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Fixed Point Theory in Soft Metric Spaces: Rise and Fall
Published in Dhananjay Gopal, Poom Kumam, Mujahid Abbas, Background and Recent Developments of Metric Fixed Point Theory, 2017
Mujahid Abbas, Ghulam Murtaza, Salvador Romaguera
There are certain limitations and deficiencies pertaining to the parametrization in fuzzy set theory (see [31]). The problem of inadequacy of parameters has been successfully solved by soft set theory which provides enough tools to deal with uncertainty in a data and represent it in a useful way. The distinguishing attribute of soft set theory is that unlike probability theory and fuzzy set theory, it does not uphold a precise quantity. This attribute facilitated applications in decision making, demand analysis, forecasting, information sciences, mathematics and other disciplines (see [12,16,23,33,35,44,45]).
Flight Planning
Published in Yasmina Bestaoui Sebbane, Multi-UAV Planning and Task Allocation, 2020
Many traditional tools for formal modeling, reasoning and computing are crisp, deterministic and precise character. However, most practical problems involve data that contain uncertainties. There have been a great amount of research in probability theory, fuzzy set theory, rough set theory, vague set theory, gray set theory, intuitionistic fuzzy set theory and interval math. Soft set and its various extensions have been applied with dealing with decision-making problems. They involve the evaluation of all the objects which are decision alternatives.
Binary Soft Connected Spaces and an Application of Binary Soft Sets in Decision Making Problem
Published in Fuzzy Information and Engineering, 2019
During the study towards possible applications in classical and non classical logic, binary soft sets and binary soft topology is very important. Nowadays, researchers daily deal with the complexities of modelling uncertain data in economics, engineering, environmental science, sociology, medical science, and many other fields. Classical methods are not always successful due to the reason that uncertainties appearing in these domains may be of various types. Zadeh [1] initiated a new approach of fuzzy set theory, which proved to be the most appropriate framework for dealing with uncertainties. While probability theory, rough sets [2], and other mathematical tools are considered as a useful approaches to describe uncertainty. Each of these theories has its own inherent difficulties as pointed out by Molodtsov [3]. Molodtsov [3,4] proposed a completely new elegant approach of soft sets theory for modelling vagueness and uncertainty which is free from the difficulties affecting existing methods. In soft set theory the problem of setting the membership function, among other related problems, simply does not arise. Soft sets are considered as neighbourhood systems, and are a special case of context-dependent fuzzy sets. Soft set theory has potential applications in many different fields, including the smoothness of functions, game theory, operations research, Riemann integration, Perron integration, probability theory, and measurement theory.
Solution to a Soft Fuzzy Group Decision-Making Problem Involving a Soft Fuzzy Number Valued Information System
Published in Fuzzy Information and Engineering, 2019
Arul Roselet Meryline S., Felbin C. Kennedy
On the other hand, the concept of a soft set as a mathematical tool for dealing uncertainty was introduced by Molodtsov [18] in 1999 to be a parameterised family of subsets of some universal set . Combination of soft sets with fuzzy sets was studied to capture the nature of entities in the problem in hand. In 2001, Maji and Roy [19] defined a fuzzy soft set to be a soft set in which the set of all subsets of were replaced by the collection of fuzzy sets on . With the on set of the new millennium, Biswas et al. [20] had applied soft sets in decision-making problems. GDM involving fuzzy soft set theory was studied by few researchers (to cite a few [21,22]).
Weak Forms of Soft Separation Axioms and Fixed Soft Points
Published in Fuzzy Information and Engineering, 2020
T. M. Al-shami, E. A. Abo-Tabl, B. A. Asaad
Molotdsov's soft set [1] was established in 1999 as a new technique for tackling real-life problems that suffer from imprecision and uncertainty. Molotdsov [1] investigated the merits of soft sets in comparison to probability theory and fuzzy set theory. The soft set-theoretic concepts were then introduced and investigated by a number of researchers, and many applications of soft sets were made in different disciplines such as decision-making [2], engineering [3] and medical science [2].