Vague multi-attribute group decision-making method based on evidence theory with a new aspect to solve weights

In order to solve the problems of weight solving and information aggregation in the Vague multi-attribute group decision-making, this paper first solves the weight of Vague evaluation value, and then fuses the information of Vague sets through evidence theory, and obtains an information aggregation algorithm for Vague multi-attribute group decision-making. Firstly, The algorithm draws on the idea of solving the weight of evidence in the improved evidence theory algorithm, and calculates the weight of Vague evaluation value, and revises the original evaluation information after obtaining the weight of each Vague evaluation value. Secondly, this algorithm analyzes the mathematical relationship between the Vague sets and the evidence theory, and uses the evidence theory to fuse the evaluation information to obtain the final Vague evaluation value of each alternative. Finally, this algorithm uses a score function to calculate the score of each alternative to determine the best alternative. The algorithm given in the paper enables decision-makers to make rational decisions in uncertain environments, and then select the best alternative.

A comprehensive runoff variation evaluation system of the Yarlung Zangbo River based on vague sets

Runoff processes are the basis for maintaining the safety of river ecosystems. The Yarlung Zangbo River (YZR) faces changes in flow regimes due to the impacts of human activities and climate change#which may threaten its fragile ecosystem. In this study#a new comprehensive system for evaluating runoff variation was constructed to investigate the degree of runoff alternation in the YZR. Based on the data from the primary hydrological stations in the YZR from 1956 to 2000#the assessment indicators of runoff variation were selected by considering the flow#sediment#and water temperature processes. Furthermore#a comprehensive evaluation system for runoff variation was constructed via multiple hydrological analysis methods and vague sets. The results showed that the variation index of the YZR from 2010 to 2013 was 0.15–0.20 compared with the flow regimes of the YZR before 2000#which were within a reasonable range#indicating that the comprehensive runoff conditions of the YZR were not greatly disturbed by human activities such as reservoir construction and river regulation during this period. These results provide a tool for evaluating the runoff change in the YZR and new references for researching runoff variation in other similar watersheds.

Some Information Measures for Fuzzy Rough Sets

Information theory is a tool to measure uncertainty; these days, it is used to solve various challenging problems that involve hybridization of information theory with the fuzzy set, rough sets, vague sets, etc. In order to solve challenging problems in scientific data analysis and visualization recently, various authors are working on hybrid measures of information theory. In this paper, using the relation between information measures, some measures are proposed for the fuzzy rough set. Firstly, an entropy measure is derived using the fuzzy rough similarity measure, and then corresponding to this entropy measure, some other measures like mutual information measure, joint entropy measure, and conditional entropy measure are also proposed. Some properties of these measures are also studied. Later, the proposed measure is compared with some existing measures to prove its efficiency. Further, the proposed measures are applied to pattern recognition, medical diagnoses, and a real-life decision-making problem for incorporating software in the curriculum at the Department of Statistics.

Nucleolus of Vague Payoff Cooperative Game

This paper focuses on the problem of cooperative game with payoff of vague value and its nucleolus. Firstly, the paper defines the score function and accuracy function of vague sets and the method for ranking of vague sets and proposes the concept of core and nucleolus of vague payoff cooperative game. Based on this, the model of vague payoff cooperative game is built. Then, the relationship between the core and the nucleolus of vague payoff cooperative game is further discussed, and the existence and unique characteristics of the nucleolus are proved. We use the ranking method defined in the paper to transform the problem of finding the nucleolus solution into a nonlinear programming problem. Finally, the paper verifies the feasibility and effectiveness of the method for finding the nucleolus with an experimental analysis.

Introducing a new type of HFSs and its application in solving MAGDM problems

Uncertainty has long been explored as an objective and inalienable reality, and then modeled via different theories such as probability theory, fuzzy sets (FSs) theory, vague sets, etc. Hesitant fuzzy sets (HFSs) as a generalization of FSs, because of their flexibility and capability, extended and applied in many practical problems very soon. However, the above theories cannot meet all the scientific needs of researchers. For example, in some decision-making problems we encounter predetermined definite data, which have inductive uncertainties. In other words, the numbers themselves are crisp in nature, but are associated with varying degrees of satisfaction or fairness from the perspective of each decision-maker/judge. To this end, in this article, hesitant fuzzy numbers as a generalization of hesitant fuzzy sets will be introduced. Some concepts such as the operation laws, the arithmetic operations, the score function, the variance of hesitant fuzzy numbers, and a way to compare hesitant fuzzy numbers will be proposed. Mean-based aggregation operators of hesitant fuzzy numbers, i.e. hesitant fuzzy weighted arithmetic averaging (HWAA), hesitant fuzzy weighted geometric averaging (HWGA), hesitant fuzzy ordered weighted arithmetic averaging (HOWAA), and hesitant fuzzy ordered weighted geometric averaging (HOWGA) operators have been discussed in this paper, too. These new concepts will be used to model, and solve an uncertain multi-attribute group decision making (MAGDM) problem. The proposed method will be illustrated by a numerical example and the validity of the obtained solution will be checked by test criteria.

Similarity measure for multi-granularity rough approximations of vague sets

Vague sets are a further extension of fuzzy sets. In rough set theory, target concept can be characterized by different rough approximation spaces when it is a vague concept. The uncertainty measure of vague sets in rough approximation spaces is an important issue. If the uncertainty measure is not accurate enough, different rough approximation spaces of a vague concept may possess the same result, which makes it impossible to distinguish these approximation spaces for charactering a vague concept strictly. In this paper, this problem will be solved from the perspective of similarity. Firstly, based on the similarity between vague information granules(VIGs), we proposed an uncertainty measure with strong distinguishing ability called rough vague similarity (RVS). Furthermore, by studying the multi-granularity rough approximations of a vague concept, we reveal the change rules of RVS with the changing granularities and conclude that the RVS between any two rough approximation spaces can degenerate to granularity measure and information measure. Finally, a case study and related experiments are listed to verify that RVS possesses a better performance for reflecting differences among rough approximation spaces for describing a vague concept.