Fundamenta Informaticae - Volume 159, issue 4

Authors: Caucal, Didier | Knapik, Teodor

Article Type: Research Article

Abstract: In the early seventies, Shelah proposed a model-theoretic construction, nowadays called “iteration”. This construction is an infinite replication in a tree-like manner where every vertex possesses its own copy of the original structure. Stupp proved that the decidability of the monadic second-order (MSO) theory is transferred from the original structure onto the iterated one. In its extended version discovered by Muchnik and introduced by Semenov, the iteration became popular in computer science logic thanks to a paper by Walukiewicz. Compared to the basic iteration, Muchnik’s iteration has an additional unary predicate which, in every copy, marks the vertex that is …the clone of the possessor of the copy. A widely spread belief that this extension is crucial is formally confirmed in the paper. Two hierarchies of relational structures generated from finite structures by MSO interpretations and either Shelah-Stupp’s iteration or Muchnik’s iteration are compared. It turns out that the two hierarchies coincide at level 1. Every level of the latter hierarchy is closed under Shelah-Stupp’s interation. In particular, the former hierarchy collapses at level 1. Show more

Keywords: infinite-state systems, structure-building operations, Shelah-Stupp’s iteration, Muchnik’s iteration

DOI: 10.3233/FI-2018-1667

Citation: Fundamenta Informaticae, vol. 159, no. 4, pp. 327-359, 2018

Authors: Farhadinia, Bahram | Xu, Zeshui

Article Type: Research Article

Abstract: Recently, an extension of typical hesitant fuzzy element (HFE) called the ordered weighted hesitant fuzzy element (OWHFE) has been proposed to allow the membership of a given element is to be defined in terms of several possible values together with their importance weights. Moreover, the concept of probabilistic linguistic term sets (PLTSs) has been defined to extend hesitant fuzzy linguistic term sets (HFLTSs) by adding probabilities without loss of any original linguistic information. In fact, the concept of PLTS allows the membership of a given element is to be defined in terms of several possible linguistic values over an object …together with the probabilistic information of the set of values. However, the PLTSs have some drawbacks in comparison to the newly defined concept OWHFEs, and such disadvantages of the PLTSs can be prevented by using the OWHFEs. This reveals the need of first defining the modified-PLTS (M-PLTS), and then transforming the M-PLTSs to the OWHFEs which will be the heart of this contribution. Finally, to demonstrate the advantage of the proposed methods, we implement again a number of practical problems that were previously associated with PLTSs. Show more

Keywords: Ordered weighted hesitant fuzzy element (OWHFE), Modified-probabilistic linguistic term set (M-PLTS), Multiple attribute decision making

DOI: 10.3233/FI-2018-1668

Citation: Fundamenta Informaticae, vol. 159, no. 4, pp. 361-383, 2018

Authors: Gao, Hui | Lu, Mao | Wei, Guiwu | Wei, Yu

Article Type: Research Article

Abstract: In this paper, we investigate the multiple attribute decision making problems with Pythagorean fuzzy information. Then, we utilize arithmetic and geometric operations to develop some Pythagorean fuzzy interaction aggregation operators: Pythagorean fuzzy interaction weighted average (PFIWA) operator, Pythagorean fuzzy interaction weighted geometric (PFIWG) operator, Pythagorean fuzzy interaction ordered weighted average (PFIOWA) operator, Pythagorean fuzzy interaction ordered weighted geometric (PFIOWG) operator, Pythagorean fuzzy interaction hybrid average (PFIHA) operator, Pythagorean fuzzy interaction hybrid geometric (PFIHG) operator, Pythagorean fuzzy interaction correlate aggregation operators, Pythagorean fuzzy interaction induced aggregation operators, Pythagorean fuzzy interaction induced correlate aggregation operators, Pythagorean fuzzy interactive power arithmetic and geometric …aggregation operators. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean fuzzy multiple attribute decision making problems. Finally, a practical example for selecting the service outsourcing provider of communications industry is given to verify the developed approach and to demonstrate its practicality and effectiveness. Show more

Keywords: Multiple attribute decision making, Pythagorean fuzzy numbers, Pythagorean fuzzy interaction weighted average (PFIWA) operator, Pythagorean fuzzy interaction weighted geometric (PFIWG) operator, power arithmetic aggregation operators, power geometric aggregation operators, service outsourcing provider, communications industry

DOI: 10.3233/FI-2018-1669

Citation: Fundamenta Informaticae, vol. 159, no. 4, pp. 385-428, 2018

Authors: Syau, Yu-Ru | Lin, En-Bing | Liau, Churn-Jung

Article Type: Research Article

Abstract: The notions of approximation and definability in classical rough set theory and their generalizations have received much attention. In this paper, we study such generalizations from the perspective of neighborhood systems. We introduce four different types of definability, called interior definability, closure definability, interior-closure (IC) definability, and weak IC definability respectively. We also point out the relationship between IC definability and other types of definability for some special kinds of neighborhood systems. Several examples are presented to illustrate the concepts introduced in this paper.

Keywords: Neighborhood systems, rough sets, rough approximations, generalized rough sets, definability

DOI: 10.3233/FI-2018-1670

Citation: Fundamenta Informaticae, vol. 159, no. 4, pp. 429-450, 2018