Notes on soft sets and aggregation operators

[EN]Under uncertainty, traditional sets may not be sufficient to represent real-world phenomena, and fuzzy sets can provide a more flexible and natural approach. The concept of fuzzy sets has been widely used in various fields, including artificial intelligence, control theory, decision-making, and pattern recognition. Fuzzy sets can also be combined with other mathematical tools, such as probability theory, to provide a more comprehensive approach to uncertainty management. In these notes, we explore the concept of fuzzy sets under uncertainty, and their applications in various fields. We discuss the fundamental concepts of fuzzy sets, including fuzzy membership functions, fuzzy operations, and fuzzy relations. We also examine different types of uncertainty, including epistemic and aleatory uncertainty, and how fuzzy sets can be used to model and manage uncertainty in these cases

Hesitant Triangular Fuzzy Information Aggregation Operators Based on Bonferroni Means and Their Application to Multiple Attribute Decision Making

We investigate the multiple attribute decision-making (MADM) problems with hesitant triangular fuzzy information. Firstly, definition and some operational laws of hesitant triangular fuzzy elements are introduced. Then, we develop some hesitant triangular fuzzy aggregation operators based on Bonferroni means and discuss their basic properties. Some existing operators can be viewed as their special cases. Next, we apply the proposed operators to deal with multiple attribute decision-making problems under hesitant triangular fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness

Aggregation operators in group decision making: Identifying citation classics via H-classics

To analyze the past, present and future of a particular research field, classic papers are usually studied because they identify the highly cited papers being a relevant reference point in that specific research area. As a result of the possible mapping between high quality research and high citation counts, highly cited papers are very interesting. The objective of this study is to use the H-classics method, which is based on the popular h-index, to identify and analyze the highly cited documents published about aggregation operators in the research area of group decision making. According to the H-classics method, this research area is represented by 87 citation classics, which have been published from 1988 to 2014. Authors, affiliations (universities/institutions and countries), journals, books and conferences, and the topics covered by these 87 highly cited papers are studied.The authors would like to thank FEDER financial support from the Projects TIN2013-40658-P and TIN2016- 75850-P

A linguistic multi-criteria decision-aiding system to support university career services

In this paper we introduce a linguistic multi-criteria decision-aiding model to support college students with the internship job market application. It considers a fuzzy ordered weighted averaging (FOWA) operator in the matching to capture the inherent uncertainty and vague nature of personnel selection processes. The decision model is integrated in a software tool able to capture data from university student resume and internship databases. The application assesses position characteristics implicitly by means of linguistic descriptions according to each student's preferences. The software tool is enabled with the ability to propose positions according to student preferences. The system selects a reduced list of alternatives from the set of job offers, helping students to decide on which positions to focus their applications.Peer ReviewedPostprint (author's final draft

A novel method based on extended uncertain 2-tuple linguistic muirhead mean operators to MAGDM under uncertain 2-tuple linguistic environment

The present work is focused on multi-attribute group decision-making (MAGDM) problems with the uncertain 2-tuple linguistic information (ULI2–tuple) based on new aggregation operators which can capture interrelationships of attributes by a parameter vector P. To begin with, we present some new uncertain 2-tuple linguistic MM aggregation (UL2–tuple-MM) operators to handle MAGDM problems with ULI2–tuple, including the uncertain 2-tuple linguistic Muirhead mean (UL2–tuple-MM) operator, uncertain 2-tuple linguistic weighted Muirhead mean (UL2–tuple-WMM) operator. In addition, we extend UL2–tuple-WMM operator to a new aggregation operator named extended uncertain 2-tuple linguistic weighted Muirhead mean (EUL2–tuple-WMM) operators in order to handle some decision-making problems with ULI2–tuple whose attribute values are expressed in ULI2–tuple and attribute weights are also 2-tuple linguistic information. Whilst, the some properties of these new aggregation operators are obtained and some special cases are discussed. Moreover, we propose a new method to solve the MAGDM problems with ULI2–tuple. Finally, a numerical example is given to show the validity of the proposed method and the advantages of proposed method are also analysed

The legacy of 50 years of fuzzy sets: A discussion

International audienceThis note provides a brief overview of the main ideas and notions underlying fifty years of research in fuzzy set and possibility theory, two important settings introduced by L.A. Zadeh for representing sets with unsharp boundaries and uncertainty induced by granules of information expressed with words. The discussion is organized on the basis of three potential understanding of the grades of membership to a fuzzy set, depending on what the fuzzy set intends to represent: a group of elements with borderline members, a plausibility distribution, or a preference profile. It also questions the motivations for some existing generalized fuzzy sets. This note clearly reflects the shared personal views of its authors

Pythagorean 2-tuple linguistic power aggregation operators in multiple attribute decision making

In this paper, we investigate the multiple attribute decision making problems with Pythagorean 2-tuple linguistic information. Then, we utilize power average and power geometric operations to develop some Pythagorean 2-tuple linguistic power aggregation operators: Pythagorean 2-tuple linguistic power weighted average (P2TLPWA) operator, Pythagorean 2-tuple linguistic power weighted geometric (P2TLPWG) operator, Pythagorean 2-tuple linguistic power ordered weighted average (P2TLPOWA) operator, Pythagorean 2-tuple linguistic power ordered weighted geometric (P2TLPOWG) operator, Pythagorean 2-tuple linguistic power hybrid average (P2TLPHA) operator and Pythagorean 2-tuple linguistic power hybrid geometric (P2TLPHG) operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean 2-tuple linguistic multiple attribute decision making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness

A Historical Account of Types of Fuzzy Sets and Their Relationships

In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used