مقاله انگلیسی رایگان در مورد روش تصمیم گیری گروهی مبتنی بر مجموعه N-Soft – الزویر ۲۰۱۹

In this article, we introduce a new hybrid model called hesitant N-soft sets by a suitable combination of hesitancy with N-soft sets, a model that extends N-soft sets. Our novel concept is illustrated with real life examples. Moreover, we investigate some useful properties of hesitant N-soft sets and construct fundamental operations on them. We describe potential applications of hesitant N-soft sets in group decision-making, and finally we present some group decision-making methods as algorithms.

Introduction

Data related to most of our practical life problems including medical science, engineering, economics and environmental sciences among others, are imprecise and their corresponding solutions require the use of mathematical conventions based on imprecision and uncertainty. We cannot use traditional mathematical tools to overcome uncertainties existing in these problems. Consequently and in order to handle such uncertainties, a number of theories have been introduced including fuzzy set theory (Zadeh, 1965) and its extensions (Bustince et al., 2016, 2008), probability, rough set theory (Greco, Matarazzo & Slowinski, 2001, 2002; Liu, Qin & Mart´ınez, 2018; Pawlak, 1982), et cetera. Merig´o, Gil-Lafuente & Yager (2015) and Blanco-Mesa, Merig´o Gil-Lafuente (2017) are updated overviews of fuzzy research and fuzzy decision making with respective biblio-metric indicators. Anyhow all of these theories have their immanent difficulties (Paternain et al., 2012), a drawback that motivated Molodtsov (1999) to introduce the idea of soft sets as a new mathematical tool to tackle some of their difficulties. Soft set theory has significant use in game theory, smoothness of functions, medicine, operational research and probability theory (Alcantud & Santos-Garc´ıa, 2017; Molodtsov, 1999, 2004). Their algebraic analysis and applications developed rapidly. Maji, Biswas, & Roy (2003) presented some basic algebraic operations on soft sets and provide an analytical approach to theory of soft sets. Ali et al. (2009) suggested some different operations for soft sets and developed the idea of complement of soft set. They showed that certain De Morgan’s laws are valid in soft sets. Maji, Biswas, & Roy (2002) discussed the use of soft sets in decision making problems. It is observed that fuzzy sets, soft sets and rough sets are conveniently related notions. Maji, Biswas, & Roy (2001) combined soft sets with other mathematical structures and introduced an hybrid model called fuzzy soft sets, which is the natural fuzzy generalization of soft sets. They investigated many useful results related to this model. Optimization in this setting has been recently studied in Alcantud (2015, 2016a), Alcantud & Mathew (2017) and Liu, Qin & Pei (2017), see also Khameneh & Kili¸cman (2018) for an updated survey. Afterwards Majumdar & Samanta (2010) revised the definition of fuzzy soft set and proposed the concept of generalized fuzzy soft sets based on Maji, Biswas, & Roy (2003).