B. K. Tripathy

A New Approach to Interval-Valued Fuzzy Soft Sets and Its Application in Decision-Making

Soft set (SS) theory was introduced by Molodtsov to handle uncertainty. It uses a family of subsets associated with each parameter. Hybrid models have been found to be more useful than the individual components. Earlier interval-valued fuzzy set (IVFS) was introduced as an extension of fuzzy set (FS) by Zadeh. Yang introduced the concept of IVFSS by combining and soft set models. Here, we define IVFSS through the membership function approach to define soft set by Tripathy et al. very recently. Several concepts, such as complement of an IVFSS, null IVFSS, absolute IVFSS, intersection, and union of two IVFSSs, are redefined. To illustrate the application of IVFSSs, a decision-making (DM) algorithm using this notion is proposed and illustrated through an example.

Fuzzy Soft Set Theory and Its Application in Group Decision Making

Soft set theory was introduced by Molodtsov to handle uncertainty. It uses a family of subsets associated with each parameter. Hybrid models have been found to be more useful than the individual components. Earlier fuzzy set and soft set were combined to form fuzzy soft sets (FSS). Soft sets were defined from a different point of view in Tripathy et al. (Int J Reasoning-Based Intell Syst 7(3/4), 224–253, 2015) where they used the notion of characteristic functions. Hence, many related concepts were also redefined. In Tripathy et al. (Proceedings of ICCIDM-2015, 2015) membership function for FSSs was defined. We propose a new algorithm by following this approach which provides an application of FSSs in group decision making. The performance of this algorithm is substantially improved than that of the earlier algorithm.

On Intuitionistic Fuzzy Soft Sets and Their Application in Decision-Making

Molodtsov introduced soft set theory as a new mathematical approach to handle uncertainty. Hybrid models have been found to be more useful than the individual components. Following this trend fuzzy soft sets (FSS) and intuitionistic fuzzy soft sets (IFSS) were introduced. Recently, soft sets were introduced by Tripathy and Arun (Int J Reasoning-Based Intell Syst 7(3/4):244–253, 2015) [6] using the notion of characteristic function. This led to the redefinitions of concepts like complement, intersection, union of IFSS, Null and absolute IFSS. In this paper, we follow the approach of Tripathy et al. in redefining IFSS and present an application of IFSS in decision-making which substantially improve and is more realistic than the algorithms proposed earlier by several authors.

On intuitionistic fuzzy soft set and its application in group decision making

Soft set theory introduced by Molodtsov is a new mathematical approach to handle the uncertainty problems. It is a family of subsets associated with each parameter in a soft space. Hybrid models have been found to be more useful than the individual components. Earlier fuzzy set and soft set were combined to form fuzzy soft sets and similarly intuitionistic fuzzy soft sets (IFSS) were introduced. Like the soft sets, IFSS is also a notion which allows fuzziness over a soft set model. So far, many attempts have been made to define this concept. Maji et.al defined intuitionistic fuzzy soft sets and several operations on them. Following the definition of soft sets provided by Tripathy et.al (2015) through characteristic function, in this paper we improve the group decision algorithm proposed by Tripathy et al earlier and provide an application in handling the decision making problem.

A New Approach to Fuzzy Soft Set Theory and Its Application in Decision Making

Soft set theory is a new mathematical approach to vagueness introduced by Molodtsov. This is a parameterized family of subsets defined over a universal set associated with a set of parameters. In this paper, we define membership function for fuzzy soft sets. Like the soft sets, fuzzy soft set is a notion which allows fuzziness over a soft set model. So far, more than one attempt has been made to define this concept. Maji et al. defined fuzzy soft sets and several operations on them. In this paper we followed the definition of soft sets provided by Tripathy et al. through characteristic functions in 2015. Many related concepts like complement of a fuzzy soft set, null fuzzy soft set, absolute fuzzy soft set, intersection of fuzzy soft sets and union of fuzzy soft sets are redefined. We provide an application of fuzzy soft sets in decision making which substantially improve and is more realistic than the algorithm proposed earlier by Maji et al.

A New Approach to Intuitionistic Fuzzy Soft Sets and Its Application in Decision-Making

Soft set theory (Comput Math Appl 44:1007–1083, 2002) is introduced recently as a model to handle uncertainty. Recently, characteristic functions for soft sets and hence operations on them using this approach were introduced in (Comput Math Appl 45:555–562, 2003). Following this approach, in this paper we redefine intuitionistic fuzzy soft sets (IFSS) and define operations on them. We also present an application of IFSS in decision-making which substantially improve and is more realistic than the algorithms proposed earlier by several authors.

A Modified Representation of IFSS and Its Usage in GDM

Soft set is a new mathematical approach to solve the uncertainty problems. It is a tool which has the prospects of parameterization. Maji et al. defined intuitionistic fuzzy soft set (IFSS). However, using the approach of provided by Tripathy et al. (2015) we re-define IFSS and use it in deriving group decision making (GDM). An application is used for illustration of the process.

IVIFS and Decision-Making

Many models handle uncertainty problems. Fuzzy set (FS) is one of them. The next one is intuitionistic fuzzy set (IFS). Further generalization is interval-valued fuzzy set (IVFS). But all those models had some difficulty due to lack of parameterization tool, which motivated mathematician Molodtsov to introduce soft set model in 1999. Hybrid models of these models are more efficient. Interval-valued intuitionistic fuzzy soft set (IVIFSS) introduced by Jiyang. Following their characteristic function approach Tripathy et al. introduced fuzzy soft set as a hybrid model in 2015. Here, we continue this further to define IVI fuzzy soft sets (IVIFSS). Many related concepts like complement, null, and absolute IVIFSS are introduced and operations like intersection and union of IVIFSSs are also redefined. Recently, soft set is applied in various forms to derive decision-making (DM) by Tripathy et al. We extend it further by proposing an algorithm which uses IVIFSS in order to achieve DM. These algorithms are much improved and applicable than that of Jiyang. Also, it generalizes all the previous algorithms in this direction.

Hesitant Fuzzy Soft Set Theory and Its Application in Decision Making

There are several models of uncertainty found in the literature like fuzzy set, rough 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 and fuzzy sets. In this paper we redefined the hesitant fuzzy soft sets (HFSS) with the help of membership function. We also provide a decision making algorithm.

Interval Valued Hesitant Fuzzy Soft Sets and Its Application in Stock Market Analysis

Molodtsov introduced soft set theory in 1999 to handle uncertainty. It has been found that hybrid models are more useful than that of individual components. Yang et al. introduced the concept of interval valued fuzzy soft set (IVFSS) by combining the interval valued fuzzy sets (IVFS) and soft set model. In this paper we extend it by introducing interval valued hesitant fuzzy soft sets (IVHFSS) through the membership function approach introduced by Tripathy et al. in 2015. To illustrate the application of the new model, we provide a decision making algorithm and use it in stock market analysis,