An invariant approach to dynamical fuzzy spaces with a three-index variable

A dynamical fuzzy space might be described by a three-index variable C_{ab}^c, which determines the algebraic relations f_a f_b =C_{ab}^c f_c among the functions f_a on the fuzzy space. A fuzzy analogue of the general coordinate transformation would be given by the general linear transformation on f_a. I study equations for the three-index variable invariant under the general linear transformation, and show that the solutions can be generally constructed from the invariant tensors of Lie groups. As specific examples, I study SO(3) symmetric solutions, and discuss the construction of a scalar field theory on a fuzzy two-sphere within this framework.Comment: Typos corrected, 12 pages, 8 figures, LaTeX, JHEP clas

Aggregating fuzzy subgroups and T-vague groups

Fuzzy subgroups and T-vague groups are interesting fuzzy algebraic structures that have been widely studied. While fuzzy subgroups fuzzify the concept of crisp subgroup, T-vague groups can be identified with quotient groups of a group by a normal fuzzy subgroup and there is a close relation between both structures and T-indistinguishability operators (fuzzy equivalence relations). In this paper the functions that aggregate fuzzy subgroups and T-vague groups will be studied. The functions aggregating T-indistinguishability operators have been characterized [9] and the main result of this paper is that the functions aggregating T-indistinguishability operators coincide with the ones that aggregate fuzzy subgroups and T-vague groups. In particular, quasi-arithmetic means and some OWA operators aggregate them if the t-norm is continuous Archimedean.Peer ReviewedPostprint (author's final draft

UNIFYING VARIOUS FUZZY STRUCTURES USING BRANDT GROUPOIDS

The purpose of this note is to introduce a notion of T-fuzzy groupoid (in the sense of Brandt) that allows to study within a unified framework various fuzzy structures such as fuzzy sets, fuzzy groups, fuzzy equivalence relations and fuzzy transformation groups

The use of two relations in L-fuzzy contexts

In the analysis of relations among the elements of two sets it is usual to obtain different values depending on the point of view from which these relations are measured. The main goal of the paper is the modelization of these situations by means of a generalization of the L-fuzzy concept analysis called L-fuzzy bicontext. We study the L-fuzzy concepts of these L-fuzzy bicontexts obtaining some interesting results. Specifically, we will be able to classify the biconcepts of the L-fuzzy bicontext. Finally, a practical case is developed using this new tool.This work has been partially supported by the Research Group “Intelligent Systems and Energy (SI+E)” of the Basque Government, under Grant IT677-13, by the Research Groups “Artificial Intelligence and Approximate Reasoning” and “Adquisición de conocimiento y minería de datos, funciones especiales y métodos numéricos avanzados” of the Public University of Navarra and by project TIN2013-40765-P

δ-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis

Intuitionistic fuzzy set is capable of handling uncertainty with counterpart falsities which exist in nature. Proximity measure is a convenient way to demonstrate impractical significance of values of memberships in the intuitionistic fuzzy set. However, the related works of Pappis (Fuzzy Sets Syst 39(1):111–115, 1991), Hong and Hwang (Fuzzy Sets Syst 66(3):383–386, 1994), Virant (2000) and Cai (IEEE Trans Fuzzy Syst 9(5):738–750, 2001) did not model the measure in the context of the intuitionistic fuzzy set but in the Zadeh’s fuzzy set instead. In this paper, we examine this problem and propose new notions of δ-equalities for the intuitionistic fuzzy set and δ-equalities for intuitionistic fuzzy relations. Two fuzzy sets are said to be δ-equal if they are equal to an extent of δ. The applications of δ-equalities are important to fuzzy statistics and fuzzy reasoning. Several characteristics of δ-equalities that were not discussed in the previous works are also investigated. We apply the δ-equalities to the application of medical diagnosis to investigate a patient’s diseases from symptoms. The idea is using δ-equalities for intuitionistic fuzzy relations to find groups of intuitionistic fuzzified set with certain equality or similar degrees then combining them. Numerical examples are given to illustrate validity of the proposed algorithm. Further, we conduct experiments on real medical datasets to check the efficiency and applicability on real-world problems. The results obtained are also better in comparison with 10 existing diagnosis methods namely De et al. (Fuzzy Sets Syst 117:209–213, 2001), Samuel and Balamurugan (Appl Math Sci 6(35):1741–1746, 2012), Szmidt and Kacprzyk (2004), Zhang et al. (Procedia Eng 29:4336–4342, 2012), Hung and Yang (Pattern Recogn Lett 25:1603–1611, 2004), Wang and Xin (Pattern Recogn Lett 26:2063–2069, 2005), Vlachos and Sergiadis (Pattern Recogn Lett 28(2):197– 206, 2007), Zhang and Jiang (Inf Sci 178(6):4184–4191, 2008), Maheshwari and Srivastava (J Appl Anal Comput 6(3):772–789, 2016) and Support Vector Machine (SVM)

An algorithm to compute the strength of competing interactions in the Bering Sea based on pythagorean fuzzy hypergraphs

[EN] The networks of various problems have competing constituents, and there is a concern to compute the strength of competition among these entities. Competition hypergraphs capture all groups of predators that are competing in a community through their hyperedges. This paper reintroduces competition hypergraphs in the context of Pythagorean fuzzy set theory, thereby producing Pythagorean fuzzy competition hypergraphs. The data of real-world ecological systems posses uncertainty, and the proposed hypergraphs can efficiently deal with such information to model wide range of competing interactions. We suggest several extensions of Pythagorean fuzzy competition hypergraphs, including Pythagorean fuzzy economic competition hypergraphs, Pythagorean fuzzy row as well as column hypergraphs, Pythagorean fuzzy k-competition hypergraphs, m-step Pythagorean fuzzy competition hypergraphs and Pythagorean fuzzy neighborhood hypergraphs. The proposed graphical structures are good tools to measure the strength of direct and indirect competing and non-competing interactions. Their aptness is illustrated through examples, and results support their intrinsic interest. We propose algorithms that help to compose some of the presented graphical structures. We consider predator-prey interactions among organisms of the Bering Sea as an application: Pythagorean fuzzy competition hypergraphs encapsulate the competing relationships among its inhabitants. Specifically, the algorithm which constructs the Pythagorean fuzzy competition hypergraphs can also compute the strength of competing and non-competing relations of this scenario.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCL

Model for revelation of unfriendly information impacts in mass-media which are directed on change of public opinion

In this article we proposes the mathematical model for revelation of deliberate unfriendly information impacts which are fulfilled by means of specially prepared information messages (news, reviews and others) in mass-media. The model calculates the quantitative measure for fact determination of purposeful information impact and evaluation of potential damage to interests of state (party, corporation) from impact fulfilment. The model use the following data: intensity and direction of information streams (publication frequency and themes of news), structure of important state and public problems, structure of social groups of a society, priorities of these social groups, mass-media popularity in social groups, priorities of a state policy. The model is the semantic network in which the relations between concepts we formalize by use of fuzzy measures by Sugeno. We have used this model for revelation of information impacts on public opinion of Russian-speaking national minority of Crimea (Ukraine) during 01.2002 - 02.2005 (final stage of presidential elections). The model also can has important implications for evaluation of election cleanness, for neutralization of dirty voting technologies, for facts determination of unfair competition, when corporations involve a public opinion into own competitive activity.Information impact; public opinion; fuzzy measures; preferences; social groups

A study of fuzzy sets and systems with applications to group theory and decision making

In this study we apply the knowledge of fuzzy sets to group structures and also to decision-making implications. We study fuzzy subgroups of finite abelian groups. We set G = Z[subscript p[superscript n]] + Z[subscript q[superscript m]]. The classification of fuzzy subgroups of G using equivalence classes is introduced. First, we present equivalence relations on fuzzy subsets of X, and then extend it to the study of equivalence relations of fuzzy subgroups of a group G. This is then followed by the notion of flags and keychains projected as tools for enumerating fuzzy subgroups of G. In addition to this, we use linear ordering of the lattice of subgroups to characterize the maximal chains of G. Then we narrow the gap between group theory and decision-making using relations. Finally, a theory of the decision-making process in a fuzzy environment leads to a fuzzy version of capital budgeting. We define the goal, constraints and decision and show how they conflict with each other using membership function implications. We establish sets of intervals for projecting decision boundaries in general. We use the knowledge of triangular fuzzy numbers which are restricted field of fuzzy logic to evaluate investment projections