Decision-making is a technique which all of us do every day in different contexts. In Decision-making several alternates are there from which the best one is to be selected. But the alternates may not be crisp many times. So, uncertainty based techniques are necessary to solve these problems. Among the different models of uncertainty, we have fuzzy sets, intuitionistic fuzzy sets and soft sets. There are other variations of fuzzy sets like the interval valued fuzzy sets. Also, we have hybrid models obtained by combining two or more of these models. Molodtsov introduced the notion of soft set in 1999, which has better parameterization capability than most of the other such models. The hybrid model of interval valued fuzzy set and soft set was introduced by Yang in 2009. In this paper, we extend it to define interval valued intuitionistic fuzzy parameterized soft set (IVIFPSS) and establish their properties. Continuing the earlier works on using hybrid models in decision-making, in this paper we use IVIFPSS to put forth two algorithms on decision-making. Out of these two one is on individual decision-making and the other one is on group decision making, which we illustrate through examples. © 2016 IEEE.

Balakrushna Tripathy

Department of Analytics

School of Computer Science and Engineering

Vellore Campus

Panigrahi A.

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

&nbsp;

&nbsp;

VIT University

Interval-valued intuitionistic fuzzy parameterized soft set theory and its application in decision-making

2016 10th International Conference on Intelligent Systems and Control (ISCO)

As seed selection is a challenging task due to the presence of hundreds of varieties of seeds of each kind, some homework is necessary for selecting suitable seeds as new varieties and kinds of seeds are introduced in the market every year having their own strengths and weaknesses. The complexities involved in the characteristics in the form of parameters results in uncertainties and as a result some uncertainty based model or hybrid models of more than is required to model the scenario and come out with a decision. Soft sets have enough of parameterization tools to support and hence is the most suitable one for such a study. However, as hybrid models are more efficient, the authors select a model called the interval valued fuzzy soft set (IVFSS) and propose a decision-making algorithm for the selection of seeds. A real database of seeds is used for experimental verification of the efficiency of the algorithm. This is the first attempt for such a study. The use of signed priorities and intervals for the membership of values for entities makes the study more efficient and realistic.

Fulltext

International Journal of Fuzzy System Applications

An Interval Valued Fuzzy Soft Set Based Optimization Algorithm for High Yielding Seed Selection

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. © Springer Science+Business Media Singapore 2017.

Advances in Intelligent Systems and Computing Advances in Computational Intelligence

A New Approach to Interval-Valued Fuzzy Soft Sets and Its Application in 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. © 2016 IEEE.

2016 International Conference on Emerging Trends in Engineering, Technology and Science (ICETETS)

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

Soft set theory is a new mathematical approach to vagueness introduced by Molodtsov (1999). This is a parameterised family of subsets defined over a universal set using a set of parameters. In this paper, we introduce the notion of characteristic function of a soft set, which helps us in defining the basic operations on soft sets concisely; several concepts associated with it efficiently and make the proofs of properties more elegant. We rectified the definition of complement of a soft set and the earlier definition of complement is now called as the negation of a multiset. Like the crisp multisets, soft multiset is a notion which allows multiple occurrences of elements in a model. So far, more than one attempt has been made to define this concept. Out of these the one put forth by Majumdar (2012) is the most appropriate one and so we use it in this paper. We redefined the concepts of complement of a soft multiset, null soft multiset and absolute soft multiset and introduced many operations on soft multisets like the union and intersection of soft multisets and cardinality of soft multisets. Also, we defined the concepts of addition and deletion of elements from a soft multiset. Two new operations, called the addition and difference of two soft multisets are introduced. We establish several properties of these operations on soft multisets including the De Morgan's Law, associative and distributive properties. A real life example is being used for the purpose of illustration of the notions and concepts. © 2015 Inderscience Enterprises Ltd.

Journal	Data powered by Typeset2016 10th International Conference on Intelligent Systems and Control (ISCO)
Publisher	Data powered by TypesetIEEE
Open Access	0