Intuitionistic fuzzy similarity measures and their role in classification

We present some similarity and distance measures between intuitionistic fuzzy sets (IFSs). Thus, we propose two semi-metric distance measures between IFSs. The measures are applied to classification of shapes and handwritten Arabic sentences described with intuitionistic fuzzy information. The experimental results permitted to do a comparative analysis between intuitionistic fuzzy similarity and distance measures, which can facilitate the selection of such measure in similar applications

Spatial Metric Space for Pattern Recognition Problems

The definition of weighted distance measure involves weights. The paper proposes a weighted distance measure without the help of weights. Here, weights are intrinsically added to the measure, and for this, the concept of metric space is generalized based on a novel divided difference operator. The proposed operator is used over a two-dimensional sequence of bounded variation, and it generalizes metric space with the introduction of a multivalued metric space called spatial metric space. The environment considered for the study is a two-dimensional Atanassov intuitionistic fuzzy set (AIFS) under the assumption that membership and non-membership components are its independent variables. The weighted distance measure is proposed as a spatial distance measure in the spatial metric space. The spatial distance measure consists of three branches. In the first branch, there is a domination of membership values, non-membership values dominate the second branch, and the third branch is equidominant. The domination of membership and non-membership values are not in the form of weights in the proposed spatial distance measure, and hence it is a measure independent of weights. The proposed spatial metric space is mathematically studied, and as an implication, the spatial similarity measure is multivalued in nature. The spatial similarity measure can recognize a maximum of three patterns simultaneously. The spatial similarity measure is tested for the pattern recognition problems and the obtained classification results are compared with some other existing similarity measures to show its potency. This study connects the double sequence to the application domain via a divided difference operator for the first time while proposing a novel divided difference operator-based spatial metric space.Comment: 2

New Entropy-Based Similarity Measure between Interval-Valued Intuitionstic Fuzzy Sets

In this paper we propose a new approach to construct similarity measures using the entropy measure for Interval-Valued Intuitionistic Fuzzy Sets. In addition, we provide several illustrative examples to demonstrate the practicality and effectiveness of the proposed formula. Finally, we use the new proposed similarity measure to develop new approach for solving problems of pattern recognition and multi-criteria fuzzy decision making

Uncertain Query Processing using Vague Set or Fuzzy Set: Which One Is Better?

In this paper we attempt to make a theoretical comparison between fuzzy sets and vague sets in processing uncertain queries. We have designed an architecture to process uncertain i.e. fuzzy or vague queries. In the architecture we have presented an algorithm to find the membership value that generates the fuzzy or vague representation of the attributes with respect to the given uncertain query. Next, a similarity measure is used to get each tuples similarity value with the uncertain query for both fuzzy and vague sets. Finally, a decision maker will supply a threshold or α-cut value based on which a corresponding SQL statement is generated for the given uncertain query. This SQL retrieves different result sets from the database for fuzzy or vague data. It has been shown with examples that vague sets give more accurate  result in comparison with fuzzy sets for any uncertain query

Intuitionistic fuzzy similarity measures and their role in classification

We present some similarity and distance measures between intuitionistic fuzzy sets (IFSs). Thus, we propose two semi-metric distance measures between IFSs. The measures are applied to classification of shapes and handwritten Arabic sentences described with intuitionistic fuzzy information. The experimental results permitted to do a comparative analysis between intuitionistic fuzzy similarity and distance measures, which can facilitate the selection of such measure in similar applications

Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches