, a new extension of fuzzy sets so-called hesitant fuzzy sets has been introduced to deal with hesitant situations, which were not well managed by the previous tools. Hesitant fuzzy sets have attracted very quickly the attention of many researchers that have proposed diverse extensions, several types of operators to compute with such types of information, and eventually some applications have been developed. Because of such a growth, this paper presents an overview on hesitant fuzzy sets with the aim of providing a clear perspective on the different concepts, tools and trends related to this extension of fuzzy sets.

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Hesitant Fuzzy Sets: State of the Art and Future Directions

Studies in Fuzziness and Soft Computing

Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets

A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress

Despite of several generalizations of fuzzy set theory, the notion of hesitant fuzzy set (HFS), which permits the membership having a set of possible values, is interesting and very useful in modeling real-life problems with anonymity. In this article, we introduce a new score function for ranking hesitant fuzzy elements (HFEs), which are the fundamental units of HFSs. Comparison with the existing score function shows that the proposed method meets all the well-known properties of a ranking measure and has no counterintuitive examples. On the basis of the relationships between the aggregation operators for HFEs, we derive a series of interesting properties of the new score function. Finally, we apply the proposed score function to solve the hesitant fuzzy multiattribute decision-making problems.

A Novel Method of Ranking Hesitant Fuzzy Values for Multiple Attribute Decision-Making Problems

In this study, we extend the hesitant fuzzy set (HFS) to its higher order type and refer to it as the higher order hesitant fuzzy set (HOHFS). HOHFS is the actual extension of HFS that enables us to define the membership of a given element in terms of several possible generalized type of fuzzy sets (G-Type FSs). The rationale behind HOHFS can be seen in the case that the decision makers are not satisfied by providing exact values for the membership degrees and therefore the HFS is not applicable. However, in order to indicate HOHFSs have a good performance in decision making, we first introduce some information measures for HOHFSs and then apply them to multiple attribute decision making with higher order hesitant fuzzy information.

Distance and similarity measures for higher order hesitant fuzzy sets

Ever since fuzzy set has been introduced, several extensions have been established, such as interval-valued fuzzy sets, Atanassov's intuitionistic fuzzy sets, interval-valued Atanassov's intuitionistic fuzzy sets, fuzzy multisets, hesitant fuzzy sets, interval-valued hesitant fuzzy sets, and dual hesitant fuzzy sets. In this contribution, we propose dual interval-valued hesitant fuzzy sets, which encompass fuzzy sets and its aforementioned extensions as special cases. Because of the importance of correlation measure in data analysis, we propose an approach for deriving the correlation coefficient of dual hesitant fuzzy sets, and then extend the approach to the dual interval-valued hesitant fuzzy set theory. We also put forward some formulas to create new correlation coefficients for fuzzy sets and its extensions in a general way. In addition, we give a practical example to illustrate the application of correlation coefficient for dual hesitant fuzzy sets in medical diagnosis.

Bahram Farhadinia

Papers

Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets

A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress

A Novel Method of Ranking Hesitant Fuzzy Values for Multiple Attribute Decision-Making Problems

Distance and similarity measures for higher order hesitant fuzzy sets

Correlation for Dual Hesitant Fuzzy Sets and Dual Interval‐Valued Hesitant Fuzzy Sets