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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]

In this work, soft covered ideals in semigroups are constructed and in this concept, soft covered semigroups, soft covered left (right) ideals, soft covered interior ideals, soft covered (generalized) bi-ideals and soft covered quasi ideals of a semigroup are defined. Various properties of these ideals are introduced and the interrelations of these soft covered ideals and the relations of soft anti covered ideals and soft covered ideals are investigated.

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]

In this paper, we introduce Interval valued q- Rung Orthopair Hesitant fuzzy sets (IVq-ROHFS) with motivation of Interval valued pythagorean Hesitant fuzzy sets [44] as a new concept. Then, we give some basic operations as complement, union, intersection, addition, scalar multiplication, scalar power. Also, we combine to (IVq-ROHFS) and choquet integral together with aggregating operators and develop to Interval valued q- rung orthopair hesitant fuzzy Choquet averaging operator (IVq-ROHCA) and Interval valued q- rung orthopair hesitant fuzzy Choquet geometric operator (IVq-ROHCG). Then, we offer to indicate soft approach of proposed IVq-ROHCA and IVq-ROHCG an example adopted from Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS (IVIHCI) [43]. The obtained results are agreement with IVIHCI but presented IVq-ROHCA and IVq-ROHCG have more advantages than existing structures as Interval-valued intuitionistic hesitant fuzzy sets (IVIHFS), interval-valued Pythagorean Hesitant fuzzy sets (IVPHFS) owing to reasons changing according to need, requirement, prefer of decision makers and moreover because of IVIHFS and IVPHFS are special cases of IVq-ROHFS. It is open from comparative analysis that while some of offered approaches like IVIHFS, IVPHFS etc. are giving no solution for some values, our operators present to needed results. [ABSTRACT FROM AUTHOR]

In this paper, we develop to a new operator which Interval Valued Bipolar Fuzzy Prioritized Weighted Dombi Averaging operator (IVBFPWDA) by using together IVBFS and Dombi operators. This construction is important because of presenting priotrized flexible approach. The soft concept provides to rank into its own structure. Thus, the obtained rankings act to find to ideal alternative and non-ideal alternative for many k values. Then, the some properties of this concept are introduced like addition, scalar multiplication, scalar power, multiplication. Moreover, we present to score function over (IVBFSs) [8] for ranking of aggregated values. Also, the offered operator is applied over an investment example under the Multi Criteria Decision Making (MCDM) method with five steps. Firstly, the components of Decision Making Matrix are turned into aggregated values thanks to IVBFPWDA and score values are calculated. The obtained values are ranked and determined the most desired alternative. The results show that our operator is reality, objective and agreement in its own. Also, a comparative analysis is proposed by using Hamacher operators over Interval Valued Bipolar fuzzy sets (IVBFSs) [8]. As can be seen from comparison analysis, the results are agreement. But our defined operator has several advantages than operators over IVBFS for example; our operator is flexible and variable. Thus; prefer, need and requirement of decision makers can be satisfied. [ABSTRACT FROM AUTHOR]

Recently, many researchers have studied some types of sets which are extension of fuzzy sets widely. Some of them are interval‐valued fuzzy set, intuitionistic fuzzy sets, type‐2 fuzzy sets, type‐n fuzzy sets, hesitant fuzzy sets (HFSs), dual fuzzy sets, and neutrosophic sets. In solving decision‐making problems, these sets have more advantages than classical sets. In this paper, we introduce a new concept called dual type‐2 hesitant fuzzy sets (DT2HFSs) by combining concepts of the dual HFS and the type‐2 fuzzy set. Then we give correlation coefficient formulas and weighted correlation coefficient formulas between two DT2HFSs and obtain some results related to the proposed correlation coefficient formulas. On the basis of the proposed correlation coefficient formulas, we develop the clustering method under DT2HF environment. Finally, we present an application of the proposed method for a problem to illustrate the process and validate the proposed method. [ABSTRACT FROM AUTHOR]