With the increasing complexity of the human social environment, it is impossible to describe each object in detail with accurate numbers when solving multiple attribute decision-making (MADM) problems. Compared with the fuzzy set (FS), the intuitionistic fuzzy set (IFS) not only has obvious advantages in allocating ambiguous values to the object to be considered, but also takes into account the degree of membership and non-membership, so it is more suitable for decision makers (DMs) to deal with complex realistic problems. Therefore, it is of great significance to propose a MADM method under an intuitionistic fuzzy environment. Moreover, compared with the traditional 2WD, by putting forward the option of delay, the decision-making risk can be effectively reduced using three-way decision (3WD). In addition, the binary relations between objects in the decision-making process have been continuously generalized, such as equivalence relation which have symmetrical relationship, dominance relation and outranking relation, which are worthy of study. In this paper, we propose 3WD-MADM method based on IF environment and the objective IFS is calculated by using the information table. Then, the hybrid information table is used to solve the supplier selection problem to demonstrate the effectiveness of the proposed method.

https://www.mdpi.com/2073-8994/13/8/1384/pdf

Three-Way Multi-Attribute Decision Making Based on Outranking Relations under Intuitionistic Fuzzy Environments

Three-way concept analysis (3WCA) is extended research of formal concept analysis (FCA) by combining three-way decision. The three-way object oriented concept lattice (OEOL) is one of the important data structures which integrates rough set, concept lattice and three-way decision in 3WCA. In the paper, we investigate the characteristics of formal context based on the isomorphic relationship among the kinds of concept lattices with OEOL. Firstly, II-dual intersectable attributes and II-dual intersectable context are proposed and the relationship between the type I-dual intersectable context(dual intersectable context) and the type II-dual intersectable context are studied. In addition, the relationship among the kinds of concept lattices with OEOL are studied when the formal context is both I-dual intersectable context and II-dual intersectable context. Finally, the inverse problems of the above conclusions are discussed and the following two conclusions are obtained: (1) the formal context is the type II-dual intersectable context, when the object oriented concept lattice and OEOL are isomorphic. (2) In addition, the formal context is the type I-dual intersectable context, when the concept lattice and OEOL are anti-isomorphic.

The Feature Description of Formal Context Based on the Relationships among Concept Lattices.

Knowledge acquisition in intuitionistic fuzzy information systems is of importance because those fuzzy information systems are often encountered in many real-life problems. Formal concept analysis is a simple and effective tool for knowledge acquisition. However, there is still little work on introducing knowledge acquisition methods based on formal concept analysis into intuitionistic fuzzy information systems. This paper mainly extends the formal concept theory into intuitionistic fuzzy information systems. Firstly, two pairs of adjoint mappings are defined in intuitionistic fuzzy formal contexts. It is verified that both pairs of adjoint mappings form Galois connections. Secondly, two types of intuitionistic fuzzy concept lattices are constructed. After that, we also present the main theorems and propositions of the intuitionistic fuzzy concept lattices. Thirdly, we deeply discuss the attribute characteristics for type-1 generalized one-sided intuitionistic fuzzy concept lattice. Furthermore, a discernibility matrix-based algorithm is proposed for attribute reduction and the effectiveness of this algorithm is demonstrated by a practical example. The construction of intuitionistic fuzzy conceptS is meaningful for the complex and fuzzy information in real life.

Attribute reduction in intuitionistic fuzzy formal concepts

It is crystal clear that discovering the rules for finding a specific pattern among given data for extraction of association rules in rule-based learning systems has been defined in previous researches. Making use of game theory for the processes contributing to discovery of rules can be seen in numerous researches. In recent years, modeling based on game theory in rule learning sphere has gained much more attention for computer scientists. When two or more players use different strategies independently, the strategy game modeling could be used. In this view, strategic play is a desirable model for situations with no permanent strategic relationship among interactions. In addition, Nash equilibrium is the most widely used solution concept in game theory. This concept is a state-of-the-art interpretation of a strategy game. Each player has an accurate prediction of other players’ behavior and acts according to such a rational prediction. In the present study, by extracting rules from frequent patterns we have presented a model that can extract learning rules by abstraction based on game theory, which can be used not only for association rules but also for rule-based learning systems. Also, the introduced method can be easily generalized to fuzzy data. To find Nash equilibrium (FNE) in the proposed method, we used meta-heuristic bus transportation algorithm. The results indicated that the method reduces computational complexity in the associate rule discovery process and rule learning, provided that FNE is solved.

Using BTA Algorithm for finding Nash equilibrium problem aiming the extraction of rules in rule learning

Abstract This paper develops a personalized individual semantics (PISs) model for computing with linguistic intuitionistic fuzzy information and applies to evaluating different brands of mobile phones. First, considering that a linguistic term means different things to different decision-makers, a consistency-driven optimization model for checking the additive consistent linguistic intuitionistic fuzzy preference relations (LIFPRs) is constructed by considering the PISs of a decision maker. Besides, several optimization models is built to determine the PISs of linguistic terms in LIFPRs and obtain the acceptable additive consistent LIFPRs. Second, a new definition of Hamming distance between linguistic intuitionistic fuzzy numbers (LIFNs) is developed by considering the PISs of a decision maker, and several of its desirable properties are discussed. Then, the method of deriving the weight vectors of criteria is calculated based on the proposed distance measure. Subsequently, a framework of group decision making process with LIFPRs is offered, and the application of the proposed method is illustrated by using a multi-criteria decision-making problem about evaluating different brands of mobile phones. Finally, the comparative analysis is conducted to show the feasibility of proposed group decision-making method. 

Xiaoying Song

Papers

Rule extraction based on linguistic-valued intuitionistic fuzzy layered concept lattice