Search

The basic notions in rough set theory are lower and upper approximation operators defined by a fixed binary relation. This paper proposes an intuitionistic fuzzy rough set (IFRS) model which is a combination of intuitionistic fuzzy set (IFS) and rough set. We approximate an IFS by using soft binary relations instead of fixed binary relations. By using this technique, we get two pairs of intuitionistic fuzzy (IF) soft sets, called the upper approximation and lower approximation with respect to foresets and aftersets. Properties of newly defined rough set model (IFRS) are studied. Similarity relations between IFS with respect to this rough set model (IFRS) are also studied. Finally, an algorithm is constructed depending on these approximations of IFSs and score function for decision-making problems, although a method of decision-making algorithm has been introduced for fuzzy sets already. But, this new IFRS model is more accurate to solve the problem because IFS has degree of nonmembership and degree of hesitant. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and study different kinds of fuzzy soft β-neighborhoods called fuzzy soft β-adhesion neighborhoods and to analyze some of their properties. Further, the concepts of soft β-adhesion neighborhoods are investigated and the related properties are studied. Then, we present new kinds of lower and upper approximations by means of different fuzzy soft β-neighborhoods. The relationships among our models (i.e., Definitions 3.9, 3.12, 3.15 and 3.18) and Zhang models [48] are also discussed. Finally, we construct an algorithm based on Definition 3.12, when k = 1 to solve the decision-making problems and illustrate its applicability through a numerical example. [ABSTRACT FROM AUTHOR]

• New point operators for picture fuzzy sets are defined. • Memoryless multiple rounds voting process is stated. • A multi-attribute decision making algorithm is presented to address the problems. • Superiority of the algorithm is demonstrated through numerical examples. Picture fuzzy set (PFS), a generalization of the Atanassov-intuitionistic fuzzy set, is one of the most trustworthy tool to handle the uncertainties in the data during the decision-making process. The objective of this paper is to present some different kinds of the point operators for the PFS. The key feature of the presented point operators is to provide a smaller degree of uncertainty which is equivalent to the corresponding PFS. The desirable properties of the proposed operators are also derived in details. Also, we provide a memoryless multiple rounds voting process under the PFS environment to strength the result, and hence deduce a relationship between the proposed PFS and the existing set. In addition to this, we address the MADM (multiple attribute decision-making) problems by presented an algorithm to solve the problem based on the proposed point operators. The applicability and the superiority of the proposed algorithm are shown through two numerical examples. At last, the validity of the proposed algorithm is tested using different test criteria. [ABSTRACT FROM AUTHOR]

Abstract: Many individual attributes considered for personnel selection such as organizing ability, creativity, personality, and leadership exhibit vagueness and imprecision. The fuzzy set theory appears as an essential tool to provide a decision framework that incorporates imprecise judgments inherent in the personnel selection process. In this paper, a fuzzy multi-criteria decision making (MCDM) algorithm using the principles of fusion of fuzzy information, 2-tuple linguistic representation model, and technique for order preference by similarity to ideal solution (TOPSIS) is developed. The proposed method is apt to manage information assessed using both linguistic and numerical scales in a decision making problem with multiple information sources. Furthermore, it enables managers to deal with heterogeneous information. The decision making framework presented in this paper employs ordered weighted averaging (OWA) operator that encompasses several operators as the aggregation operator since it can implement different aggregation rules by changing the order weights. The aggregation process is based on the unification of information by means of fuzzy sets on a basic linguistic term set (BLTS). Then, the unified information is transformed into linguistic 2-tuples in a way to rectify the problem of loss information of other fuzzy linguistic approaches. The computational procedure of the proposed framework is illustrated through a personnel selection problem reported in an earlier study. [Copyright &y& Elsevier]

This paper discusses decision making based on intuitionistic fuzzy soft sets by means of grey relational analysis and D-S theory of evidence. An algorithm on this decision making is presented and an example is employed to show the algorithm is efficient for solving decision problems. [ABSTRACT FROM AUTHOR]

Abstract: Molodtsov’s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty. By combining the multi-fuzzy set and soft set models, the purpose of this paper is to introduce the concept of multi-fuzzy soft sets. Some operations on a multi-fuzzy soft set are defined, such as complement operation, “AND” and “OR” operations, Union and Intersection operations. Then, the DeMorgan’s laws are proved. Finally, by means of level soft set, an algorithm is presented, and a decision problem is analyzed using multi-fuzzy soft set. [Copyright &y& Elsevier]

Binary relations are most important in various fields of pure and applied sciences. The concept of linear Diophantine fuzzy sets (LDFSs) proposed by Riaz and Hashmi is a novel mathematical approach to model vagueness and uncertainty in decision-making problems. In LDFS theory, the use of reference or control parameters corresponding to membership and non-membership grades makes it most accommodating towards modeling uncertainties in real-life problems. The main purpose of this paper is to establish a robust fusion of binary relations and LDFSs, and to introduce the concept of linear Diophantine fuzzy relation (LDF-relation) by making the use of reference parameters corresponding to the membership and non-membership fuzzy relations. The novel concept of LDF-relation is more flexible to discuss the symmetry between two or more objects that is superior to the prevailing notion of intuitionistic fuzzy relation (IF-relation). Certain basic operations are defined to investigate some significant results which are very useful in solving real-life problems. Based on these operations and their related results, it is analyzed that the collection of all LDF-relations gives rise to some algebraic structures such as semi-group, semi-ring and hemi-ring. Furthermore, the notion of score function of LDF-relations is introduced to analyze the symmetry of the optimal decision and ranking of feasible alternatives. Additionally, a new algorithm for modeling uncertainty in decision-making problems is proposed based on LDFSs and LDF-relations. A practical application of proposed decision-making approach is illustrated by a numerical example. Proposed LDF-relations, their operations, and related results may serve as a foundation for computational intelligence and modeling uncertainties in decision-making problems. [ABSTRACT FROM AUTHOR]