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This paper aims to present Bipolar valued probabilistic hesitant fuzzy sets (BVPHFSs) by combining bipolar fuzzy sets and probabilistic hesitant fuzzy sets (PHFSs). PHFSs are a strong version of hesitant fuzzy sets (HFSs) in terms of evaluated as probabilistic of each element. Probabilistic hesitant fuzzy sets (PHFSs) are a set structure that argues that each alternative should be evaluated probabilistically. In this framework, the proposed cluster allows probabilistic evaluation of decision- makers' opinions as negative. Thus, this case proposes flexibility about selection of an element and aids to overcome with noise channels. Furthermore, some new aggregation operators are discussed called bipolar valued probabilistic hesitant fuzzy weighted average operator (BVPHFWA), Generalized bipolar valued probabilistic hesitant fuzzy weighted average operator (GBVPHFWA), bipolar valued probabilistic hesitant fuzzy weighted geometric operator (BVPHFWG), Generalized bipolar valued probabilistic hesitant fuzzy weighted geometric operator (GBVPHFWG), bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric operator (BVPHFHWAG) and Generalized bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric (GBVPHFHWAG) and some basic properties are presented. A score function is defined ranking alternatives. Moreover, two different algorithms are put forward with helping to TOPSIS method and by using aggregation operators over BVPHFSs. The validity of proposed operators are analyzed with an example and results are compared in their own. [ABSTRACT FROM AUTHOR]

With the increase of complex information in applications of decision making problems, the use of probabilistic hesitant fuzzy set structure has expanded. Therefore, this paper aims to present two new operators namely q-rung orthopair probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric (q-ROPHHWAG) operator and q-rung orthopair probabilistic hesitant fuzzy hybrid ordered weighted arithmetic and geometric (q-ROPHHOWAG) operator for q>0. The presented operators are better than existing operators in many respects as adding a new parameter, having more flexible structure and presenting comparative analysis in its own. Moreover, we mention from some properties of the proposed operators. In addition to, we give an algorithm and example to indicate effective, reality and flexible of presented method and operators. Then, we solve an example over Pythagorean probabilistic hesitant fuzzy sets with our operators and the results are agreement and the offered operators have superior effect than other operators. [ABSTRACT FROM AUTHOR]

In this paper, we define the concepts of soft anti-covered semigroup, soft anti-covered left (right) ideal, soft anti-covered interior ideal, soft anti-covered (generalized) bi-ideal, soft anti-covered quasi-ideal of a semigroup. We investigate their properties by various examples. Moreover, we focus on the interrelations of them. We construct a new approach to anti-covered ideals of a semigroup via soft set theory. [ABSTRACT FROM AUTHOR]

Similarity measure (SM) formulas are very useful tool for Multi-criteria decision-making (MCDM) problems, machine learning, medical diagnosis, psychology, etc. In this paper, some SM methods are introduced under single-valued type-2 neutrosophic (SVT2N) information, based on the Dice and Jaccard vector measures. Also, Cosine and weighted Cosine SMs between two SVT2N sets are defined for SVT2NSs. Then, motivated by the idea of vector measures, Hybrid SM and weighted Hybrid SM are developed by combining Dice and Cosine SMs. After then, a decision-making method is put forward based on technique for order of preference by similarity to ideal solution (TOPSIS) method. Immediately after, a real example is given to indicate the practicality and effectiveness of the proposed measures. In here, Hybrid SMs are discussed for different values of λ and compared with the Hybrid SMs and weighted Hybrid SMs in their own. Furthermore, a comparative analysis is made based on the TOPSIS among the vector measures, distance measures and Hybrid SMs and the agreement between the results with other measures shows that the Hybrid SM is strong and essential to minimize error margin for decision makers. [ABSTRACT FROM AUTHOR]

The fuzzy set has an important role in the modeling of uncertainties. However, the fuzzy set is not sufficient in modeling of the problems, when the decision makers do not have the same opinion about membership degree of an element. To overcome this problem, the concept of hesitant fuzzy set was defined by Torra and Narukawa. Recently, the concept of the type 2 hesitant fuzzy set was defined by Feng and a ranking method among elements of a type 2 hesitant fuzzy element was given. In this paper, firstly, we point out some shortcomings in the ranking method given by Feng and then we give a new ranking method among elements of a type 2 hesitant fuzzy element. The distance and similarity measures are the effective mathematical tools to solve the problems such as medical diagnosis, decision making, pattern recognition and marketing strategy selection. Therefore, we introduce some distance measure methods between two type 2 hesitant fuzzy sets based on Hamming, Euclidean and Hausdorff distance measures. We obtain some properties of the proposed distance measure methods. We also develop a multi-criteria group decision-making method by integrating the TOPSIS method and the proposed distance measure methods under the type 2 hesitant fuzzy environment. Furthermore, we present a numerical example of multi-criteria group decision-making problem to choose the best alternative among firms to invest in order to illustrate the process and validate of the proposed method. [ABSTRACT FROM AUTHOR]