Alka Tripathi

Generalized Intuitionistic Fuzzy Entropy Measure of Order α and Degree β and Its Applications to Multi-Criteria Decision Making Problem

The objective of this manuscript is divided into two fold. Firstly, a more generalized intuitionistic fuzzy entropy measure of order and degree has been presented for measuring the degree of fuzziness of the set with a proof of its validity. A structured linguistic variable has been taken as an illustrative example to show its validity and superiority than the existing measures. Furthermore, based on this measure, an approach to deal with multi-criteria decision making MCDM problem is developed. Finally, a practical example is provided to illustrate the decision making process. A computed result is compared with the help of existing results. A sensitivity analysis on the different values of the parameters will make a decision maker more choice for accessing their results.

Approximate equalities using topological space

Rough equivalence of sets generalises the concept of rough approximate equalities. Two sets may not be rough equal but may be rough equivalent. This leads to study of approximate equality in higher level. In this paper, we have studied rough set from topological point of view. Here, we have proposed definitions of rough equality, rough equivalence, approximate rough equality and approximate rough equivalence of two sets with the help of interior and closure. Some properties related to proposed equalities are proved topologically (with the help of interior and closure). Real life example is given to understand the rough equivalence situations.

Intuitionistic Group Decision Making to Identify the Status of Student's Knowledge Acquisition in E-Learning Systems

Learners performance evaluation in an E-learning environment is a multi-criteria decision problem and important to personalize the sequence of learning concepts according to their knowledge level. Crisp responses, leads uncertainty in the evaluation process due to successful guesses or choosing a more probable answer. Analysis of learners response to a complex/subjective questions needs more effort. Moreover, due to uncertainty and imprecise nature of learner, traditional methods are inadequate to assess, how much time he has spent on studying the learning contents and also the number of backtracking he followed. This paper proposes an intuitionistic fuzzy multicriteria decision making that investigates the use of an intuitionistic fuzzy technique for order preference by similarity to ideal solution TOPSIS method for the evaluation of student in an E-learning environment. Synthetic data are created for the criterias that affect the student evaluation in E-learning domain and thereafter results are evaluated.

Fuzzy approach to detect learning style using McCarthy model as a tool for e-learning system

This study suggests a soft computing approach to extract knowledge which can decide learners learning style in e-learning environment. The approach uses the rules of the learning style instrument(LSI) designed by Marlene Lefever which is based on the McCarthy Model. There are e-learning system which detect the learning style of a particular learner in a crisp manner. Due to the fuzzy nature of the learner a fuzzy approach is used to decide the learning style of the learner. The proposed method has used the McCarthy Model as a tool to detect the learning style of the student. This increase the efficiency of the learning because most of the systems are based on the notion that each student has only one learning style which is not true.

Rough Fuzzy Automata and Rough Fuzzy Grammar

Automata theory plays a key role in computational theory as many computational problems can be solved with its help. Formal grammar is a special type of automata designed for linguistic purposes. Formal grammar generates formal languages. Rough grammar and rough languages were introduced to incorporate the imprecision of real languages in formal languages. These languages have limitations on uncertainty. The authors have considered both uncertainty and approximations to define rough fuzzy grammar and rough fuzzy languages. Under certain restrictions, their grammar reduces to formal grammar. Furthermore, the authors have proposed definition of rough fuzzy automata that accepts rough fuzzy regular language.

Equalities based on rough intuitionistic fuzzy topology

Approximation space is the main component of rough set theory based on equivalence classes. These approximations are named as lower approximations, upper approximations and boundary. The notion of rough set and fuzzy set are based on uncertainty and approximations. In rough topology, these approximations are defined in terms of interior and closure. If two sets are unequal, then both could be approximate equivalent. In this article, we have generalized the rough fuzzy topology with rough intuitionistic fuzzy set. It is based on interior and closure of rough intuitionistic fuzzy topology. Further, intuitionistic fuzzy topological space generalizes approximate equalities. The idea of approximate equalities using intuitionistic fuzzy topological space is generalized. Basic definitions of generalized approximate equalities such as rough equality, rough equivalence, approximate rough equality and approximate rough equivalence are recognized.

Approximate equalities using generalized topological spaces

Rough set is a model of uncertainty that depends on equivalence classes. The significant feature of sets is equality. Two sets may not be equal but may be approximate equal. In this article, we have generalized the idea of approximate rough equalities using fuzzy topology and its interior and closure. We have proposed definition of generalized approximate equalities and related properties in this article.

Modified CURE algorithm with enhancement to identify number of clusters

In this paper, we present an effective way of identifying number of clusters k based on density of data in given dataset and optimality of clusters formed. We have used internal evaluation of clustering to choose optimal set of clusters after narrowing the selection space to a small ideal range. This range is identified by partitioning dataset into a number of partitions using kd-tree so that partitions created contains densely packed data objects. We have used the concept of multi-representative points of a cluster in partitioning and evaluation of clustering and implemented it by modifying CURE algorithm. In this paper, linear transformation method PCA is applied to reduce high dimensional data into lower dimensions.

Choquet integral-based intuitionistic fuzzy bonferroni mean operator

The objective of work is to present a Choquet integral-based intuitionistic fuzzy bonferroni mean operator for fuse the different information. Since Choquet integral not only consider the individual criteria but the correlation between the criteria is also taken into account. Based on it, a decision making method has been presented and has been explained through an illustrative example.