Asma Khalid

Distance Measures and Operations in Intuitionistic and Interval-Valued Intuitionistic Fuzzy Soft Set Theory

In this paper, a similarity measure between intuitionistic fuzzy soft sets based on Hausdorff distance is defined and a possible application of this measure in medical diagnosis is presented. Also, Hamming and Euclidean distances are defined for interval-valued fuzzy soft and interval-valued intuitionistic fuzzy soft sets.

Incomplete interval valued fuzzy preference relations

An interval valued preference relation is a preference structure that is used to describe uncertainty in complex decision making problems. Retrieving complete information from experts is improbable in real life scenarios. Discarding incomplete information leads to loss of important data. In this paper, we introduce an upper bound condition to deal with incomplete interval valued fuzzy preference relations. With the help of this condition, missing preferences are estimated such that they are expressible. Moreover, the resultant complete relation is consistent. In case if an expert is unable to abide by the proposed upper bound condition, an algorithm is formulated to assist the expert in complying to the upper bound condition.

Incomplete preference relations: An upper bound condition

In decision making, consistency in fuzzy preference relations is associated with the study of transitivity property. While using additive consistency property to complete incomplete preference relations, the preference values found may lie outside the interval [0, 1] or the resultant relation may itself be inconsistent. This paper proposes a method that avoids inconsistency and completes an incomplete preference relation using an upper bound condition. Additionally, the paper extends the upper bound condition for multiplicative reciprocal preference relations. The proposed methods ensure that if n-1 preference values are provided by an expert, such that they satisfy the upper bound condition, then the preference relation is completed such that the estimated values lie inside the unit interval [0, 1] in the case of preference relations and [1/9, 9] in the case of multiplicative preference relation. Moreover, the resultant preference relation obtained using the proposed method is transitive.

Incomplete Hesitant Fuzzy Preference Relations in Group Decision Making

In this article, incomplete hesitant fuzzy preference relations are under consideration. In order to estimate expressible missing preferences, a hesitant upper bound condition (hubc) is defined for decision makers presenting incomplete information. With the help of this condition, the estimated preference intensities lie inside the defined domain and thus are expressible. An algorithm is proposed to revise minimal possible preferences so that the resultant satisfies property (hubc). Moreover, ranking rule, HF-Borda count, for hesitant fuzzy preference relations is defined. This method dissolves possible ties among alternatives.

Comparing ranking methods: Complete RCI preference and multiplicative preference relations

The focus of this paper is comparison of ranking methods. Several methods have been introduced in literature to rank relations and it is noticed that different methods lead to different and possibly contradictory outcomes. To justify why some methods are better than others, a performance parameter needs to be established. We restrict ourselves to the class of Incomplete fuzzy and multiplicative preference relations that can be completed by methods defined by Khalid and Awais (12) and result in additive transitive and Saatys consistent multiplicative preference relations. For the purpose of ranking, methods are proposed and compared pairwise with the famous fuzzy Borda rule. Also, fuzzy Borda rule for multiplicative preference relations is introduced. To appreciate the most suitable ranking method, we set the performance parameter to be the number of ties produced by each of these methods. So the best rule to rank additive transitive and Saatys consistent relations is the one producing least number of ties. We prove some useful properties withheld by the considered relations, which helps conclude that these ranking methods are equally efficient for such relations since they produce equal number of ties in the same alternatives. We identify the reason of reaching ties and propose a solution.

Completing 2-tuple linguistic preference relations based on upper bound condition

The purpose of this paper is to propose a method to estimate missing preference values when handling incomplete linguistic preference relations assessed by using 2-tuple linguistic preference values. We assert that additive transitivity alone may result in estimated values that do not qualify as 2-tuple linguistic preference values. Therefore, an upper bound condition based on additive transitivity is proposed to deal with incomplete 2-tuple linguistic preference relations (2TLPRs). We prove that if experts with incomplete information abide by this property, then the missing preference values can be estimated such that they are expressible. Additionally, because of this property, the resultant complete 2TLPR is proved to be consistent. Based on additive transitivity and the upper bound condition, an interactive completing algorithm is developed to estimate the missing entries in incomplete 2TLPR. When the upper bound condition is not satisfied or there exist entries that do not coincide with the real opinions of the experts, the proposed algorithm can automatically adjust the known entries by interacting with the experts. By using the proposed algorithm, the completed 2TLPR is not only additively consistent, but also can accurately reflect the actual preference of the experts.

Multi scale entropy based adaptive fuzzy contrast image enhancement for crowd images

Contrast enhancement is a very important issue in image processing, pattern recognition and computer vision. Fuzzy logic based techniques perform enhancement using more detailed information of grayness of an image. However, these methods do not perform well on images taken in uncontrolled environment which pose different challenges such as illumination variation, perspective distortion and viewpoint variation. In this paper, we have worked to devise a more robust image enhancement method using fuzzy logic. We propose a novel multi scale entropy based measurement performed using fuzzy logic image processing and utilize it to define and enhance the contrast. For this purpose, we present a mathematical formula to calculate contrast using an adaptive amplification constant. Our approach uses both the local and global entropy information. We have experimented our algorithm on images from Crowd Counting UCF dataset, which contains very dense crowds and complex texture that stands in line with the challenges targeted in this paper. The results show an improved quality than original dataset images and prove that our method enhances the images with a more dynamic ranged contrast as well as better visual results.

Comparing distance to consensus of collective relations using OWA operators

Consensus is understood as a unanimous agreement by all experts in a group. The goal of consensus is not the selection of several options but to develop one decision that suits the interests of the entire group under consideration. In this paper, it is assumed that collective preferences are developed with the help of commonly used ordered weighted averaging operators but resultant relations do not exhibit any property of a consensus type. That is, consensus is not reached at the first attempt of ranking alternatives. Under such circumstances, the measure of distance to consensus can be successfully used to determine how far a group collectively is from consensus. The aim of this paper is to compare, where possible, the distance to consensus of collective relations compiled with the help of most commonly used ordered weighted averaging operators. The innovative part is that this measure helps in defining an upper and lower bound of distance to consensus of the resultant collective relations. With such an analysis at hand, experts can choose a suitable ordered weighting averaging operator to formulate a collective relation that exhibits a lower distance to consensus.