Intuitionistic Hesitant Fuzzy Soft Set and Its Application in Decision Making

Abstract: Currently, the tasks of emergency evacuation based on the flow theory have been studying extensively due to the increasing number of emergency situations, natural disasters, fires, terrorist attacks and other phenomena. However, the main issue of the evacuation simulation is the necessity to tackle dynamic environmental factors, such as road capacities and evacuation time parameters, as well as the fuzzy nature of the evacuation. Traffic delays have become ubiquitous during evacuation, whereas evacuation and rescue flows move in opposite directions. To address the aforementioned issues a method for the partial contraflow evacuation is examined to increase the total outbound capacity and reverse the arcs of the modelled network up to the required capacity. The main contribution to the paper is the proposal for the fuzzy lexicographic maximum dynamic evacuation according to the partial lane reversal strategy using multiple attribute group decision making method based on TOPSIS in intuitionistic fuzzy setting for ordering the terminals during evacuation. The main goal of the proposed algorithm is to transport the maximum number of aggrieved from origins to destinations that have different levels of priority due to the level of reachability, capacity of destination nodes, reliability (security) and total expenses. A case study is conducted to illustrate the proposed algorithm.

Abstract: There are several models of uncertainty found in the literature like fuzzy set (FS), rough set, intuitionistic fuzzy set, soft set, and hesitant fuzzy set. Also, several hybrid models have come up as a combination of these models and have been found to be more useful than the individual models. In everyday life, we make many decisions. Making efficient decisions under uncertainty needs better techniques. Many such techniques have been developed in the recent past. These techniques involve soft sets (SS) and intuitionistic fuzzy sets. It is well known that intuitionistic hesitant fuzzy sets are more general than intuitionistic fuzzy sets. In this paper, we redefine interval-valued intuitionistic hesitant fuzzy soft sets (IVIHFSS) and also propose a decision-making technique which extends some of the recently developed algorithms. We also provide an application from real-life situations which illustrates the working of the algorithm and its efficiency over the other algorithms.

Abstract: One of the latest models to handle uncertainty is soft set It associates each parameter in its set of parameters to a subset of elements in the universe of discourse In its introductory article itself, Molodtsov has shown the applications of this new tool in many different areas But, over the years, soft sets have been used by many researchers for decision-making applications over uncertainty-based datasets It has been observed that appropriate hybridization of models is always better than the route ones Following this, many hybrid models of soft set have already been added to the literature by different researchers So far, multiple attempts have been made to use intuitionistic fuzzy soft set (IFSS) for decision-making This paper introduces the concept of interval-valued fuzzy (IVF) priority for decision-making using IFSS It also provides an improved approach to deal with group decision-making (GDM) using IFSS and an application of IFSS in GDM

Abstract: A definition of the concept 'intuitionistic fuzzy set' (IFS) is given, the latter being a generalization of the concept 'fuzzy set' and an example is described. Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.

Abstract: The soft set theory offers a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. The main purpose of this paper is to introduce the basic notions of the theory of soft sets, to present the first results of the theory, and to discuss some problems of the future.

Abstract: In this paper, the authors study the theory of soft sets initiated by Molodtsov. The authors define equality of two soft sets, subset and super set of a soft set, complement of a soft set, null soft set, and absolute soft set with examples. Soft binary operations like AND, OR and also the operations of union, intersection are defined. De Morgan's laws and a number of results are verified in soft set theory.

Abstract: In this paper, we apply the theory of soft sets to solve a decision making problem using rough mathematics.