Abstract
We propose a new method for ordering bipolar fuzzy numbers. In this method, for comparison of bipolar LR fuzzy numbers, we use an extension of Kerre’s method being used in ordering of unipolar fuzzy numbers. We give a direct formula to compare two bipolar triangular fuzzy numbers in O(1) operations, making the process useful for many optimization algorithms. Also, we present an application of bipolar fuzzy number in a real life problem.
Highlights
Fuzzy sets are useful mathematical structures to represent a collection of objects whose boundary is vague
Zhang [7] initiated the concept of bipolar fuzzy sets as a generalization of fuzzy sets
Tahmasbpour and Borzooei [12] introduced two different approaches corresponding to chromatic number of a bipolar fuzzy graph. They computed total chromatic number based on αP-cut and αN-cut of a bipolar fuzzy graph with the edges and vertices both being bipolar fuzzy sets
Summary
Fuzzy sets are useful mathematical structures to represent a collection of objects whose boundary is vague. Zhou and Li [1] presented the concepts of bipolar fuzzy h-ideals and normal bipolar fuzzy h-ideals They investigated characterizations of bipolar fuzzy h-ideals by means of positive t-cut, negative s-cut, homomorphism, and equivalence relation. Tahmasbpour and Borzooei [12] introduced two different approaches corresponding to chromatic number of a bipolar fuzzy graph They computed total chromatic number based on αP-cut and αN-cut of a bipolar fuzzy graph with the edges and vertices both being bipolar fuzzy sets. Kerre’s method [13] for comparison of two unipolar fuzzy numbers is a well-known method in ordering unipolar fuzzy numbers.
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