Showing papers by "Yiyu Yao published in 2021"

Three-Way Multiattribute Decision-Making Based on Outranking Relations

Abstract: In contrast to two-way decisions (2WD), three-way decisions (3WD) can effectively reduce decision risks by utilizing a new delayed decision option. This article incorporates 3WD into multiattribute decision-making (MADM) based on an outranking relation. We construct the outranked set for each alternative and introduce a hybrid information table that combines an MADM matrix with a loss function table. We propose three strategies to design a new 3WD model for MADM. The rationality and effectiveness of the proposed 3WD method are demonstrated by solving a problem of enterprise project investment target selections. Finally, we provide the comparative analysis and two experimental evaluations. The results show that the proposed 3WD method is effective and practically useful.

The geometry of three-way decision

Abstract: A theory of three-way decision concerns the art, science, and practice of thinking, problem solving, and information processing in threes. It explores the effective uses of triads of three things, for example, three elements, three parts, three perspectives, and so on. In this paper, I examine geometric structures, graphical representations, and semantical interpretations of triads in terms of basic geometric notions of dots, lines, triangles, circles, as well as more complex structures derived from these basic notions. I use examples from different disciplines and fields to illustrate the uses of these structures and their physical interpretations for triadic thinking, triadic computing, and triadic processing. Following the principles of triadic thinking, this paper blends together three common ways to think, namely, numerical thinking, textual thinking, and visual thinking.

Set-theoretic models of three-way decision

Abstract: The theory of three-way decision is about a philosophy of thinking in threes, a methodology of working with threes, and a mechanism of processing in threes. We approach a whole through three parts, in terms of three units, or from three perspectives. A trisecting–acting–outcome (TAO) model of three-way decision involves trisecting a whole into three parts and acting on the three parts, in order to produce an optimal outcome. In this paper, we further explore the TAO model in a set-theoretic setting and make three new contributions. The first contribution is an examination of three-way decision with nonstandard sets for representing concepts under the two kinds of objective/ontic and subjective/epistemic uncertainty. The second contribution is an introduction of an evaluation-based framework of three-way decision. We present a classification of trisections and investigate the notion of an evaluation space. The third contribution is, within the proposed framework, a systematical study of three-way decision with rough sets, interval sets, fuzzy sets, shadowed sets, rough fuzzy sets, interval fuzzy sets (or equivalently, vague sets, interval-valued fuzzy sets, intuitionistic fuzzy sets), and soft sets.

Attribution reduction based on sequential three-way search of granularity

Abstract: Most existing results about attribute reduction are reported by considering one and only one granularity, especially for the strategies of searching reducts. Nevertheless, how to derive reduct from multi-granularity has rarely been taken into account. One of the most important advantages of multi-granularity based attribute reduction is that it is useful in investigating the variation of the performances of reducts with respect to different granularities. From this point of view, the concept of Sequential Granularity Attribute Reduction (SGAR) is systemically studied in this paper. Different from previous attribute reductions, the aim of SGAR is to find multiple reducts which are derived from a family of ordered granularities. Assuming that a reduct related to the previous granularity may offer the guidance for computing a reduct related to the current granularity, the idea of the three-way is introduced into the searching of sequential granularity reduct. The three different ways in such process are: (1) the reduct related to the previous granularity is precisely the reduct related to the current granularity; (2) the reduct related to the previous granularity is not the reduct related to the current granularity; (3) the reduct related to the previous granularity is possible to be the reduct related to the current granularity. Therefore, a three-way based forward greedy searching is designed to calculate the sequential granularity reduct. The main advantage of our strategy is that the number of times to evaluate the candidate attributes can be reduced. Experimental results over 12 UCI data sets demonstrate the following: (1) three-way based searching is superior to some state-of-the-art acceleration algorithms in time consumption of deriving reducts; (2) the sequential granularity reducts obtained by proposed three-way based searching will provide well-matched classification performances. This study suggests new trends concerning the problem of attribute selection.

A model of three-way approximation of intuitionistic fuzzy sets

Abstract: A three-way approximation of a fuzzy set, as a generalization of the core and the support of the fuzzy set, provides a generalized qualitatively interpretation of a fuzzy set. An intuitionistic fuzzy set (IFS) generalizes a fuzzy set by using jointly a membership function and a nonmembership function. In this paper, we present a model for constructing a three-way approximation of an IFS according to the TAO (trisecting-acting-outcome) framework of three-way decision (3WD). Given an IFS, we use its membership and nonmembership functions as a pair of evaluations to trisect a universe of objects to produce a three-way approximation of the IFS. We present a general optimization model for determining the required parameters according to the principle of the minimum cost with respect to a distance function and costs of three actions. We use Manhattan distance to illustrate the basic ideas of the optimization model.

Algebraic approaches to granular computing

Abstract: We study the granular structures in granular computing from algebraic views. We model a granular structure based on an algebra that consists of a universe and a closure operator. Based on this formulation, we define the basic granules in a granular structure through the notion of subalgebras. Using formal concept analysis and rough set analysis as two examples, we demonstrate that the proposed formulation can unify a number of current studies on the related areas of granular computing. Moreover, by modelling the granular structures in rough sets with algebraic approaches, we generalize the notion of approximations in rough sets into a general granular structure. The algebraic approaches provide a mathematical formulation of granular structures, which may assist us in the construction and interpretation of granules and granular structures.

3RD: A Multi-criteria Decision-Making Method Based on Three-Way Rankings

Abstract: By combining ideas from three-way decision theory, prospect theory, and several families of multi-criteria decision-making (MCDM) methods, including ELECTRE, PROMETHEE, TODIM, and dominance-based rough set analysis (DRSA), we propose a new ranking-based MCDM method called 3RD. With respect to a single criterion, we construct a three-way ranking (i.e., trilevel ranking) of a set of decision alternatives by using an alternative as a reference in the sense of prospect theory and a family of three-way rankings from all alternatives. With respect to a set of criteria, we have multiple families of three-way rankings. By adopting the TODIM procedure, we introduce a ranking function to rank the set of alternatives according to these multiple families of trilevel rankings.

Trilevel Multi-criteria Decision Analysis Based on Three-Way Decision

Abstract: Based on the principles of three-way decision as thinking in threes, this paper proposes a framework of trilevel multi-criteria decision analysis (3LMCDA). The main motivations and contributions are a new understanding of multi-criteria decision analysis at three levels: 1) single-criterion-level analysis with respect to individual criteria, 2) multi-criteria-level aggregation by pooling results from many criteria, and 3) multi-methods-level ensemble of different multi-criteria decision analysis methods. A full understanding of multi-criteria decision analysis requires understandings at the three levels. While the existing studies have been focused on the first two levels, new efforts at the third level may enable us to take advantages of many different multi-criteria decision analysis methods.