Pattern Recognition Using the Picture Fuzzy Set Similarity Measure

Zadeh [1] was the first to establish the idea of a fuzzy set. The fuzzy set can express the state between ―belong to‖ and ―not belong to‖ by assigning a membership degree between 0 and 1 to items with respect to a set. As a result, fuzzy sets can be used to explain a large number of uncertainties that aren‘t adequately represented by classical sets. Since its inception, fuzzy set theory has been employed in a large number of applications, counting automatic control, pattern recognition, and decision-making. The hypothesis of fuzzy sets has been found to be unsatisfactory in many actual circumstances. As a result, numerous higher theories have arisen over time, such as intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets, q-rung fuzzy sets [2], and so on. Intuitionistic fuzzy sets [3] are a higher hypothesis that is a notion of fuzzy sets that ask specialists to provide non-membership opinions on set elements. As a result, IFSs are frequently employed in pattern recognition applications [4].The tools that are frequently employed in those application challenges are similarity and distance measures. These two ideas are complimentary in the sense that by subtracting one from a unit, one can be derived from the other. Because of their global choice of relevancy, these measures came to be intensively explored since their initiation .Picture fuzzy set‘s similarity measure can be used to solve problems in a diversity of fields, including decision making, machine learning, and pattern detection[7, 8]. Despite the fact that IFSs are more effective than FSs at communicating ambiguous and hazy material, they shortfall a crucial notion, namely degree of neutrality, which is relevant in a variety of circumstances such includes human voting, medical diagnosis, and personal selection, to name a few examples. When it comes to general election, a person has four choices: poll in favour, poll against, abstain from polling, or refuse to poll. Cuong and Kreinvoch [9] created PFS, a novel generalization of FSs and IFSs, to cope with such circumstances. The degree of membership, non-membership, and neutrality for per capita sole element in a PFS is defined, as well as the requirement that a total of these grades that is less than or equal to one. We‘ll also show some examples of how our measure compares to Wei‘s similarity measures [6,8].

1. New similarity measures have been proposed that can be used to compare PFSs. 2. We‘ve also shown its properties in order to confirm that the recommended measures are present. 3. To show pattern recognition, some numerical examples are provided.

Where stands for membership degree of in the set such that 0 ≤ ≤ 1

in the set such that 0 ≤ ≤ 1

Wei [8] introduced Set-theoretic similarity measure:- Wei [6] introduced Cosine function-based similarity measures:- Wei [6] introduced cotangent function-based similarity measure by:-

The correlation coefficient, as we all know, counts the direct dependant level of two things. The correlation coefficient rises in proportion to the degree of trust. Digital image processing, clustering analysis, pattern identification, and decision making are just a few of the applications (Meng et al.) [11]. In pattern recognition, an unknown pattern is classified into some known patterns using numerous fuzzy information measures such as the divergence measure, correlation coefficient, distance measure, similarity measure, and others. As a result, in this part, we make use of our proposed similarity measures to identify patterns while also demonstrating the supremacy of our proposed similarity measures using correlation, similarity, and divergence metrics developed by other researchers. In general, in an image fuzzy environment, we can frame a pattern detection task as follows: Given m patterns, a pattern recognition problem and a sample D in a universal set as a picture fuzzy set, where for y=1,2,..,m and

Which of the, y=1,2,...,m patterns does D belong to? The following methods are used to answer this question: We achieve this in two steps with the correlation and similarity measures: ST1: Calculate the correlation and similarity measure. C(, D) ∀ y=1,2,...,m ST2: Allow D to be a part of pattern ; in which C( , D) = max(C(, D) : y = 1, 2, ..., m)

Consider three known patterns, are picture fuzzy sets on the universal set by

= ((, 0.1, 0.2, 0.5),(, 0.4, 0.5, 0.1)) = ((, 0.3, 0.3, 0.1),(, 0.4, 0.2, 0.1)) = ((, 0.1, 0.2, 0.1),(, 0.2, 0.5, 0.2))

Let D be an unknown sample on the universal set, which is also a picture fuzzy set

D= ((, 0.5, 0.2, 0.0),(, 0.3, 0.2, 0.1))

We categorize the unknown sample D to one of the known patterns using several fuzzy compatibility measures, and Table displays the results. Measures Comments

0.6268 0.8946 0.6823 0.3947 0.8781 0.6448 0.7991 0.9693 0.8500 0.5135 0.7903 0.5611 0.3500 0.7500 0.5000

From above table we have seen that: 1) In Measure , B belongs to the pattern class. 2) In Measure , B belongs to the pattern class. 3 ) In Measure , B belongs to the pattern class. 4) In Measure , B belongs to the pattern class. 5) In Measure , B belongs to the pattern class. Thus, proposed measures are performing consistently with existing measures and it is also an potent method because it is providing precise decision.

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Assistant Professor, Mathematics Department, DAV College (Lahore), Ambala city E-mail: rozygura93@gmail.com