A sequential three-way decision model based on hesitant fuzzy sets

As a new extended model of fuzzy sets, hesitant fuzzy set theory is a useful tool to process uncertain information in decision making problems. The traditional hesitant fuzzy multi-attribute decision making (MADM) can only choose an optimal strategy, which is not suitable for all of the complex scenarios. Typically, in practical application, decision making problems may be more complicated involving three options of acceptance, non-commitment and rejection decisions. Three-way decisions, which divide universe into three disjoint regions by a pair of thresholds, are more efficient to deal with these problems. Therefore, how to utilize three-way decision theory to process hesitant fuzzy information is an essential issue to be studied. In this paper, from the perspective of hesitant fuzzy distance, a hesitant fuzzy three-way decision model is proposed. First, because hesitant fuzzy element (HFE) is a set of several possible membership degrees, it cannot be compared with thresholds directly. Hence, this paper converts it into the comparison between the distance and the thresholds. Then, to calculate thresholds more reasonably, shadowed set theory is introduced to avoid the subjectivity of threshold acquisition. Furthermore, sequential strategy is adopted to solve the multi-attribute decision making problems. Finally, an example of medical diagnosis and simulation experiments are given to prove the accuracy and efficiency of the proposed hesitant fuzzy three-way decision model.

An Extended VIKOR Method Based on q-Rung Orthopair Shadowed Set and Its Application to Multi-Attribute Decision Making

In the multi-attribute decision making (MADM) process, the attribute values are sometimes provided by experts or the public in the form of words. To model the linguistic evaluation more accurately, this paper proposes the q-rung orthopair shadowed set (q-ROSS) to represent attribute values and extends the VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje) method to solve MADM problems in the q-ROSS context. First, we propose the q-ROSS to express evaluation information. Some basic operation rules and distance measures are investigated accordingly. When the amount of data is large, the left and right endpoints of the collected interval numbers will obey symmetric normal distribution. Secondly, based on the normal distribution assumption, the collected data intervals are mapped to shadowed sets through a data processing approach. Furthermore, we extend the VIKOR model to tackle the MADM problem where the evaluation values are expressed by q-rung orthopair shadowed numbers. A location selection problem verifies the practicability of our method, and the effectiveness and superiority of the presented approach are reflected through comparative analysis.

Shadowed Sets-Based Linguistic Term Modeling and Its Application in Multi-Attribute Decision-Making

For many multi-attribute decision-making (MADM) problems, linguistic variables are more convenient for people to express the attribute values. In this paper, a novel shadowed set-based method is proposed to deal with linguistic terms, where the linguistic term sets are symmetrical both in meaning and form. Firstly, to effectively express the linguistic variables, we develop a data-driven method to construct the shadowed set model for the linguistic terms. Secondly, the Pythagorean shadowed set is defined, and some theorems are subsequently explored. Thirdly, we propose the score function of the Pythagorean shadowed number and develop a new MADM method on the basis of the Pythagorean shadowed set. Finally, a case study of the supplier selection problem is provided to illustrate the effectiveness of the proposed method, and the superiority of our method is demonstrated by comparison analysis.

Application of Fuzzy Sets and Shadowed Sets in Predicting Time Series Data

In recent years, several methods for forecasting fuzzy time series have been presented in different areas, such as stock price, student enrollments, climatology, production sector, etc. Choice of data partitioning technique is a central factor and it highly influences the forecast accuracy. In all existing works on fuzzy time series model, cluster with highest membership is used to form fuzzy logical relationships. But the position of the element within the cluster is not considered. The present study incorporates the idea of fuzzy discretization and shadowed set theory in defining intervals and uses the positional information of elements within a cluster in selection of rules for decision making. The objective of this work is to show the effect of the elements, lying outside the core area on forecast. Performance of the presented model is evaluated on standard datasets.