Fuzzy number

About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.

Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm

Abstract: Archimedean t-conorm and t-norm are generalizations of a lot of other t-conorms and t-norms, such as Algebraic, Einstein, Hamacher and Frank t-conorms and t-norms or others, and some of them have been applied to intuitionistic fuzzy set, which contains three functions: the membership function, the non-membership function and the hesitancy function describing uncertainty and fuzziness more objectively. Recently, Beliakov et al. [3] constructed some operations about intuitionistic fuzzy sets based on Archimedean t-conorm and t-norm, from which an aggregation principle is proposed for intuitionistic fuzzy information. In this paper, we propose some other operations on intuitionistic fuzzy sets, study their properties and relationships, and based on which, we study the properties of the aggregation principle proposed by Beliakov et al. [3], and give some specific intuitionistic fuzzy aggregation operators, which can be considered as the extensions of the known ones. In the end, we develop an approach for multi-criteria decision making under intuitionistic fuzzy environment, and illustrate an example to show the behavior of the proposed operators.

Fuzzy sets and probability: misunderstandings, bridges and gaps

Abstract: One of the most controversial issues in uncertainty modeling and information sciences is the relationship between probability theory and fuzzy sets The literature pertaining to this debate is surveyed The authors address some classical misunderstandings between fuzzy sets and probabilities They consider probabilistic interpretations of membership functions that may help in membership function assessment Nonprobabilistic interpretations of fuzzy sets are identified The literature on possibility-probability transformations is examined, and some lurking controversies on that topic are clarified Several subfields of fuzzy set research where fuzzy sets and probability are conjointly used are discussed >

Supplier selection and order allocation based on fuzzy SWOT analysis and fuzzy linear programming

Abstract: Supplier selection is a multi criteria decision-making problem that comprises tangible and intangible factors. The majority of previous supplier selection techniques do not consider strategic perspective. Besides, uncertainty is one of the most important obstacles in supplier selection. In this paper, quantified SWOT is applied in the context of supplier selection for the first time. SWOT (Strengths, Weaknesses, Opportunities and Threats) is one of the most well-known techniques for conducting a strategic study. In addition, the fuzzy logic and triangular fuzzy numbers are integrated with SWOT analysis - as a novel innovation - to deal with vagueness of human thought. SWOT analysis can consider both qualitative and quantitative criteria. The managers can understand the position of suppliers in a competitive environment with a glance at SWOT matrix. Moreover, a fuzzy linear programming model is proposed to determine how much should be purchased from each supplier. It is supposed that the demand is a fuzzy number. Besides, the capacity of warehouse is considered as a constraint. A case study is utilized concurrently to show the efficiency of the proposed model.

Generalized hesitant fuzzy sets and their application in decision support system

Abstract: Hesitant fuzzy sets are very useful to deal with group decision making problems when experts have a hesitation among several possible memberships for an element to a set. During the evaluating process in practice, however, these possible memberships may be not only crisp values in [0,1], but also interval values. In this study, we extend hesitant fuzzy sets by intuitionistic fuzzy sets and refer to them as generalized hesitant fuzzy sets. Zadeh's fuzzy sets, intuitionistic fuzzy sets and hesitant fuzzy sets are special cases of the new fuzzy sets. We redefine some basic operations of generalized hesitant fuzzy sets, which are consistent with those of hesitant fuzzy sets. Some arithmetic operations and relationships among them are discussed as well. We further introduce the comparison law to distinguish two generalized hesitant fuzzy sets according to score function and consistency function. Besides, the proposed extension principle enables decision makers to employ aggregation operators of intuitionistic fuzzy sets to aggregate a set of generalized hesitant fuzzy sets for decision making. The rationality of applying the proposed techniques is clarified by a practical example. At last, the proposed techniques are devoted to a decision support system.

A Hybrid Method for Pythagorean Fuzzy Multiple-Criteria Decision Making

Abstract: As a generalization of intuitionistic fuzzy set, the Pythagorean fuzzy set is interesting and very useful in modeling uncertain information in real-world decision-making problems. In this paper, we develop a new method for Pythagorean fuzzy multiple-criteria decision-making (MCDM) problems with aggregation operators and distance measures. First, we present the Pythagorean fuzzy ordered weighted averaging weighted average distance (PFOWAWAD) operator. The main advantage of the PFOWAWAD operator is that it uses distance measures in a unified framework between the ordered weighted averaging (OWA) operator and weighted average (WA) that considers the degree of importance of each concept in the aggregation. Some of its main properties and special cases are studied. Then, based on the proposed operator, a hybrid TOPSIS method, called PFOWAWAD-TOPSIS is introduced for Pythagorean fuzzy MCDM problem. Finally, a numerical example is provided to illustrate the practicality and feasibility of the developed method.