A Multiple Attribute Decision Making Approach Based on New Similarity Measures of Interval-valued Hesitant Fuzzy Sets

Hesitant fuzzy sets, as an extension of fuzzy sets to deal with uncertainty, have attracted much attention since its introduction, in both theory and application aspects. The present work is focused on the interval-valued hesitant fuzzy sets (IVHFSs) to manage additional uncertainty. Now that distance and similarity as a kind of information measures are essential and important numerical indexes in fuzzy set theory and all their extensions, the present work aims at investigating distance and similarity measures in the IVHFSs and then employing them into multiple attribute decision making application. To begin with, II-type generalized interval-valued hesitant fuzzy distance is firstly introduced in the IVHFS, along with its properties and its relationships with the traditional Hamming-Distance and the Euclidean distance. Afterwards, another interval-valued hesitant fuzzy Lp distance based on Lp metric is proposed and its relationship with the Hausdorff distance is discussed. In addition, different from most of similarity measures with dependent on the corresponding distances, a new similarity measure based on set-theoretic approach for IVHFSs is introduced and its properties are discussed; especially, a relative similarity measure is proposed based on the positive ideal IVHFS and the negative ideal IVHFS. Finally, we describe how the IVHFS and its relative similarity measure can be applied to multiple attribute decision making. A numerical example is then provided to illustrate the effectiveness of the proposed method

Decision making with both diversity supporting and opposing membership information

Online big data provides large amounts of decision information to decision makers, but supporting and opposing information are present simultaneously. Dual hesitant fuzzy sets (DHFSs) are useful models for exactly expressing the membership degree of both supporting and opposing information in decision making. However, the application of DHFSs requires an improved distance measure. This paper aims to improve distance measure models for DHFSs and apply the new distance models to generate a technique for order preference by similarity to an ideal solution (TOPSIS) method for multiple attribute decision making (MADM)

Enhancement of dronogram aid to visual interpretation of target objects via intuitionistic fuzzy hesitant sets

In this paper, we address the hesitant information in enhancement task often caused by differences in image contrast. Enhancement approaches generally use certain filters which generate artifacts or are unable to recover all the objects details in images. Typically, the contrast of an image quantifies a unique ratio between the amounts of black and white through a single pixel. However, contrast is better represented by a group of pix- els. We have proposed a novel image enhancement scheme based on intuitionistic hesi- tant fuzzy sets (IHFSs) for drone images (dronogram) to facilitate better interpretations of target objects. First, a given dronogram is divided into foreground and background areas based on an estimated threshold from which the proposed model measures the amount of black/white intensity levels. Next, we fuzzify both of them and determine the hesitant score indicated by the distance between the two areas for each point in the fuzzy plane. Finally, a hyperbolic operator is adopted for each membership grade to improve the pho- tographic quality leading to enhanced results via defuzzification. The proposed method is tested on a large drone image database. Results demonstrate better contrast enhancement, improved visual quality, and better recognition compared to the state-of-the-art methods.Web of Science500866

Multiple-Attribute Decision-Making Method Using Similarity Measures of Hesitant Linguistic Neutrosophic Numbers Regarding Least Common Multiple Cardinality

Linguistic neutrosophic numbers (LNNs) are a powerful tool for describing fuzzy information with three independent linguistic variables (LVs), which express the degrees of truth, uncertainty, and falsity, respectively. However, existing LNNs cannot depict the hesitancy of the decision-maker (DM). To solve this issue, this paper first defines a hesitant linguistic neutrosophic number (HLNN), which consists of a few LNNs regarding an evaluated object due to DMs’ hesitancy to represent their hesitant and uncertain information in the decision-making process. Then, based on the least common multiple cardinality (LCMC), we present generalized distance and similarity measures of HLNNs, and then develop a similarity measure-based multiple-attribute decision-making (MADM) method to handle the MADM problem in the HLNN setting. Finally, the feasibility of the proposed approach is verified by an investment decision case

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches