Orthopairs and granular computing

Abstract

Pairs of disjoint sets (orthopairs) naturally arise or have points in common with many tools to manage uncertainty: rough sets, shadowed sets, version spaces, three-valued logics, etc. Indeed, they can be used to model partial knowledge, borderline cases, consensus, examples and counter-examples pairs. Moreover, generalized versions of orthopairs are the well known theories of Atanassov intuitionistic fuzzy sets and possibility theory and the newly established three-way decision theory. Thus, it is worth studying them on an abstract level in order to outline general properties that can then be casted to the different paradigms they are in connection with. In this paper, we will review how to define orthopairs and a hierarchy on them in the light of granular computing. Aggregation operators will also be discussed as well as possible generalizations and connections with different paradigms. This will permit us to point out new facets of these paradigms and outline some possible future developments.

New Operations of Picture Fuzzy Relations and Fuzzy Comprehensive Evaluation

“…Future research will focus on other new methods for fuzzy comprehensive evaluation problems, especially applying some new granular computing techniques (see [18][19][20][21][22][23][24][25][26][27]) to develop a comprehensive evaluation model about investment risk.…”

“…Most of them are vague than precise, and uncertainty is a common research topic of many branches of science (economics, engineering, environment, management science, medical science, and so on). However, uncertainty is an unintelligible expression without a straightforward description, and many theories were established, such as probability theory, fuzzy set theory [1][2][3], intuitionistic fuzzy set theory [4], hesitant fuzzy set theory [5][6][7][8], soft set theory [9][10][11][12], rough set theory [13][14][15][16][17], granular computing [18][19][20][21][22][23][24][25][26][27], et al…”

Granular computing: from granularity optimization to multi-granularity joint problem solving

“…3, based on the definition of parameter concept clarity, A-GCT could generate multi-granularity concepts by clustering academicians in Chinese Academy of Engineering with regards to age, which is also the process of granularity conversion. In addition, there are some other granular computing models, cluster (Rodriguez and Laio 2014), shadowed sets (Pedrycz 1998), orthopairs (Ciucci 2016); they have common points with above mentioned models to manage uncertainty.…”

Multi-attribute decision-making based on the SPIFGIA operators

“…MADM problems and granular computing have got more attentions from the literatures (Beliakov et al 2011;Beliakov et al 2010;Wei and Zhao 2012;Chen 2014;Bedregal et al 2014;Livi and Sadeghian 2015;Pedrycz and Chen 2015;Chen and Chang 2015;Rodríguez et al 2012Rodríguez et al , 2013Rodríguez et al , 2014He et al 2015;Chen et al 2016;Apolloni et al 2016;Antonelli et al 2016;Ciucci 2016;Lingras et al 2016;Loia et al 2016;Maciel et al 2016;Min and Xu 2016;Peters and Weber 2016;Skowron et al 2016;Wilke and Portmann 2016;Xu and Wang 2016;Yao 2016). Considering the different backgrounds of experts, Xu and Wang (2016) gave an overview on managing multigranularity linguistic term sets for MADM problems.…”