Some geometrical methods for constructing contradiction measures on Atanassov's intuitionistic fuzzy sets

Trillas et al. (1999, Soft computing, 3 (4), 197–199) and Trillas and Cubillo (1999, On non-contradictory input/output couples in Zadeh's CRI proceeding, 28–32) introduced the study of contradiction in the framework of fuzzy logic because of the significance of avoiding contradictory outputs in inference processes. Later, the study of contradiction in the framework of Atanassov's intuitionistic fuzzy sets (A-IFSs) was initiated by Cubillo and Castiñeira (2004, Contradiction in intuitionistic fuzzy sets proceeding, 2180–2186). The axiomatic definition of contradiction measure was stated in Castiñeira and Cubillo (2009, International journal of intelligent systems, 24, 863–888). Likewise, the concept of continuity of these measures was formalized through several axioms. To be precise, they defined continuity when the sets ‘are increasing’, denominated continuity from below, and continuity when the sets ‘are decreasing’, or continuity from above. The aim of this paper is to provide some geometrical construction methods for obtaining contradiction measures in the framework of A-IFSs and to study what continuity properties these measures satisfy. Furthermore, we show the geometrical interpretations motivating the measures

Decision making and Atanassov's approach to fuzzy sets

In this paper we stress the role that decision making, and therefore an underlying binary (bipolar) approach, plays in Atanassov's intuitionistic view of fuzzy sets. Moreover, we point out that such a bipolar view can be found in classical multicriteria models

Fredkin Gates for Finite-valued Reversible and Conservative Logics

The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to d-valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typical connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As a result, some possible three-valued and d-valued universal gates are described which realize a functionally complete set of fundamental connectives.Comment: 57 pages, 10 figures, 16 tables, 2 diagram

Averaging aggregation functions for preferences expressed as Pythagorean membership grades and fuzzy orthopairs

Rather than denoting fuzzy membership with a single value, orthopairs such as Atanassov\u27s intuitionistic membership and non-membership pairs allow the incorporation of uncertainty, as well as positive and negative aspects when providing evaluations in fuzzy decision making problems. Such representations, along with interval-valued fuzzy values and the recently introduced Pythagorean membership grades, present particular challenges when it comes to defining orders and constructing aggregation functions that behave consistently when summarizing evaluations over multiple criteria or experts. In this paper we consider the aggregation of pairwise preferences denoted by membership and non-membership pairs. We look at how mappings from the space of Atanassov orthopairs to more general classes of fuzzy orthopairs can be used to help define averaging aggregation functions in these new settings. In particular, we focus on how the notion of \u27averaging\u27 should be treated in the case of Yager\u27s Pythagorean membership grades and how to ensure that such functions produce outputs consistent with the case of ordinary fuzzy membership degrees

An Extended TODIM Method for Group Decision Making with the Interval Intuitionistic Fuzzy Sets

For a multiple-attribute group decision-making problem with interval intuitionistic fuzzy sets, a method based on extended TODIM is proposed. First, the concepts of interval intuitionistic fuzzy set and its algorithms are defined, and then the entropy method to determine the weights is put forward. Then, based on the Hamming distance and the Euclidean distance of the interval intuitionistic fuzzy set, both of which have been defined, function mapping is given for the attribute. Finally, to solve multiple-attribute group decision-making problems using interval intuitionistic fuzzy sets, a method based on extended TODIM is put forward, and a case that deals with the site selection of airport terminals is given to prove the method

Plithogenic Fuzzy Whole Hypersoft Set, Construction of Operators and their Application in Frequency Matrix Multi Attribute Decision Making Technique

In this paper, initially a matrix representation of Plithogenic Hypersoft Set (PHSS) is introduced and then with the help of this matrix some local operators for Plithogenic Fuzzy Hypersoft set (PFHSS) are developed. These local operators are used to generalize PFHSS to Plithogenic Fuzzy Whole Hypersoft set (PFWHSS). The generalized PFWHSS set is hybridization of Fuzzy Hypersoft set (which represent multiattributes and their subattributes as a combined whole membership i.e. case of having an exterior view of the event) and the Plithogenic Fuzzy Hypersoft set (in which multi attributes and their subattributes are represented with individual memberships case of having interior view). Thus, the speciality of PFWHSS is its presentation of an exterior and interior view of a situation simultaneously. Later, the PFWHSS is employed in development of multi attributes decision making scheme named as Frequency Matrix Multi Attributes Decision making scheme (FMMADMS). This innovative technique is not only simpler than any of the former MADM techniques, but also has a unique capability of dealing mathematically a variety of human mind psychologies at every level that are working in different environments (fuzzy, intuitionistic, neutrosophic, plithogenic). Besides, FMMADMS also provides the percentage authenticity of the final ranking which in itself is a new idea providing a transparent and unbiased ranking. Moreover, the new introduced idea of frequency matrix handles the ranking ties in the best possible way and has an ability to provide the authenticity comparative analysis of previously developed schemes. Lastly, application of this FMMADMS is described as a numerical example for a case of ranking and selecting the best alternative