An Adjustable Approach to Interval-Valued Intuitionistic Fuzzy Soft Sets Based Decision Making (original) (raw)
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International Journal of Open Problems in Computer Science and Mathematics, 2015
Soft Set theory is one of the recent topics gaining significance in finding rational and logical solutions to various real life problems which involve uncertainty, impreciseness and vagueness. In this article we have introduced the notions of reduct weighted intuitionistic fuzzy soft multi sets of weighted interval valued intuitionistic fuzzy soft multi set and propose an adjustable approach to weighted interval-valued intuitionistic fuzzy soft set based decision making by using reduct weighted intuitionistic fuzzy soft sets and level soft sets of reduct intuitionistic fuzzy soft sets. Some illustrative example is employed to show the feasibility of our approach in practical applications.
Parameter reduction methods have been adopted by many scientific communities since it provides the basic concept for removing irrelevant features and subset of parameters that provides the same descriptive or decision ability as the entire set of parameters. Several reduction approaches have been proposed for fuzzy-soft set in making decision of datasets with fuzzy-soft values. However, existing fuzzy soft set reduction approaches suffer to handle interval-valued intuitionistic fuzzy soft datasets. To overcome this issue, we introduce an adjustable reduction approach of interval-valued intuitionistic fuzzy soft sets (AR-IIFSS) for decision making. The novelty of APR-IIFSS is that we generalize the existing approaches on reduction of fuzzy soft sets (R-FSS), interval-valued fuzzy soft sets (R-ITFSS), and intuitionistic fuzzy soft sets (R-ICFSS) for decision making. Therefore, this is the first attempt on reduction approach of interval-valued intuitionistic fuzzy soft datasets. We also introduce an adjustable reduction approach of weighted interval-valued intuitionistic fuzzy soft sets (AR-WIIFSS) and investigate its application for decision making. We make extensive analysis for AR-IIFSS and AR-WIIFSS approaches to show their feasibility in practical applications of decision making
Interval-valued intuitionistic fuzzy soft sets and their properties
Computers & Mathematics with Applications, 2010
Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. However, it has been pointed out that classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In this paper, the notion of the interval-valued intuitionistic fuzzy soft set theory is proposed. Our interval-valued intuitionistic fuzzy soft set theory is a combination of an interval-valued intuitionistic fuzzy set theory and a soft set theory. In other words, our interval-valued intuitionistic fuzzy soft set theory is an interval-valued fuzzy extension of the intuitionistic fuzzy soft set theory or an intuitionistic fuzzy extension of the interval-valued fuzzy soft set theory. The complement, ''and'', ''or'', union, intersection, necessity and possibility operations are defined on the interval-valued intuitionistic fuzzy soft sets. The basic properties of the interval-valued intuitionistic fuzzy soft sets are also presented and discussed.
An Intuitionistic Fuzzy Soft Set Theoretic Approach to Decision Making Problems
MATEMATIKA, 2018
In general most of real life problem of decision making involve imprecise parameters. In recent past the major emphasis of research workers in this area have been to develop the reliable models to deal with such imprecision and vagueness effectively. Several theories have been developed such as fuzzy set theory, interval valued fuzzy set, intuitionistic fuzzy set, and interval valued intuitionistic fuzzy set, rough set and soft set. The primary objectives of all the above developed theories are to deal with various kinds of uncertainty, imprecision and vagueness but unfortunately every theory has certain limitations. In the present paper we briefly introduced the notion of soft set, fuzzy soft set and intuitionistic fuzzy soft set. We extend the Jurio et al construction method of converting fuzzy set into intuitionistic fuzzy set to fuzzy soft set into intuitionistic fuzzy soft set. Here we consider a problem of decision making in fuzzy soft set and presented a method to generalize ...
Interval valued intuitionistic fuzzy parameterized soft set theory and its decision making
Journal of Intelligent & Fuzzy Systems, 2016
Although some statistical tools, such as mean and median, used for modelling a problem containing parameters or alternatives with multiple intuitionistic fuzzy values because these values are obtained in a specific period, decrease uncertainty, they lead to data loss. However, interval-valued intuitionistic fuzzy values can overcome such a concern. For this reason, the present study proposes the concept of interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft sets (d-sets) and presents several of its basic properties. Moreover, by using d-sets, we suggest a new soft decision-making method and apply it to a problem concerning the eligibility of candidates for two vacant positions in an online job advertisement. Since it is the first method proposed in relation to this structure (d-sets), it is impossible to compare this method with another in this sense. To deal with this difficulty, we introduce four new concepts, i.e. mean reduction, mean bireduction, mean bireduction-reduction, and mean reduction-bireduction. By using these concepts, we apply four state-of-the-art soft decision-making methods to the problem. We then compare the ranking performances of the proposed method with those of the four methods. Besides, we apply five methods to a real problem concerning performance-based value assignment to some filters used in image denoising and compare the ranking performances of these methods. Finally, we discuss d-sets and the proposed method for further research.
Group Decision Making Through Interval Valued Intuitionistic Fuzzy Soft Sets
International Journal of Fuzzy System Applications, 2018
This article describes how the lack of adequate parametrization in some of the earlier uncertainty based models like fuzzy sets, rough sets motivated Molodtsov to introduce a new model in soft set. A suitable combination of individual models leads to hybrid models, which are more efficient than their individual components. So, the authors find the introduction of many hybrid models of soft sets, like the fuzzy soft set (FSS), intuitionistic fuzzy soft sets (IFSS), interval valued fuzzy soft set (IVFSS) and the interval valued intuitionistic fuzzy soft set (IVIFSS). Following the characteristic function approach to define soft sets introduced by Tripathy et al., they re-define IVIFSS in this article. One of the most attractive applications of soft set theory and its hybrid models has been decision making in the form of individual decision making or group decision making. Here, the authors propose a group decision making algorithm using IVIFSS, which generalises many of our earlier al...
Applied Intelligence, 2017
Interval-valued intuitionistic fuzzy (IVIF) soft set is one of the useful extensions of the fuzzy soft set which efficiently deals with the uncertain data for the decisionmaking processes. In this paper, an attempt has been made to present a nonlinear-programming (NP) model based on the technique for order preference by similarity to ideal solution (TOPSIS), to solve multi-attribute decision-making problems. In this approach, both ratings of alternatives on attributes and weights of attributes are represented by IVIF sets. Based on the available information, NP models are constructed on the basis of the concepts of the relativecloseness coefficient and the weighted distance. Some NP models are further deduced to calculate relative-closeness of sets of alternatives which can be used to generate the ranking order of the alternatives. A real example is taken to demonstrate the applicability and validity of the proposed methodology.
International Conferences on Science and Technology Natural Science and Technology, 2019
The concept of intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets (ifpifs-sets) is a new and useful mathematical tool propounded to model uncertainties. In this study, to improve this concept, we first present the difference and the symmetric difference between two intuitionistic fuzzy sets (if-sets) and investigate some properties. Secondly, on ifpifs-sets, we propose some new operations such as the relative union/intersection/difference and study some properties. We then suggest a new soft decision-making method and apply this method to a decision-making problem. Finally, we discuss ifpifs-sets and the method mentioned above for further research.
Soft Interval-Valued Intuitionistic Fuzzy Rough Sets
Studies in Fuzziness and Soft Computing, 2015
Soft set theory, fuzzy set theory and rough set theory are all mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the discussions of the combinations of intervalvalued intuitionistic fuzzy set, rough set and soft set. A new model, namely soft interval-valued intuitionistic fuzzy rough set is proposed and it's properties are derived. Also a soft interval-valued intuitionistic fuzzy rough set based multi criteria group decision making scheme is presented. The proposed scheme is illustrated by an example regarding the car selection problem.
Intuitionistic Multi Fuzzy Soft Set and its Application in Decision Making
Lecture Notes in Computer Science, 2013
Soft set theory initiated by Molodtsov in 1999 has been emerging as a generic mathematical tool for dealing with uncertainty. A noticeable progress is found concerning the practical use of soft set in decision making problems. This paper introduces the concept of intuitionistic multi fuzzy soft set (IMFSS) by combining the intuitionistic multi fuzzy set (IMFS) and soft set models. Then an algorithmic approach is presented by using induced fuzzy soft set and level soft set for dealing with decision making problem based on IMFSS. Finally the proposed algorithm has also been illustrated through a numerical example.