Fuzzy relations are mappings from pairs of elements into the interval [0, 1]. As a replacement for the complement operation one can use the mapping that sends x to 1 − x. Together with the concepts of t-norm and t-conorm a weak form of Boolean algebra can be defined. However, to our knowledge so far no notion of domain or codomain has been investigated for fuzzy relations. These might, however,...

It is an open question whether a non-trivial convex combination of triangular norms (resp. conorms) can be a triangular norm (resp. conorm). We investigate the analogous question for S-implications and R-implications.

This paper presents a real-time fullprogrammable fuzzy processor using piecewiselinear intelpolation techniques and implements it using the SSE (Streaming SIMD Extensions) set of instructions of an Intel Pentium III. A fullprogrammable fuzzy processor is defined as a system where the set of rules, the membership finctions, the t-norm, the t-conorm, the aggregation operator, the propagation oper...

This paper presents a method to construct an interval-valued fuzzy set from a fuzzy set and the representation of the lack of knowledge or ignorance that experts are subject to when they define the membership values of the elements to that fuzzy set. With this construction method, it is proved that membership intervals of equal length to the ignorance associated to the elements are obtained whe...

Aggregation operators perform a valuable and significant role in various decision-making processes. Averaging geometric aggregation are both used for capturing the interrelationships of aggregated preferences, even if preferences independent. The purpose this paper is to analyze theory complex linguistic fuzzy (CLF) sets their important laws, such as algebraic score values, accuracy describe re...

A contribution of this article is to introduce new q-rung Orthopair fuzzy (q-ROF) aggregation operators (AOs) as the consequence Aczel–Alsina (AA) t-norm (TN) (AATN) and t-conorm (TCN) (AATCN) their specific advantages in handling real-world problems. In beginning, we a few q-ROF numbers (q-ROFNs) operations, including sum, product, scalar power operations based on AATN AATCN. At that point, co...

The main ‘philosophical’ outcome of this article is to demonstrate that the structural description of residuated lattices requires the use of the co-residuated setting. A construction, called skew symmetrization, which generalizes the well-known representation of an ordered Abelian group obtained from the positive (or negative) cone of the algebra is introduced here. Its definition requires lea...

When we perform algebraic operations on membership degrees, we must be sure that they are compatible with the kind of scale on which these degrees are measured. For example, we will not add (in a weighted average) membership degrees that are measured on an ordinal scale. An important question is therefore how to determine on which kind of scale we measure the membership. There are several techn...

Soft sets have been regarded as a useful mathematical tool to deal with uncertainty. In recent years, many scholars have shown an intense interest in soft sets and extended standard soft sets to intuitionistic fuzzy soft sets, interval-valued fuzzy soft sets, and generalized fuzzy soft sets. In this paper, hesitant fuzzy soft sets are defined by combining fuzzy soft sets with hesitant fuzzy set...