A New Approach to Intuitionistic Fuzzy Soft Sets and Its Application in Decision-Making
01 Jan 2016-Vol. 439, pp 93-100
TL;DR: This paper redefine intuitionistic fuzzy soft sets (IFSS) and define operations on them and presents an application of IFSS in decision-making which substantially improve and is more realistic than the algorithms proposed earlier by several authors.
Abstract: 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.
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TL;DR: Several proposals for decision making based on both fuzzy soft sets and rough soft sets are provided, including a novel adjustable approach based on decision rules and a multi-criteria group decision making approach.
39 citations
01 Jan 2016
TL;DR: A new algorithm is proposed by following this approach which provides an application of FSSs in group decision making and the performance is substantially improved than that of the earlier algorithm.
Abstract: 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.
37 citations
01 Jan 2017
TL;DR: IVFSS is defined through the membership function approach to define soft set by Tripathy et al. very recently, and several concepts, such as complement of an IVFSS, null IVF SS, absolute IVFFS, intersection, and union of two IVFsss, are redefined.
Abstract: 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.
29 citations
01 Jan 2017
TL;DR: This work defines IVI fuzzy soft sets (IVIFSS) and proposes an algorithm which uses IVIFSS in order to achieve decision-making (DM) and generalizes all the previous algorithms in this direction.
Abstract: 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.
11 citations
01 Jan 2017
TL;DR: This paper redefined the hesitant fuzzy soft sets (HFSS) with the help of membership function and provides a decision making algorithm.
Abstract: 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.
9 citations
References
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TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
52,705 citations
TL;DR: 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.
13,376 citations
TL;DR: 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 the theory, and to discuss some problems of the future.
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.
3,759 citations
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TL;DR: The authors define equality of two soft sets, subset and super set of a soft set, complement of asoft set, null soft set and absolute soft set with examples and De Morgan's laws and a number of results are verified in soft set theory.
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.
2,114 citations
TL;DR: In this article, the theory of soft sets was applied to solve a decision-making problem using rough mathematics, and the results showed that soft sets can be used to solve decision making problems.
Abstract: In this paper, we apply the theory of soft sets to solve a decision making problem using rough mathematics.
1,491 citations